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class="vector-toc-numb">2</span> <span>Structure and use</span> </div> </a> <button aria-controls="toc-Structure_and_use-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Structure and use subsection</span> </button> <ul id="toc-Structure_and_use-sublist" class="vector-toc-list"> <li id="toc-Diatonic_key_signatures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diatonic_key_signatures"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Diatonic key signatures</span> </div> </a> <ul id="toc-Diatonic_key_signatures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modulation_and_chord_progression" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Modulation_and_chord_progression"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Modulation and chord progression</span> </div> </a> <ul id="toc-Modulation_and_chord_progression-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Circle_closure_in_non-equal_tuning_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Circle_closure_in_non-equal_tuning_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Circle closure in non-equal tuning systems</span> </div> </a> <ul id="toc-Circle_closure_in_non-equal_tuning_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Equal-tempered_tunings_with_more_than_twelve_notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Equal-tempered_tunings_with_more_than_twelve_notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Equal-tempered tunings with more than twelve notes</span> </div> </a> <ul id="toc-Equal-tempered_tunings_with_more_than_twelve_notes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Use" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Use"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Use</span> </div> </a> <button aria-controls="toc-Use-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Use subsection</span> </button> <ul id="toc-Use-sublist" class="vector-toc-list"> <li id="toc-Baroque_era" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Baroque_era"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Baroque era</span> </div> </a> <ul id="toc-Baroque_era-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nineteenth_century" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nineteenth_century"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Nineteenth century</span> </div> </a> <ul id="toc-Nineteenth_century-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Jazz_and_popular_music" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Jazz_and_popular_music"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Jazz and popular music</span> </div> </a> <ul id="toc-Jazz_and_popular_music-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Related_concepts" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Related_concepts"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Related concepts</span> </div> </a> <button aria-controls="toc-Related_concepts-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Related concepts subsection</span> </button> <ul id="toc-Related_concepts-sublist" class="vector-toc-list"> <li id="toc-Diatonic_circle_of_fifths" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diatonic_circle_of_fifths"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Diatonic circle of fifths</span> </div> </a> <ul id="toc-Diatonic_circle_of_fifths-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chromatic_circle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Chromatic_circle"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Chromatic circle</span> </div> </a> <ul id="toc-Chromatic_circle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relation_with_chromatic_scale" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relation_with_chromatic_scale"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Relation with chromatic scale</span> </div> </a> <ul id="toc-Relation_with_chromatic_scale-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Enharmonic_equivalents,_theoretical_keys,_and_the_spiral_of_fifths" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Enharmonic_equivalents,_theoretical_keys,_and_the_spiral_of_fifths"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Enharmonic equivalents, theoretical keys, and the spiral of fifths</span> </div> </a> <ul id="toc-Enharmonic_equivalents,_theoretical_keys,_and_the_spiral_of_fifths-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Circle of fifths</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 39 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-39" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">39 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D8%A6%D8%B1%D8%A9_%D8%A7%D9%84%D8%AE%D8%A7%D9%85%D8%B3%D8%A7%D8%AA" title="دائرة الخامسات – Arabic" lang="ar" hreflang="ar" data-title="دائرة الخامسات" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-frp mw-list-item"><a href="https://frp.wikipedia.org/wiki/Cicllo_de_les_quintes" title="Cicllo de les quintes – Arpitan" lang="frp" hreflang="frp" data-title="Cicllo de les quintes" data-language-autonym="Arpetan" data-language-local-name="Arpitan" class="interlanguage-link-target"><span>Arpetan</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cercle_de_quintes" title="Cercle de quintes – Catalan" lang="ca" hreflang="ca" data-title="Cercle de quintes" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kvintov%C3%BD_kruh" title="Kvintový kruh – Czech" lang="cs" hreflang="cs" data-title="Kvintový kruh" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kvintcirkel" title="Kvintcirkel – Danish" lang="da" hreflang="da" data-title="Kvintcirkel" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Quintenzirkel" title="Quintenzirkel – German" lang="de" hreflang="de" data-title="Quintenzirkel" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kvindiring" title="Kvindiring – Estonian" lang="et" hreflang="et" data-title="Kvindiring" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/C%C3%ADrculo_de_quintas" title="Círculo de quintas – Spanish" lang="es" hreflang="es" data-title="Círculo de quintas" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kvintociklo" title="Kvintociklo – Esperanto" lang="eo" hreflang="eo" data-title="Kvintociklo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Bostunen_zirkulua" title="Bostunen zirkulua – Basque" lang="eu" hreflang="eu" data-title="Bostunen zirkulua" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D8%A7%DB%8C%D8%B1%D9%87_%D9%BE%D9%86%D8%AC%D9%85%E2%80%8C%D9%87%D8%A7" title="دایره پنجم‌ها – Persian" lang="fa" hreflang="fa" data-title="دایره پنجم‌ها" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Cycle_des_quintes" title="Cycle des quintes – French" lang="fr" hreflang="fr" data-title="Cycle des quintes" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%98%A4%EB%8F%84%EA%B6%8C" title="오도권 – Korean" lang="ko" hreflang="ko" data-title="오도권" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Fimmundahringurinn" title="Fimmundahringurinn – Icelandic" lang="is" hreflang="is" data-title="Fimmundahringurinn" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Circolo_delle_quinte" title="Circolo delle quinte – Italian" lang="it" hreflang="it" data-title="Circolo delle quinte" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A2%D7%92%D7%9C_%D7%94%D7%A7%D7%95%D7%95%D7%99%D7%A0%D7%98%D7%95%D7%AA" title="מעגל הקווינטות – Hebrew" lang="he" hreflang="he" data-title="מעגל הקווינטות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B8%D0%BD%D1%82%D0%B0%D0%BB%D1%8B%D2%9B_%D1%88%D0%B5%D2%A3%D0%B1%D0%B5%D1%80" title="Квинталық шеңбер – Kazakh" lang="kk" hreflang="kk" data-title="Квинталық шеңбер" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Kvintu_aplis" title="Kvintu aplis – Latvian" lang="lv" hreflang="lv" data-title="Kvintu aplis" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kvintk%C3%B6r" title="Kvintkör – Hungarian" lang="hu" hreflang="hu" data-title="Kvintkör" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kwintencirkel" title="Kwintencirkel – Dutch" lang="nl" hreflang="nl" data-title="Kwintencirkel" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BA%94%E5%BA%A6%E5%9C%8F" title="五度圏 – Japanese" lang="ja" hreflang="ja" data-title="五度圏" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Kwintenkrais" title="Kwintenkrais – Northern Frisian" lang="frr" hreflang="frr" data-title="Kwintenkrais" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kvintsirkel" title="Kvintsirkel – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Kvintsirkel" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kvintsirkel" title="Kvintsirkel – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Kvintsirkel" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ko%C5%82o_kwintowe" title="Koło kwintowe – Polish" lang="pl" hreflang="pl" data-title="Koło kwintowe" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/C%C3%ADrculo_de_quintas" title="Círculo de quintas – Portuguese" lang="pt" hreflang="pt" data-title="Círculo de quintas" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-rm mw-list-item"><a href="https://rm.wikipedia.org/wiki/Circul_da_quintas" title="Circul da quintas – Romansh" lang="rm" hreflang="rm" data-title="Circul da quintas" data-language-autonym="Rumantsch" data-language-local-name="Romansh" class="interlanguage-link-target"><span>Rumantsch</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B8%D0%BD%D1%82%D0%BE%D0%B2%D1%8B%D0%B9_%D0%BA%D1%80%D1%83%D0%B3" title="Квинтовый круг – Russian" lang="ru" hreflang="ru" data-title="Квинтовый круг" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Circle_of_fifths" title="Circle of fifths – Simple English" lang="en-simple" hreflang="en-simple" data-title="Circle of fifths" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kvintov%C3%BD_kruh" title="Kvintový kruh – Slovak" lang="sk" hreflang="sk" data-title="Kvintový kruh" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B8%D0%BD%D1%82%D0%BD%D0%B8_%D0%B8_%D0%BA%D0%B2%D0%B0%D1%80%D1%82%D0%BD%D0%B8_%D0%BA%D1%80%D1%83%D0%B3" title="Квинтни и квартни круг – Serbian" lang="sr" hreflang="sr" data-title="Квинтни и квартни круг" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kvinttiympyr%C3%A4" title="Kvinttiympyrä – Finnish" lang="fi" hreflang="fi" data-title="Kvinttiympyrä" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kvintcirkeln" title="Kvintcirkeln – Swedish" 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src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Circle_of_fifths_deluxe_4.svg/400px-Circle_of_fifths_deluxe_4.svg.png" decoding="async" width="400" height="400" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Circle_of_fifths_deluxe_4.svg/600px-Circle_of_fifths_deluxe_4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Circle_of_fifths_deluxe_4.svg/800px-Circle_of_fifths_deluxe_4.svg.png 2x" data-file-width="600" data-file-height="600" /></a><figcaption>Circle of fifths showing major and minor keys</figcaption></figure> <p>In <a href="/wiki/Music_theory" title="Music theory">music theory</a>, the <b>circle of fifths</b> (sometimes also <b>cycle of fifths</b>) is a way of organizing <a href="/wiki/Pitch_(music)" title="Pitch (music)">pitches</a> as a sequence of <a href="/wiki/Perfect_fifth" title="Perfect fifth">perfect fifths</a>. Starting on a C, and using the standard system of tuning for Western music (<a href="/wiki/12_equal_temperament" title="12 equal temperament">12-tone equal temperament</a>), the sequence is: C, G, D, A, E, B, F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>/G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>/D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>/A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>/E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>/B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, F, and C. This order places the most closely related <a href="/wiki/Key_signature" title="Key signature">key signatures</a> adjacent to one another. </p><p>Twelve-tone equal temperament tuning divides each octave into twelve equivalent semitones, and the circle of fifths leads to a C seven octaves above the starting point. If the fifths are tuned with an exact frequency ratio of 3:2 (the system of tuning known as <a href="/wiki/Just_intonation" title="Just intonation">just intonation</a>), this is not the case (the circle does not "close"). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The circle of fifths organizes pitches in a sequence of <a href="/wiki/Perfect_fifth" title="Perfect fifth">perfect fifths</a>, generally shown as a circle with the pitches (and their corresponding keys) in clockwise order. It can be viewed in a counterclockwise direction as a circle of fourths. Harmonic progressions in Western music commonly use adjacent keys in this system, making it a useful reference for musical composition and harmony.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The top of the circle shows the <a href="/wiki/Key_(music)" title="Key (music)">key</a> of C Major, with no <a href="/wiki/Sharp_(music)" title="Sharp (music)">sharps</a> or <a href="/wiki/Flat_(music)" title="Flat (music)">flats</a>. Proceeding clockwise, the pitches ascend by fifths. The key signatures associated with those pitches change accordingly: the key of G has one sharp, the key of D has 2 sharps, and so on. Proceeding counterclockwise from the top of the circle, the notes change by descending fifths and the key signatures change accordingly: the key of F has one flat, the key of B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> has 2 flats, and so on. Some keys (at the bottom of the circle) can be notated <a href="/wiki/Enharmonic" class="mw-redirect" title="Enharmonic">either in sharps or in flats</a>. </p><p>Starting at any pitch and ascending by a fifth generates all tones before returning to the beginning pitch class (a pitch class consists of all of the notes indicated by a given letter regardless of octave—all "C"s, for example, belong to the same pitch class). Moving counterclockwise, the pitches descend by a fifth, but ascending by a <a href="/wiki/Perfect_fourth" title="Perfect fourth">perfect fourth</a> will lead to the same note an octave higher (therefore in the same pitch class). Moving counter-clockwise from C could be thought of as descending by a fifth to F, or ascending by a fourth to F. </p> <style data-mw-deduplicate="TemplateStyles:r1216972533">.mw-parser-output .col-begin{border-collapse:collapse;padding:0;color:inherit;width:100%;border:0;margin:0}.mw-parser-output .col-begin-small{font-size:90%}.mw-parser-output .col-break{vertical-align:top;text-align:left}.mw-parser-output .col-break-2{width:50%}.mw-parser-output .col-break-3{width:33.3%}.mw-parser-output .col-break-4{width:25%}.mw-parser-output .col-break-5{width:20%}@media(max-width:720px){.mw-parser-output .col-begin,.mw-parser-output .col-begin>tbody,.mw-parser-output .col-begin>tbody>tr,.mw-parser-output .col-begin>tbody>tr>td{display:block!important;width:100%!important}.mw-parser-output .col-break{padding-left:0!important}}</style><div> <table class="col-begin" role="presentation"> <tbody><tr> <td class="col-break"> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/r/n/rn1zaakvsmp2icu895k7e1obrhuy0lw/rn1zaakv.midi"><img src="//upload.wikimedia.org/score/r/n/rn1zaakvsmp2icu895k7e1obrhuy0lw/rn1zaakv.png" width="399" height="59" alt=" {
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" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/r/n/rn1zaakvsmp2icu895k7e1obrhuy0lw/rn1zaakv.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/r/n/rn1zaakvsmp2icu895k7e1obrhuy0lw/rn1zaakv.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Circle of fifths clockwise within one octave</div></div></div></div> </td> <td class="col-break"> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/0/o/0o49ravgwlc79gcegjwhghscsq6rprw/0o49ravg.midi"><img src="//upload.wikimedia.org/score/0/o/0o49ravgwlc79gcegjwhghscsq6rprw/0o49ravg.png" width="399" height="56" alt=" {
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\layout { \context {\Score \omit BarNumber} line-width = #100 }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/0/o/0o49ravgwlc79gcegjwhghscsq6rprw/0o49ravg.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/0/o/0o49ravgwlc79gcegjwhghscsq6rprw/0o49ravg.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Circle of fifths counterclockwise within one octave</div></div></div></div> <p>  </p> </td></tr></tbody></table></div> <div class="mw-heading mw-heading2"><h2 id="Structure_and_use">Structure and use</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=2" title="Edit section: Structure and use"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Diatonic_key_signatures">Diatonic key signatures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=3" title="Edit section: Diatonic key signatures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Each pitch can serve as the tonic of a major or <a href="/wiki/Relative_key" title="Relative key">minor</a> key, and each of these keys will have a <a href="/wiki/Diatonic_scale" title="Diatonic scale">diatonic scale</a> associated with it. The circle diagram shows the number of sharps or flats in each <a href="/wiki/Key_signature" title="Key signature">key signature</a>, with the major key indicated by a capital letter and the minor key indicated by a lower-case letter. Major and minor keys that have the same key signature are referred to as <a href="/wiki/Relative_key" title="Relative key"><i>relative major</i> and <i>relative minor</i></a> of one another. </p> <div class="mw-heading mw-heading3"><h3 id="Modulation_and_chord_progression">Modulation and chord progression</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=4" title="Edit section: Modulation and chord progression"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Tonality" title="Tonality">Tonal music</a> often <a href="/wiki/Modulation_(music)" title="Modulation (music)">modulates</a> to a new tonal center whose key signature differs from the original by only one flat or sharp. These closely-related keys are a fifth apart from each other and are therefore adjacent in the circle of fifths. <a href="/wiki/Chord_progression" title="Chord progression">Chord progressions</a> also often move between chords whose roots are related by perfect fifth, making the circle of fifths useful in illustrating the "harmonic distance" between chords. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:The_circle_of_fifths_on_umbilic_torus_surface.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/The_circle_of_fifths_on_umbilic_torus_surface.gif/220px-The_circle_of_fifths_on_umbilic_torus_surface.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/The_circle_of_fifths_on_umbilic_torus_surface.gif/330px-The_circle_of_fifths_on_umbilic_torus_surface.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/The_circle_of_fifths_on_umbilic_torus_surface.gif/440px-The_circle_of_fifths_on_umbilic_torus_surface.gif 2x" data-file-width="800" data-file-height="600" /></a><figcaption>Major 7th progressing on <a href="/wiki/Umbilic_torus" title="Umbilic torus">umbilic torus</a> surface</figcaption></figure> <p>The circle of fifths is used to organize and describe the <a href="/wiki/Diatonic_function" class="mw-redirect" title="Diatonic function">harmonic or tonal function</a> of <a href="/wiki/Chord_(music)" title="Chord (music)">chords</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Chords can progress in a pattern of ascending perfect fourths (alternately viewed as descending perfect fifths) in "functional succession". This can be shown "...by the circle of fifths (in which, therefore, <a href="/wiki/Scale_degree" class="mw-redirect" title="Scale degree">scale degree</a> II is closer to the <a href="/wiki/Dominant_(music)" title="Dominant (music)">dominant</a> than scale degree IV)".<sup id="cite_ref-FOOTNOTENattiez1990225_3-0" class="reference"><a href="#cite_note-FOOTNOTENattiez1990225-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In this view the tonic or tonal center is considered the end point of a <a href="/wiki/Chord_progression" title="Chord progression">chord progression</a> derived from the circle of fifths. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ii-V-I_turnaround_in_C.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ii-V-I_turnaround_in_C.png/220px-Ii-V-I_turnaround_in_C.png" decoding="async" width="220" height="108" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ii-V-I_turnaround_in_C.png/330px-Ii-V-I_turnaround_in_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ii-V-I_turnaround_in_C.png/440px-Ii-V-I_turnaround_in_C.png 2x" data-file-width="534" data-file-height="263" /></a><figcaption><a href="/wiki/Ii%E2%80%93V%E2%80%93I_progression" title="Ii–V–I progression">ii–V–I progression</a>, in C, illustrating the similarity between them<figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Ii-V-I_turnaround_in_C.mid" data-mwprovider="wikimediacommons" resource="/wiki/File:Ii-V-I_turnaround_in_C.mid"><source src="//upload.wikimedia.org/wikipedia/commons/e/e6/Ii-V-I_turnaround_in_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e6/Ii-V-I_turnaround_in_C.mid/Ii-V-I_turnaround_in_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e6/Ii-V-I_turnaround_in_C.mid/Ii-V-I_turnaround_in_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span><figcaption>Subdominant, supertonic seventh, and supertonic chords</figcaption></figure></figcaption></figure> <p>According to <a href="/wiki/Richard_Franko_Goldman" title="Richard Franko Goldman">Richard Franko Goldman</a>'s <i>Harmony in Western Music</i>, "the IV chord is, in the simplest mechanisms of diatonic relationships, at the greatest distance from I. In terms of the [descending] circle of fifths, it leads away from I, rather than toward it."<sup id="cite_ref-FOOTNOTEGoldman196568_4-0" class="reference"><a href="#cite_note-FOOTNOTEGoldman196568-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> He states that the progression I–ii–V–I (an <a href="/wiki/Authentic_cadence" class="mw-redirect" title="Authentic cadence">authentic cadence</a>) would feel more final or <a href="/wiki/Resolution_(music)" title="Resolution (music)">resolved</a> than I–IV–I (a <a href="/wiki/Plagal_cadence" class="mw-redirect" title="Plagal cadence">plagal cadence</a>). Goldman<sup id="cite_ref-FOOTNOTEGoldman1965chapter_3_5-0" class="reference"><a href="#cite_note-FOOTNOTEGoldman1965chapter_3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> concurs with Nattiez, who argues that "the chord on the fourth degree appears long before the chord on II, and the subsequent final I, in the progression I–IV–vii<sup>o</sup>–iii–vi–ii–V–I", and is farther from the tonic there as well.<sup id="cite_ref-FOOTNOTENattiez1990226_6-0" class="reference"><a href="#cite_note-FOOTNOTENattiez1990226-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> (In this and related articles, upper-case Roman numerals indicate major triads while lower-case Roman numerals indicate minor triads.) </p> <div class="mw-heading mw-heading3"><h3 id="Circle_closure_in_non-equal_tuning_systems">Circle closure in non-equal tuning systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=5" title="Edit section: Circle closure in non-equal tuning systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Using the exact 3:2 ratio of frequencies to define a perfect fifth (<a href="/wiki/Just_intonation" title="Just intonation">just intonation</a>) does not quite result in a return to the <a href="/wiki/Pitch_class" title="Pitch class">pitch class</a> of the starting note after going around the circle of fifths. <a href="/wiki/Twelve-tone_equal_temperament" class="mw-redirect" title="Twelve-tone equal temperament">Twelve-tone equal temperament</a> tuning produces fifths that return to a tone exactly seven <a href="/wiki/Octave" title="Octave">octaves</a> above the initial tone and makes the frequency ratio of the chromatic semitone the same as that of the diatonic semitone. The standard tempered fifth has a frequency ratio of 2<sup>7/12</sup>:1 (or about 1.498307077:1), approximately two cents narrower than a justly tuned fifth. </p><p>Ascending by twelve justly tuned fifths fails to close the circle by an excess of approximately 23.46 <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a>, roughly a quarter of a <a href="/wiki/Semitone" title="Semitone">semitone</a>, an interval known as the <a href="/wiki/Pythagorean_comma" title="Pythagorean comma">Pythagorean comma</a>. If limited to twelve pitches per octave, Pythagorean tuning markedly shortens the <a href="/wiki/Interval_(music)" title="Interval (music)">width</a> of one of the twelve fifths, which makes it severely <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">dissonant</a>. This anomalous fifth is called the <a href="/wiki/Wolf_fifth" class="mw-redirect" title="Wolf fifth">wolf fifth</a> – a humorous reference to a wolf howling an off-pitch note. Non-extended <a href="/wiki/Quarter-comma_meantone" title="Quarter-comma meantone">quarter-comma meantone</a> uses eleven fifths slightly narrower than the equally tempered fifth, and requires a much wider and even more dissonant wolf fifth to close the circle. More complex tuning systems based on just intonation, such as <a href="/wiki/5-limit_tuning" class="mw-redirect" title="5-limit tuning">5-limit tuning</a>, use at most eight justly tuned fifths and at least three non-just fifths (some slightly narrower, and some slightly wider than the just fifth) to close the circle. </p> <div class="mw-heading mw-heading3"><h3 id="Equal-tempered_tunings_with_more_than_twelve_notes">Equal-tempered tunings with more than twelve notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=6" title="Edit section: Equal-tempered tunings with more than twelve notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nowadays, with the advent of electronic <a href="/wiki/Isomorphic_keyboard" title="Isomorphic keyboard">isomorphic keyboards</a>, equal temperament tunings with more than twelve notes per octave can be used to close the circle of fifths for other tunings. For example, <a href="/wiki/31-tone_equal_temperament" class="mw-redirect" title="31-tone equal temperament">31-tone equal temperament</a> closely approximates quarter-comma meantone, and <a href="/wiki/53-tone_equal_temperament" class="mw-redirect" title="53-tone equal temperament">53-tone equal temperament</a> closely approximates Pythagorean tuning. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=7" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Diletsky_circle.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Diletsky_circle.jpg/200px-Diletsky_circle.jpg" decoding="async" width="200" height="267" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Diletsky_circle.jpg/300px-Diletsky_circle.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Diletsky_circle.jpg/400px-Diletsky_circle.jpg 2x" data-file-width="857" data-file-height="1143" /></a><figcaption>Circle of fifths in <i>Idea grammatikii musikiyskoy</i> (Moscow, 1679)</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Heinichen_musicalischer_circul.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Heinichen_musicalischer_circul.png/220px-Heinichen_musicalischer_circul.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Heinichen_musicalischer_circul.png/330px-Heinichen_musicalischer_circul.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Heinichen_musicalischer_circul.png/440px-Heinichen_musicalischer_circul.png 2x" data-file-width="627" data-file-height="627" /></a><figcaption><a href="/wiki/Johann_David_Heinichen" title="Johann David Heinichen">Heinichen</a>'s musical circle (German: <i>Musicalischer Circul</i>) (1711)</figcaption></figure> <p>The circle of fifths developed in the late 1600s and early 1700s to theorize the modulation of the Baroque era (see <a href="#Baroque_era">§ Baroque era</a>). </p><p>The first circle of fifths diagram appears in the <i>Grammatika</i> (1677) of the composer and theorist <a href="/wiki/Nikolay_Diletsky" title="Nikolay Diletsky">Nikolay Diletsky</a>, who intended to present <a href="/wiki/Music_theory" title="Music theory">music theory</a> as a tool for composition.<sup id="cite_ref-Jensen_7-0" class="reference"><a href="#cite_note-Jensen-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> It was "the first of its kind, aimed at teaching a Russian audience how to write Western-style polyphonic compositions." </p><p>A circle of fifths diagram was independently created by German composer and theorist <a href="/wiki/Johann_David_Heinichen" title="Johann David Heinichen">Johann David Heinichen</a> in his <i>Neu erfundene und gründliche Anweisung</i> (1711),<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> which he called the "Musical Circle" (German: <i>Musicalischer Circul</i>).<sup id="cite_ref-FOOTNOTEBarnett2002444_9-0" class="reference"><a href="#cite_note-FOOTNOTEBarnett2002444-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTELester1989110–112_10-0" class="reference"><a href="#cite_note-FOOTNOTELester1989110–112-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> This was also published in his <i>Der General-Bass in der Composition</i> (1728). </p><p>Heinichen placed the relative minor key next to the major key, which did not reflect the actual proximity of keys. <a href="/wiki/Johann_Mattheson" title="Johann Mattheson">Johann Mattheson</a> (1735) and others attempted to improve this—<a href="/wiki/David_Kellner" title="David Kellner">David Kellner</a> (1737) proposed having the major keys on one circle, and the relative minor keys on a second, inner circle. This was later developed into <a href="/wiki/Chordal_space" title="Chordal space">chordal space</a>, incorporating the parallel minor as well.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Some sources imply that the circle of fifths was known in antiquity, by <a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> This is a misunderstanding and an anachronism.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Tuning by fifths (so-called <a href="/wiki/Pythagorean_tuning" title="Pythagorean tuning">Pythagorean tuning</a>) dates to Ancient Mesopotamia;<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> see <a href="/wiki/Music_of_Mesopotamia#Music_theory" title="Music of Mesopotamia">Music of Mesopotamia § Music theory</a>, though they did not extend this to a twelve note scale, stopping at seven. The <a href="/wiki/Pythagorean_comma" title="Pythagorean comma">Pythagorean comma</a> was calculated by <a href="/wiki/Euclid" title="Euclid">Euclid</a> and by Chinese mathematicians (in the <i><a href="/wiki/Huainanzi" title="Huainanzi">Huainanzi</a></i>); see <a href="/wiki/Pythagorean_comma#History" title="Pythagorean comma">Pythagorean comma § History</a>. Thus, it was known in antiquity that a cycle of twelve fifths was almost exactly seven octaves (more practically, alternating ascending fifths and descending fourths was almost exactly an octave). However, this was theoretical knowledge, and was not used to construct a repeating twelve-tone scale, nor to modulate. This was done later in <a href="/wiki/Meantone_temperament" title="Meantone temperament">meantone temperament</a> and <a href="/wiki/Twelve-tone_equal_temperament" class="mw-redirect" title="Twelve-tone equal temperament">twelve-tone equal temperament</a>, which allowed modulation while still being in tune, but did not develop in Europe until about 1500. Although popularized as the circle of fifths, its Anglo-Saxon etymological origins trace back to the name "wheel of fifths." </p> <div class="mw-heading mw-heading2"><h2 id="Use">Use</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=8" title="Edit section: Use"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In musical pieces from the <a href="/wiki/Baroque_music" title="Baroque music">Baroque music</a> era and the <a href="/wiki/Classical_era_of_music" class="mw-redirect" title="Classical era of music">Classical era of music</a> and in Western <a href="/wiki/Popular_music" title="Popular music">popular music</a>, <a href="/wiki/Traditional_music" class="mw-redirect" title="Traditional music">traditional music</a> and <a href="/wiki/Folk_music" title="Folk music">folk music</a>, when pieces or songs modulate to a new key, these modulations are often associated with the circle of fifths. </p><p>In practice, compositions rarely make use of the entire circle of fifths. More commonly, composers make use of "the compositional idea of the 'cycle' of 5ths, when music moves consistently through a smaller or larger segment of the tonal structural resources which the circle abstractly represents."<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The usual practice is to derive the circle of fifths progression from the seven tones of the diatonic scale, rather from the full range of twelve tones present in the chromatic scale. In this diatonic version of the circle, one of the fifths is not a true fifth: it is a tritone (or a diminished fifth), e.g. between F and B in the "natural" diatonic scale (i.e. without sharps or flats). Here is how the circle of fifths derives, through <a href="/wiki/Permutation" title="Permutation">permutation</a> from the diatonic major scale: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/k/0/k0beficxuf483opnkhmq1escfcidyzi/k0beficx.midi"><img src="//upload.wikimedia.org/score/k/0/k0beficxuf483opnkhmq1escfcidyzi/k0beficx.png" width="607" height="48" alt=" {
\omit Score.TimeSignature
\relative c' { \clef F \time 8/4
 c b a g f e d c \bar "||" c' f, b e, a d, g c, \bar "||"
} }
\layout { \context { \Score \override SpacingSpanner.base-shortest-duration = #(ly:make-moment 1/16) } }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/k/0/k0beficxuf483opnkhmq1escfcidyzi/k0beficx.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/k/0/k0beficxuf483opnkhmq1escfcidyzi/k0beficx.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Diatonic scale and the circle of fifths derived from it – major</div></div></div></div> <p>And from the (natural) minor scale: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/0/v/0vpin3pk5ixqdosiwvoceyla3o61iho/0vpin3pk.midi"><img src="//upload.wikimedia.org/score/0/v/0vpin3pk5ixqdosiwvoceyla3o61iho/0vpin3pk.png" width="608" height="46" alt=" {
\omit Score.TimeSignature
\relative c' { \key c \major \clef bass \time 8/4
 a g f e d c b a \bar "||" a' d, g c, f b, e a, \bar "||"
} }
\layout { \context { \Score \override SpacingSpanner.base-shortest-duration = #(ly:make-moment 1/16) } }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/0/v/0vpin3pk5ixqdosiwvoceyla3o61iho/0vpin3pk.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/0/v/0vpin3pk5ixqdosiwvoceyla3o61iho/0vpin3pk.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Diatonic scale and the circle of fifths derived from it – minor</div></div></div></div> <p>The following is the basic sequence of chords that can be built over the major bass-line: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/n/r/nr0dy1qbm31u3gwnolb5w4anl5hu0zb/nr0dy1qb.midi"><img src="//upload.wikimedia.org/score/n/r/nr0dy1qbm31u3gwnolb5w4anl5hu0zb/nr0dy1qb.png" width="529" height="135" alt=" {
\omit Score.TimeSignature
\new PianoStaff << 
 \new ChordNames \chordmode {
 c f b,:dim e:m a,:m d:m g, c
 }
 \new Staff \relative c' { \time 8/4
 <g' c e> <a c f> <f b d> <g b e> <e a c> <f a d> <d g b> <e g c> \bar "||"
 }
 \new Staff \relative c' { \clef F \time 8/4
 c f, b e, a d, g c,
 } >> }
\layout { \context { \Score \override SpacingSpanner.base-shortest-duration = #(ly:make-moment 1/128) } }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/n/r/nr0dy1qbm31u3gwnolb5w4anl5hu0zb/nr0dy1qb.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/n/r/nr0dy1qbm31u3gwnolb5w4anl5hu0zb/nr0dy1qb.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Circle of fifths chord progression – major</div></div></div></div> <p>And over the minor: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/5/z/5z8i3iqdpvj0xb27krns6b2qnj336xn/5z8i3iqd.midi"><img src="//upload.wikimedia.org/score/5/z/5z8i3iqdpvj0xb27krns6b2qnj336xn/5z8i3iqd.png" width="530" height="135" alt=" {
\omit Score.TimeSignature
\new PianoStaff << 
 \new ChordNames \chordmode {
 a,:m d:m g, c f, b,:dim e, a,:m
 }
 \new Staff \relative c' { \time 8/4
 <e a c> <f a d> <d g b> <e g c> <c f a> <d f b> <b e gis> <c e a> \bar "||"
 }
 \new Staff \relative c' { \clef F \time 8/4
 a d, g c, f b, e a,
 } >> }
\layout { \context { \Score \override SpacingSpanner.base-shortest-duration = #(ly:make-moment 1/128) } }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/5/z/5z8i3iqdpvj0xb27krns6b2qnj336xn/5z8i3iqd.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/5/z/5z8i3iqdpvj0xb27krns6b2qnj336xn/5z8i3iqd.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Circle of fifths chord progression – minor</div></div></div></div> <p>Adding sevenths to the chords creates a greater sense of forward momentum to the harmony: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/l/9/l9q4ht8r5nhtsd8m13r2zusad109mqp/l9q4ht8r.midi"><img src="//upload.wikimedia.org/score/l/9/l9q4ht8r5nhtsd8m13r2zusad109mqp/l9q4ht8r.png" width="530" height="133" alt=" {
\omit Score.TimeSignature
\new PianoStaff << 
 \new ChordNames \chordmode {
 a,:m d:m7 g,:7 c:maj7 f,:maj7 b,:m7.5- e,:7 a,:m
 }
 \new Staff \relative c' { \time 8/4
 <e a c> <f a c> <d f b> <e g b> <c e a> <d f a> <b d gis> <c e a> \bar "||"
 }
 \new Staff \relative c' { \clef F \time 8/4
 a d, g c, f b, e a,
 } >> }
\layout { \context { \Score \override SpacingSpanner.base-shortest-duration = #(ly:make-moment 1/128) } }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/l/9/l9q4ht8r5nhtsd8m13r2zusad109mqp/l9q4ht8r.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/l/9/l9q4ht8r5nhtsd8m13r2zusad109mqp/l9q4ht8r.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Circle of fifths chord progression – minor with added sevenths</div></div></div></div> <div class="mw-heading mw-heading3"><h3 id="Baroque_era">Baroque era</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=9" title="Edit section: Baroque era"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to <a href="/wiki/Richard_Taruskin" title="Richard Taruskin">Richard Taruskin</a>, <a href="/wiki/Arcangelo_Corelli" title="Arcangelo Corelli">Arcangelo Corelli</a> was the most influential composer to establish the pattern as a standard harmonic <a href="/wiki/Trope_(literature)" title="Trope (literature)">"trope"</a>: "It was precisely in Corelli's time, the late seventeenth century, that the circle of fifths was being 'theorized' as the main propellor of harmonic motion, and it was Corelli more than any one composer who put that new idea into telling practice."<sup id="cite_ref-FOOTNOTETaruskin2010184_18-0" class="reference"><a href="#cite_note-FOOTNOTETaruskin2010184-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>The circle of fifths progression occurs frequently in the music of <a href="/wiki/J._S._Bach" class="mw-redirect" title="J. S. Bach">J. S. Bach</a>. In the following, from <a href="/wiki/Jauchzet_Gott_in_allen_Landen,_BWV_51" title="Jauchzet Gott in allen Landen, BWV 51"><i>Jauchzet Gott in allen Landen</i>, BWV 51</a>, even when the solo bass line implies rather than states the chords involved: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/h/1/h131ujhgxzw3ci9ubjutdi3qmdbkyzs/h131ujhg.midi"><img src="//upload.wikimedia.org/score/h/1/h131ujhgxzw3ci9ubjutdi3qmdbkyzs/h131ujhg.png" width="591" height="105" alt=" 
{ \new Staff \relative c' { 
 \set Staff.midiInstrument = #"cello" \clef F \time 12/8
 r r8 << {a( b c) | d,( e f) g( a b) | c,( d e) f( g a) | b,( c d) e( d) e | a, c e}
 \new Staff = "chords" \with {
 \omit TimeSignature
 \magnifyStaff #2/3
 firstClef = ##f
 } \relative c' 
 { \set Staff.midiInstrument = #"cello" \clef F
 {\hide Stem a8 s s d, s s g s s c, s s f s s b, s s e s s a, s s}}
\addlyrics \with { alignAboveContext = "chords" } { \override LyricText.font-size = #-1.5 Am \markup{\concat{Dm\super{7}}} \markup{\concat{G\super{7}}} \markup{\concat{C\super{maj7}}} \markup{\concat{F\super{maj7}}} \markup{\concat{B\super{7(♭5)}}} \markup{\concat{E\super{7}}} Am
 } >>
 s1 s8
} }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/h/1/h131ujhgxzw3ci9ubjutdi3qmdbkyzs/h131ujhg.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/h/1/h131ujhgxzw3ci9ubjutdi3qmdbkyzs/h131ujhg.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Bach from Cantata 51</div></div></div></div> <p><a href="/wiki/Handel" class="mw-redirect" title="Handel">Handel</a> uses a circle of fifths progression as the basis for the <a href="/wiki/Passacaglia" title="Passacaglia">Passacaglia</a> movement from his Harpsichord suite No. 6 in G minor. </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/9/9/998vtzo0dn3kg508ntwfrvh6aa066wp/998vtzo0.midi"><img src="//upload.wikimedia.org/score/9/9/998vtzo0dn3kg508ntwfrvh6aa066wp/998vtzo0.png" width="593" height="136" alt=" {
\new PianoStaff << 
 \new Staff = "chords" << \magnifyStaff #3/4
 \new Voice \relative c' { 
 \set Staff.midiInstrument = #"harpsichord" \key g \minor
 \mark \markup { \abs-fontsize #10 { \bold { Passacaille } } }
 <bes' d>8. <c ees>16 <a c>8. <bes d>16 <c ees>8. <c ees>16 <bes d>8. <c ees>16 |
 <a c>8. <a f'>16 <g ees'>8. <a f'>16 <bes d>8. <bes d>16 <a c>8. <bes d>16 |
 <g bes>8. <a c>16 <fis a>8. <g bes>16 <a c>8. <a c>16 <g bes>8. <a c>16 |
 <fis a>8. <fis d'>16 <e c'>8. <fis d'>16 bes8 a g4 \bar "||"
} 
 \new Voice \relative c' { 
 s1 s s s2 \stemDown g'2
} 
 \new Staff \relative c' { \magnifyStaff #3/4
 \set Staff.midiInstrument = #"harpsichord" \key g \minor \clef F
 <g bes d>2 <ees g c> <f a c> <bes, d f bes> <ees g bes> <c ees a> d4 d, g2
} 
 \addlyrics \with { alignAboveContext = "chords" } { \override LyricText.font-size = #-1.5 Gm Cm F B♭ E♭ \markup{\concat{Am\super{(♭5)}}} D _ Gm }
>> >> }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/9/9/998vtzo0dn3kg508ntwfrvh6aa066wp/998vtzo0.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/9/9/998vtzo0dn3kg508ntwfrvh6aa066wp/998vtzo0.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Handel Passacaille from Suite in G minor bars 1–4</div></div></div></div> <p><a href="/wiki/Baroque_music" title="Baroque music">Baroque</a> composers learnt to enhance the "propulsive force" of the harmony engendered by the circle of fifths "by adding sevenths to most of the constituent chords." "These sevenths, being dissonances, create the need for resolution, thus turning each progression of the circle into a simultaneous reliever and re-stimulator of harmonic tension... Hence harnessed for expressive purposes."<sup id="cite_ref-FOOTNOTETaruskin2010188_19-0" class="reference"><a href="#cite_note-FOOTNOTETaruskin2010188-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Striking passages that illustrate the use of sevenths occur in the aria "Pena tiranna" in <a href="/wiki/Handel" class="mw-redirect" title="Handel">Handel</a>'s 1715 opera <i><a href="/wiki/Amadigi_di_Gaula" title="Amadigi di Gaula">Amadigi di Gaula</a></i>: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/3/f/3ftgj0qoybea6qf6me4d69mtfjbkk09/3ftgj0qo.midi"><img src="//upload.wikimedia.org/score/3/f/3ftgj0qoybea6qf6me4d69mtfjbkk09/3ftgj0qo.png" width="612" height="528" alt=" {<<
 \new Staff \with{ \magnifyStaff #3/4 instrumentName = "Bassoon" } \relative c' { 
 \set Staff.midiInstrument = #"bassoon" \key f \major \clef tenor \time 3/4
 \mark \markup { \abs-fontsize #10 { \bold { Largo } } }
 f2. ~ | f | e ~ | e | \break
 d ~ | d | cis8 a d4 \clef F d, | a a'8 g f e
} 
 \new ChoirStaff <<
 \new Staff = "chords" \with{ \magnifyStaff #3/4 instrumentName = "Violins" } <<
 \new Voice \relative c' { 
 \set Staff.midiInstrument = #"violin" \key f \major \clef treble
 <d' f a>4 <d, f a>4. r16 <d' f a> | <d f bes>8.-. <d, f bes>16 <d f bes>4. r 16 <d f bes> |
 <c e bes'>8.-. <g bes>16 <g bes>4. r16 <e'' g bes> | <e f a>4 <e, f a>4. r16 <c f a> |
 <d f a>8.-. a16 a4. r16 <d' f a> | <d e g>4 <d, e g>4. r16 <g e' g> |
 \stemUp <e' g>8.-. <f a>16 <d f>4. <cis e>8 | <cis e>4 <cis e> r
} 
 \new Voice \relative c' { 
 s2. s s s s s | \stemDown cis'4 a4. a8 | a4 a s
} >>
 \new Staff \with{ \magnifyStaff #3/4 instrumentName = "Violas"} \relative c' { 
 \set Staff.midiInstrument = #"viola" \key f \major \clef C
 a'4 a,4. r16 a' | g8.-. g,16 g4. r16 g | g8.-. e16 e4. r16 c'' | c4 c,4. r16 c |
 bes8.-. f16 f4. r16 bes' | bes4 bes,4. r16 e | e4 f e | e e r
} 
 \new Staff \with{ \magnifyStaff #3/4 instrumentName = "Bassi"} \relative c' { 
 \set Staff.midiInstrument = #"cello" \key f \major \clef F
 d4 d,4. r16 d | g4-. g, r | c-. c,4. r16 c' | f4 f, r8 f' |
 bes4 bes, r | e e, r | a' d, d, | a' a r
} 
 \addlyrics \with { alignAboveContext = "chords" } { \override LyricText.font-size = #-1.5 Dm _ _ \markup{\concat{Gm\super{7}}} _ \markup{\concat{C\super{7}}} _ _ \markup{\concat{F\super{maj7}}} _ _ \markup{\concat{B♭\super{maj7}}} _ \markup{\concat{Em\super{7(♭5)}}} _ \markup{\concat{A\super{7}}} Dm _ A }
>> >> }
\layout {
 indent = 1.0\cm
 line-width = #150
}
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/3/f/3ftgj0qoybea6qf6me4d69mtfjbkk09/3ftgj0qo.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/3/f/3ftgj0qoybea6qf6me4d69mtfjbkk09/3ftgj0qo.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Handel, aria "Pena tiranna" from <i>Amadigi</i>, orchestral introduction</div></div></div></div> <p>– and in Bach's <a href="/wiki/Weimar_concerto_transcriptions_(Bach)" title="Weimar concerto transcriptions (Bach)">keyboard arrangement</a> of <a href="/wiki/Alessandro_Marcello" title="Alessandro Marcello">Alessandro Marcello</a>'s <a href="/wiki/Oboe_Concerto_(Marcello)" title="Oboe Concerto (Marcello)">Concerto for Oboe and Strings</a>. </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/2/r/2rj0hc4pt0k6grm4sbdi8k7nqi1sdl7/2rj0hc4p.midi"><img src="//upload.wikimedia.org/score/2/r/2rj0hc4pt0k6grm4sbdi8k7nqi1sdl7/2rj0hc4p.png" width="606" height="630" alt=" { <<
 \new PianoStaff <<
 \new Staff = "chords" << \magnifyStaff #2/3
 \new Voice \relative c' { 
 \key f \major \set Score.tempoHideNote = ##t \tempo 4 = 40 \time 3/4
 \mark \markup { \abs-fontsize #10 { \bold { Adagio } } }
 d8 d d d d d | e e e e e e | g g g g g g | \stemUp d'( f) \stemNeutral f( a) a( c16 bes) | bes2 \mordent r4 | \break
 c,8( e16 d) e8( g16 f) g8( bes16 a) | a2 \mordent r4 | bes,16( c32 a bes16 d32 cis) d16( e32 cis d16 f32 e) f16( g32 e f16 a32 g) | \break
 g2 \mordent r4 | a,32( gis a b a b cis b) cis( d cis d e d e f e f g! f g f g e) | f4 \mordent s4
 }
 \new Voice \relative c' { 
 s2. | s | \stemDown e8 e e e e e | f8 
 }
 \new Staff << \magnifyStaff #2/3
 \new Voice \relative c' { 
 \key f \major \clef F \time 3/4
 R2. | d8 d d d d d | \stemUp cis cis cis cis cis cis | d <d f>[ <d f> <d f> <d f> <d f>] | <d f> <d f> <d f> <d f> <d f> <d f> | e e e e e e | <c e> <c e> <c e> <c e> <c e> <c e> | d d d d d d | <bes d> <bes d> <bes d> <bes d> <bes d> <bes d> | cis cis cis cis cis cis | d[ d] s4
 } 
 \new Voice \relative c' { \clef F 
 s2. | s | \stemDown a8 a a a a a | d, r r4 r | g8 g g g g g | c8 c c c c c | f, f f f f f | bes bes bes bes bes bes | e, e e e e e | a a a a a a | d,[ d] s4
 }
 \addlyrics \with { alignAboveContext = "chords" } { \override LyricText.font-size = #-1.5 _ _ _ _ _ _ Dm \markup{\concat{Gm\super{7}}} _ _ _ _ _ C _ _ _ _ _ \markup{\concat{F\super{maj7}}} _ _ _ _ _ B♭ _ _ _ _ _ \markup{\concat{Em\super{7(♭5)}}} _ _ _ _ _ \markup{\concat{A\super{7}}} _ _ _ _ _ Dm }
>> >> >>
\new Staff \with {
 \omit TimeSignature
 \magnifyStaff #2/3
 firstClef = ##f
 } \relative c' 
 { \hide Staff.KeySignature \key f \major \clef bass
 {\stopStaff s2. s s \startStaff \hide Stem d8 s s s s s g, s s s s s c s s s s s f, s s s s s bes s s s s s e, s s s s s a s s s s s d,}} 
 >> }
\layout { line-width = #150 }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/2/r/2rj0hc4pt0k6grm4sbdi8k7nqi1sdl7/2rj0hc4p.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/2/r/2rj0hc4pt0k6grm4sbdi8k7nqi1sdl7/2rj0hc4p.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">Bach adagio BWV 974 (after Marcello)</div></div></div></div> <div class="mw-heading mw-heading3"><h3 id="Nineteenth_century">Nineteenth century</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=10" title="Edit section: Nineteenth century"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Franz_Schubert" title="Franz Schubert">Franz Schubert</a>'s Impromptu in E-flat major, D 899, contains harmonies that move in a modified circle of fifths: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/d/t/dtvm4duj6kiry0agxrxxdahxwz84ur4/dtvm4duj.midi"><img src="//upload.wikimedia.org/score/d/t/dtvm4duj6kiry0agxrxxdahxwz84ur4/dtvm4duj.png" width="606" height="406" alt=" { <<
 \new PianoStaff <<
 \new Staff << \magnifyStaff #2/3
 \new Voice \relative c' {
 \key es \major \set Score.tempoHideNote = ##t \tempo 4 = 120 \time 3/4
 \mark \markup { \abs-fontsize #10 { \bold { Allegro } } }
 \times 2/3 {ges'8_\markup{\dynamic pp} bes aes} \times 2/3 {ges f ees} \times 2/3 {des ces bes} |
 \times 2/3 {ces ees aes} \stemDown \times 2/3 {ces ees, aes} \times 2/3 {ges ees ges} |
 \stemNeutral \times 2/3 {f ces' bes} \times 2/3 {aes ges f} \times 2/3 {ees des ces} |
 \times 2/3 {bes des ges} \stemDown \times 2/3 {bes des, ges} \times 2/3 {f des f} |
 \stemNeutral \times 2/3 {ees bes' aes} \times 2/3 {ges f ees} \times 2/3 {des ces bes} |
 \times 2/3 {aes ces f} \stemDown \times 2/3 {aes ces, f} \times 2/3 {ees ces ees} |
 \stemNeutral \times 2/3 {d aes' ges} \times 2/3 {f ees d} \times 2/3 {ces bes aes} |
 \times 2/3 {ges bes ees} \stemDown \times 2/3 {ges bes, ees} \times 2/3 {des bes des} |
 }
 \new Voice \relative c' { \stemUp
 s2. | s4 ces'2 | s2. | s4 bes2 |
 s2. | s4 aes2 | s2. | s4 ges2 |
 }
 \new Staff << \magnifyStaff #2/3
 \new Voice \relative c' {
 \key es \major \clef F \time 3/4 \stemUp \slurUp
 ees,,4( ees'2) | aes,4( aes'2) | des,,4( des'2) | ges,4( ges'2)
 ces,,4( ces'2) | f,4( f'2) | bes,,4( bes'2) | ees,4( ees'2)
 } 
 \new Voice \relative c' { \stemDown
 ees,,2. | aes2. | des,2. | ges2.
 ces,2. | f2. | bes,2. | ees2.
 } 
 >> >> >>
 \new Staff = "chords" \with {
 \omit TimeSignature
 \magnifyStaff #2/3
 } \relative c' 
 { \hide Staff.KeySignature \key ees \major \clef bass \hide Staff.Clef
 {\stopStaff s4 \startStaff \hide Stem ees,8 s s s s s aes s s s s s des, s s s s s ges s s s \stopStaff s s \startStaff ces, s s s s s f s s s s s bes, s s s s s ees}} 
\addlyrics \with { alignAboveContext = "chords" \override VerticalAxisGroup.nonstaff-relatedstaff-spacing =
 #'((basic-distance . 3)) } { \override LyricText.font-size = #-2 E♭m \markup{\concat{A♭m\super{7}}} \markup{\concat{D♭\super{7}}} \markup{\concat{G♭\super{maj7}}} \markup{\concat{C♭\super{maj7}}} \markup{\concat{Fm\super{7(♭5)}}} \markup{\concat{B♭\super{7}}} E♭m }
 >>
 }
\layout { line-width = #150 }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/d/t/dtvm4duj6kiry0agxrxxdahxwz84ur4/dtvm4duj.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/d/t/dtvm4duj6kiry0agxrxxdahxwz84ur4/dtvm4duj.mp3">download the audio file</a>.</div></audio></div></div></div></div></div></div> <p>The <a href="/wiki/Intermezzo" title="Intermezzo">Intermezzo</a> movement from <a href="/wiki/Mendelssohn" class="mw-redirect" title="Mendelssohn">Mendelssohn</a>'s <a href="/wiki/String_Quartet_No._2_(Mendelssohn)" title="String Quartet No. 2 (Mendelssohn)">String Quartet No.2</a> has a short segment with circle-of-fifths motion (the ii° is substituted by iv): </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/s/3/s3r80o3c3x0cwfj9u65fbc5f359wmtx/s3r80o3c.midi"><img src="//upload.wikimedia.org/score/s/3/s3r80o3c3x0cwfj9u65fbc5f359wmtx/s3r80o3c.png" width="587" height="306" alt=" { <<
 \new ChoirStaff <<
 \relative c' { \magnifyStaff #3/4 \set Staff.midiInstrument = #"violin" \p
 \set Score.tempoHideNote = ##t \tempo 4 = 60 \time 2/4
 \mark \markup { \abs-fontsize #10 { \bold { Allegretto con moto} } }
 \repeat volta 2 { 
 e'4( f8. e32 d | c8) d-. e4 | a, d8.( c32 b | a8) b-. e,4 |
 e'( f8. e32 d | c8) d-. e4 | a, d8.( c32 b | e8) e, a, r }
 }
 \relative c' { \magnifyStaff #3/4 \set Staff.midiInstrument = #"pizzicato strings" 
 \time 2/4
 <e c'>8_"pizz." r <f d'> r | <g, f' b> r <g e' c'> r | <c f a> r <d a'> r | e f b, r |
 <c e a> r <d a'> r | <g, f' b> r <g e' c'> r | <c f a> r <d a'> r | e gis a r |
 }
 \relative c' { \magnifyStaff #3/4 \set Staff.midiInstrument = #"pizzicato strings" 
 \clef C \time 2/4
 <c e a>8_"pizz." r <d f a> r | <g, g'> r <g g'> r | <a f'> r <a f'> r | c d gis, r |
 <a e' c'> r <a f' d'> r | <g d' b'> r <g e' c'> r | <a f' a> r <a f'> r | c d c r |
 }
 \relative c' { \magnifyStaff #3/4 \set Staff.midiInstrument = #"pizzicato strings" 
 \clef F \time 2/4
 a8_"pizz." r d, r | g r c, r | f r d r | e e e, r |
 a' r d, r | g r c, r | f r d r | e, e' a, r |
 }
 >> 
 \new Staff = "chords" \with {
 \omit TimeSignature
 \magnifyStaff #3/4
 } \relative c' 
 { \hide Staff.KeySignature \clef F
 { \hide Stem a8 s d, s g s c, s f s }} 
\addlyrics \with { alignAboveContext = "chords" \override VerticalAxisGroup.nonstaff-relatedstaff-spacing =
 #'((basic-distance . 3)) } { \override LyricText.font-size = #-2 Am Dm \markup{\concat{G\super{7}}} C F }
>>
 }
\layout { line-width = #150 }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/s/3/s3r80o3c3x0cwfj9u65fbc5f359wmtx/s3r80o3c.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/s/3/s3r80o3c3x0cwfj9u65fbc5f359wmtx/s3r80o3c.mp3">download the audio file</a>.</div></audio></div></div></div></div></div></div> <p>Robert Schumann's "Child falling asleep" from his <i><a href="/wiki/Kinderszenen" title="Kinderszenen">Kinderszenen</a></i> uses the progression, changing it at the end—the piece ends on an A minor chord, instead of the expected <a href="/wiki/Tonic_(music)" title="Tonic (music)">tonic</a> E minor. </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/1/s/1s29pv8xu5j8ox0tn51sobbah3zxwbr/1s29pv8x.midi"><img src="//upload.wikimedia.org/score/1/s/1s29pv8xu5j8ox0tn51sobbah3zxwbr/1s29pv8x.png" width="606" height="208" alt=" { <<
 \new Dynamics {
 s2 s s4 s \tempo 8 = 87 s-"rit." \tempo 8 = 82 s \tempo 8 = 77 s \tempo 8 = 72 s
 }
 \new PianoStaff <<
 \new Staff \with{ \magnifyStaff #3/4 } << 
 \new Voice \relative c' {
 \key e \minor \set Score.tempoHideNote = ##t \tempo 8 = 92 \time 2/4 \stemUp \slurUp \tieUp
 r4 b'8( fis'16 b, | b g'8.) b,8( fis'16 b, | b b'8.) c,8( b'16 c, | c a'8.^\startTextSpan) b,8( a'16 b, | b g'8.) a,8( g'16 a, | a fis'8.) e4 ~ \stopTextSpan e2 \fermata ~ e4 r \bar "|."
 }
 \new Voice \relative c' {
 \stemDown \tieDown
 s4 b'4 b b b c c b b a a a ~ a2 ~ a4 s4
 }
 \new Dynamics {
 \p
 }
 \new Staff \with{ \magnifyStaff #3/4 } <<
 \new Voice \relative c' { 
 \key e \minor \clef F \time 2/4 \stemUp \slurUp \tieUp
 g8( c16 b b fis'8.) | b,8( c16 b b fis'8.) | b,8( c16 b c b'8.) | c,8( d16 c b a'8.) | b,8( c16 b a g'8.) | a,8( b16 a ~ <a c e>4 ~ <a c e>2 \fermata ~ <a c e>4) r | 
 }
 \new Voice \relative c' { 
 \stemDown \tieDown
 e,4 <dis fis> | <e g> <dis fis> | <e g> a | <d, fis> g | <c, e> fis | <b, dis> e4 ~ e2 ~ <a, e'>4 s
 }
 \new Dynamics {
 s2 s s s\> s s s s \!
 }
 >> >> >>
 \new Staff = "chords" \with {
 \omit TimeSignature
 \magnifyStaff #2/3
 } \relative c' 
 { \hide Staff.KeySignature \hide Staff.Clef \key e \minor \clef bass
 { \hide Stem \stopStaff \once \hide \p s2 s \startStaff e,8 s a s d, s g s c, s fis s b, s e s \stopStaff}} 
\addlyrics \with { alignAboveContext = "chords" \override VerticalAxisGroup.nonstaff-relatedstaff-spacing = #'((basic-distance . 3)) } { \override LyricText.font-size = #-3 Em \markup{\concat{Am\super{9}}} \markup{\concat{D\super{7}}} \markup{\concat{G\super{maj9}}} \markup{\concat{C\super{maj7}}} \markup{\concat{F♯m\super{7♭5}}} \markup{\concat{B\super{7}}} Am}
>>
 }
\layout { line-width = #150 }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/1/s/1s29pv8xu5j8ox0tn51sobbah3zxwbr/1s29pv8x.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/1/s/1s29pv8xu5j8ox0tn51sobbah3zxwbr/1s29pv8x.mp3">download the audio file</a>.</div></audio></div></div></div></div></div></div> <p>In <a href="/wiki/Wagner" class="mw-redirect" title="Wagner">Wagner</a>'s opera, <i><a href="/wiki/G%C3%B6tterd%C3%A4mmerung" title="Götterdämmerung">Götterdämmerung</a></i>, a cycle of fifths progression occurs in the music which transitions from the end of the prologue into the first scene of Act 1, set in the imposing hall of the wealthy Gibichungs. "Status and reputation are written all over the motifs assigned to Gunther",<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> chief of the Gibichung clan: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/b/9/b9cg7s9gxq732qwfg97n25bgulyaxon/b9cg7s9g.midi"><img src="//upload.wikimedia.org/score/b/9/b9cg7s9gxq732qwfg97n25bgulyaxon/b9cg7s9g.png" width="596" height="525" alt=" {<<
 \new ChoirStaff <<
 \relative c' {
 \magnifyStaff #3/4 \set Score.tempoHideNote = ##t \tempo 4 = 60 \time 3/4 \set Staff.midiInstrument = #"trumpet" \transposition f'^"in F"
 \p \grace {s16 s} ees2( d4) | ees2( d4) | cis2. ~ cis4 r r | R2. | R | R | R | R | R
 }
 \new Staff \with{ \magnifyStaff #3/4 } <<
 \new Voice \relative c' { \override Hairpin.minimum-length = #3
 \set Staff.midiInstrument = #"trumpet" \transposition e'^"in E"
 \p \grace {s16 s} \hide \pp <g bes>2( <bes g>4) | <g bes>2( <bes g>4) | <bes d>4.( <g bes>8 <a c>4 | <bes d>2.) |<bes d>4.( <g bes>8 <a c>4 ) | <bes d>2 ees4-! | c2._"(marc.)" | s2. | R | R
 } 
 \new Voice \relative c' { \stemDown
 \hide \p \grace {s16 s} s2. | s | s | s | s | s2 ees4-! | c2. | d4-! bes2 | R2. | R2. \bar "|."
 } >> >>
 \relative c' {
 \magnifyStaff #3/4 \set Staff.midiInstrument = #"trombone" \transposition e^"in E"
 \p \grace {s16 s} \hide \pp g'2. ~ g ~ g ~ g | g ~ g2 bes4-! | g2._"(marc.)" | d'4-! bes2 | c2_"dim." r4 | \pp d2 r4 
 }
 \new ChoirStaff <<
 \relative c' {
 \magnifyStaff #3/4 \clef tenor \set Staff.midiInstrument = #"trombone"
 \p \grace {s16 s} aes2( g4) | aes2( g4) | fis2. ~ fis | fis ~ fis2 b4-! | g2._"(marc.)" | cis4-! b2 | b2_"dim." r4 | \pp ais2 r4
 }
 \relative c' {
 \magnifyStaff #3/4 \clef F \set Staff.midiInstrument = #"trombone"
 \p \grace {s16 s} \hide \pp <b, d>2. | <b d> | <b d> ~ <b d> | <b d> ~ <b d>2 <b g'>4-! | <e g>2._"(marc.)" | <fis a>4-! <d fis>2 | <e g>_"dim." r4 | \pp <cis fis>2 r4
 } >>
 \relative c' {
 \magnifyStaff #3/4 \clef F \set Staff.midiInstrument = #"trombone"
 \p \grace {s16 s} \hide \pp f,,!2( g4) | f!2( g4) | gis2. ~ gis | g! ~ g2 e4 ~ e a8._"(marc.)"[ g16 fis8. e16] | d2 g4( | cis,2_"dim.") r4 | \pp fis2 r4
 }
 \relative c' {
 \magnifyStaff #3/4 \clef F \set Staff.midiInstrument = #"timpani"
 \p \grace {b,16 b} b4 r r | \grace {b16 b} b4 r r | \grace {b16 b} b4 r r | r b b | \grace {b16 b} b4 r r | r b f' | b, r r | R2. | R | R
 }
 \relative c' {
 \magnifyStaff #3/4 \clef F \set Staff.midiInstrument = #"tuba"
 \p \grace {s16 s} R2. | R | R | R | R | r4 r e,, ~ e a8._"(marc.)"[ g16 fis8. e16] | d2 g4( cis,2_"dim." ) r4 | \pp fis2 r4
 }
 >> }
\layout { line-width = #150 }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/b/9/b9cg7s9gxq732qwfg97n25bgulyaxon/b9cg7s9g.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/b/9/b9cg7s9gxq732qwfg97n25bgulyaxon/b9cg7s9g.mp3">download the audio file</a>.</div></audio></div></div></div></div></div></div> <div class="mw-heading mw-heading3"><h3 id="Jazz_and_popular_music">Jazz and popular music</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=11" title="Edit section: Jazz and popular music"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The enduring popularity of the circle of fifths as both a form-building device and as an expressive musical trope is evident in the number of "<a href="/wiki/Standard_(music)" title="Standard (music)">standard</a>" popular songs composed during the twentieth century. It is also favored as a vehicle for improvisation by jazz musicians, as the circle of fifths helps songwriters understand intervals, chord-relationships and progressions. </p> <ul><li><a href="/wiki/Bart_Howard" title="Bart Howard">Bart Howard</a>, "<a href="/wiki/Fly_Me_to_the_Moon" title="Fly Me to the Moon">Fly Me to the Moon</a>"</li></ul> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>The song opens with a pattern of descending phrases – in essence, the hook of the song – presented with a soothing predictability, almost as if the future direction of the melody is dictated by the opening five notes. The harmonic progression, for its part, rarely departs from the circle of fifths.<sup id="cite_ref-FOOTNOTEGioia2012115_21-0" class="reference"><a href="#cite_note-FOOTNOTEGioia2012115-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></p></blockquote> <ul><li><a href="/wiki/Jerome_Kern" title="Jerome Kern">Jerome Kern</a>, "<a href="/wiki/All_the_Things_You_Are" title="All the Things You Are">All the Things You Are</a>"<sup id="cite_ref-FOOTNOTEGioia201216_22-0" class="reference"><a href="#cite_note-FOOTNOTEGioia201216-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Ray_Noble" title="Ray Noble">Ray Noble</a>, "<a href="/wiki/Cherokee_(Ray_Noble_song)" title="Cherokee (Ray Noble song)">Cherokee</a>." Many jazz musicians have found this particularly challenging as the <a href="/wiki/Middle_eight" class="mw-redirect" title="Middle eight">middle eight</a> progresses so rapidly through the circle, "creating a series of <a href="/wiki/Ii%E2%80%93V%E2%80%93I_progression" title="Ii–V–I progression">II–V–I progressions</a> that temporarily pass through several <a href="/wiki/Tonality" title="Tonality">tonalities</a>."<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li> <li>Kosma, Prévert and Mercer, "<a href="/wiki/Autumn_Leaves_(1945_song)" title="Autumn Leaves (1945 song)">Autumn Leaves</a>"<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/The_Beatles" title="The Beatles">The Beatles</a>, "<a href="/wiki/You_Never_Give_Me_Your_Money" title="You Never Give Me Your Money">You Never Give Me Your Money</a>"<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research"><span title="This claim needs references to reliable secondary sources. (October 2021)">non-primary source needed</span></a></i>]</sup></li> <li><a href="/wiki/Mike_Oldfield" title="Mike Oldfield">Mike Oldfield</a>, "<a href="/wiki/Incantations_(album)" title="Incantations (album)">Incantations</a>"<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Carlos_Santana" title="Carlos Santana">Carlos Santana</a>, "<a href="/wiki/Europa_(Earth%27s_Cry_Heaven%27s_Smile)" title="Europa (Earth's Cry Heaven's Smile)">Europa (Earth's Cry Heaven's Smile)</a>"<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2020)">citation needed</span></a></i>]</sup></li> <li><a href="/wiki/Gloria_Gaynor" title="Gloria Gaynor">Gloria Gaynor</a>, "<a href="/wiki/I_Will_Survive" title="I Will Survive">I Will Survive</a>"<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research"><span title="This claim needs references to reliable secondary sources. (October 2021)">non-primary source needed</span></a></i>]</sup></li> <li><a href="/wiki/Pet_Shop_Boys" title="Pet Shop Boys">Pet Shop Boys</a>, "<a href="/wiki/It%27s_a_Sin" title="It's a Sin">It's a Sin</a>"<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research"><span title="This claim needs references to reliable secondary sources. (October 2021)">non-primary source needed</span></a></i>]</sup></li> <li><a href="/wiki/Donna_Summer" title="Donna Summer">Donna Summer</a>, "<a href="/wiki/Love_to_Love_You_Baby_(song)" title="Love to Love You Baby (song)">Love to Love you, Baby</a>"<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research"><span title="This claim needs references to reliable secondary sources. (October 2021)">non-primary source needed</span></a></i>]</sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Related_concepts">Related concepts</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=12" title="Edit section: Related concepts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Diatonic_circle_of_fifths">Diatonic circle of fifths</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=13" title="Edit section: Diatonic circle of fifths"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Circle_progression" class="mw-redirect" title="Circle progression">Circle progression</a></div> <p>The diatonic circle of fifths is the circle of fifths encompassing only members of the diatonic scale. Therefore, it contains a diminished fifth, in C major between B and F. See <a href="/wiki/Structure_implies_multiplicity" title="Structure implies multiplicity">structure implies multiplicity</a>. The <a href="/wiki/Circle_progression" class="mw-redirect" title="Circle progression">circle progression</a> is commonly a circle of fifths through the diatonic chords, including one <a href="/wiki/Diminished_triad" title="Diminished triad">diminished chord</a>. A circle progression in C major with chords I–IV–vii<sup>o</sup>–iii–vi–ii–V–I is shown below. </p> <dl><dd><div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/s/9/s970rucxp2jgj2svj1qmmi3q4fvk07b/s970rucx.midi"><img src="//upload.wikimedia.org/score/s/9/s970rucxp2jgj2svj1qmmi3q4fvk07b/s970rucx.png" width="335" height="143" alt="
 {
 \new PianoStaff <<
 \new Staff <<
 \new Voice \relative c' {
 \stemUp e2 f d e c d b c
 }
 \new Voice \relative c' {
 \stemDown c2 c b b a a g g
 }
 >>
 \new Staff <<
 \new Voice \relative c' {
 \clef F
 \stemUp g2 a f g e f d e 
 }
 \new Voice \relative c {
 \stemDown c f, b e, a d, g c,
 }
 >>
 >> }
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/s/9/s970rucxp2jgj2svj1qmmi3q4fvk07b/s970rucx.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/s/9/s970rucxp2jgj2svj1qmmi3q4fvk07b/s970rucx.mp3">download the audio file</a>.</div></audio></div></div></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Chromatic_circle">Chromatic circle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=14" title="Edit section: Chromatic circle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Chromatic_circle" title="Chromatic circle">Chromatic circle</a></div> <p>The circle of fifths is closely related to the <a href="/wiki/Chromatic_circle" title="Chromatic circle">chromatic circle</a>, which also arranges the equal-tempered pitch classes of a particular tuning in a circular ordering. A key difference between the two circles is that the <a href="/wiki/Chromatic_circle" title="Chromatic circle">chromatic circle</a> can be understood as a continuous space where every point on the circle corresponds to a conceivable <a href="/wiki/Pitch_class" title="Pitch class">pitch class</a>, and every conceivable pitch class corresponds to a point on the circle. By contrast, the circle of fifths is fundamentally a <i>discrete</i> structure arranged through distinct <a href="/wiki/Interval_(music)" title="Interval (music)">intervals</a>, and there is no obvious way to assign pitch classes to each of its points. In this sense, the two circles are mathematically quite different. </p><p>However, for any positive integer <i>N</i>, the <a href="/wiki/Pitch_class" title="Pitch class">pitch classes</a> in <i>N</i>-tone equal temperament can be represented by the <a href="/wiki/Cyclic_group" title="Cyclic group">cyclic group</a> of order <i>N</i>, or equivalently, the <a href="/wiki/Modular_arithmetic" title="Modular arithmetic">residue classes</a> modulo equal to <i>N</i>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} /N\mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} /N\mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a2c2e5f7f463ca78e618e6c8faeced10bf30fd7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.327ex; height:2.843ex;" alt="{\displaystyle \mathbb {Z} /N\mathbb {Z} }"></span>. In twelve-tone equal temperament, the group <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} _{12}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{12}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdcf6e9070dd69a6d25f8b32e960ba09c5e499f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.427ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{12}}"></span> has four generators, which can be identified with the ascending and descending semitones and the ascending and descending perfect fifths. The semitonal generator gives rise to the <a href="/wiki/Chromatic_circle" title="Chromatic circle">chromatic circle</a> while the perfect fourth and perfect fifth give rise to the circle of fifths. In most other tunings, such as in <a href="/wiki/31_equal_temperament" title="31 equal temperament">31 equal temperament</a>, many more intervals can be used as the generator, and many more circles are possible as a result. </p> <div class="mw-heading mw-heading3"><h3 id="Relation_with_chromatic_scale">Relation with chromatic scale</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=15" title="Edit section: Relation with chromatic scale"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Chromatic_scale" title="Chromatic scale">Chromatic scale</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Pitch_class_space_star.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Pitch_class_space_star.svg/220px-Pitch_class_space_star.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Pitch_class_space_star.svg/330px-Pitch_class_space_star.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Pitch_class_space_star.svg/440px-Pitch_class_space_star.svg.png 2x" data-file-width="342" data-file-height="342" /></a><figcaption>The circle of fifths drawn within the chromatic circle as a <a href="/wiki/Star_polygon" title="Star polygon">star</a> <a href="/wiki/Dodecagram" title="Dodecagram">dodecagram</a>.<sup id="cite_ref-FOOTNOTEMcCartin1998364_30-0" class="reference"><a href="#cite_note-FOOTNOTEMcCartin1998364-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The circle of fifths, or fourths, may be mapped from the <a href="/wiki/Chromatic_scale" title="Chromatic scale">chromatic scale</a> by <a href="/wiki/Multiplication" title="Multiplication">multiplication</a>, and vice versa. To map between the circle of fifths and the chromatic scale (in <a href="/wiki/Integer_notation" class="mw-redirect" title="Integer notation">integer notation</a>) multiply by 7 (<a href="/wiki/Twelve-tone_technique" title="Twelve-tone technique">M7</a>), and for the circle of fourths multiply by 5 (P5). </p><p>In twelve-tone equal temperament, one can start off with an <a href="/wiki/Order_theory" title="Order theory">ordered</a> 12-tuple (<a href="/wiki/Tone_row" title="Tone row">tone row</a>) of integers: </p> <dl><dd>(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11)</dd></dl> <p>representing the notes of the chromatic scale: 0 = C, 2 = D, 4 = E, 5 = F, 7 = G, 9 = A, 11 = B, 1 = C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, 3 = D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, 6 = F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, 8 = G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, 10 = A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>. Now multiply the entire 12-tuple by 7: </p> <dl><dd>(0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77)</dd></dl> <p>and then apply a <a href="/wiki/Modulo_operation" class="mw-redirect" title="Modulo operation">modulo</a> 12 reduction to each of the numbers (subtract 12 from each number as many times as necessary until the number becomes smaller than 12): </p> <dl><dd>(0, 7, 2, 9, 4, 11, 6, 1, 8, 3, 10, 5)</dd></dl> <p>which is equivalent to </p> <dl><dd>(C, G, D, A, E, B, F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, F)</dd></dl> <p>which is the circle of fifths. This is <a href="/wiki/Enharmonic" class="mw-redirect" title="Enharmonic">enharmonically</a> equivalent to: </p> <dl><dd>(C, G, D, A, E, B, G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, F).</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Enharmonic_equivalents,_theoretical_keys,_and_the_spiral_of_fifths"><span id="Enharmonic_equivalents.2C_theoretical_keys.2C_and_the_spiral_of_fifths"></span>Enharmonic equivalents, theoretical keys, and the spiral of fifths</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=16" title="Edit section: Enharmonic equivalents, theoretical keys, and the spiral of fifths"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Theoretical_key" class="mw-redirect" title="Theoretical key">Theoretical key</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Spiral_of_fifths.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Spiral_of_fifths.gif/220px-Spiral_of_fifths.gif" decoding="async" width="220" height="242" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Spiral_of_fifths.gif/330px-Spiral_of_fifths.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/a/a9/Spiral_of_fifths.gif 2x" data-file-width="369" data-file-height="406" /></a><figcaption>If enharmonic notes are not equivalent, as in just intonation, fifths form a spiral, not a circle.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Pythagorean_tuning_geometric.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Pythagorean_tuning_geometric.svg/220px-Pythagorean_tuning_geometric.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Pythagorean_tuning_geometric.svg/330px-Pythagorean_tuning_geometric.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Pythagorean_tuning_geometric.svg/440px-Pythagorean_tuning_geometric.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>A sequence of twelve just fifths on a <a href="/wiki/Chromatic_circle" title="Chromatic circle">chromatic circle</a> fail to close (the size of the gap is the <a href="/wiki/Pythagorean_comma" title="Pythagorean comma">Pythagorean comma</a>), resulting in a "broken" circle of fifths.</figcaption></figure> <p><a href="/wiki/Equal_temperament" title="Equal temperament">Equal temperament</a> tunings do not use the exact 3:2 ratio of frequencies that defines a perfect fifth, whereas <a href="/wiki/Just_intonation" title="Just intonation">just intonation</a> uses this exact ratio. Ascending by fifths in equal temperament leads to a return to the starting pitch class—starting with a C and ascending by fifths leads to another C after a certain number of iterations. This does not occur if an exact 3:2 ratio is used (just intonation). The adjustment made in equal temperament tuning is called the <a href="/wiki/Pythagorean_comma" title="Pythagorean comma">Pythagorean comma</a>. Because of this difference, pitches that are enharmonically equivalent in equal temperaments (such as C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> and D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> in 12-tone equal temperament, or C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> and D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Doubleflat.svg" class="mw-file-description" title="double flat"><img alt="double flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></span> in <a href="/wiki/19_equal_temperament" title="19 equal temperament">19 equal temperament</a>) are not equivalent when using just intonation. </p><p>In just intonation the sequence of fifths can therefore be visualized as a spiral, not a circle—a sequence of twelve fifths results in a "<a href="/wiki/Comma_pump" title="Comma pump">comma pump</a>" by the Pythagorean comma, visualized as going up a level in the spiral. See also <a href="#Circle_closure_in_non-equal_tuning_systems">§ Circle closure in non-equal tuning systems</a>. </p><p>Without enharmonic equivalences, continuing a sequence of fifths results in notes with double accidentals (double sharps or double flats), or even triple or quadruple accidentals. In most equal temperament tunings, these can be replaced by enharmonically equivalent notes. </p><p>Keys with double or triple sharps and flats in key signatures are called <a href="/wiki/Theoretical_key" class="mw-redirect" title="Theoretical key">theoretical keys</a>; they are redundant in 12-tone equal temperament, and so their use is extremely rare, but if the number of notes per octave is not a multiple of 12, they are distinguished. Notation in these cases is not standardized. </p> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/p/j/pjog3jqt8hf2uhlo7x2zlksj1ya2bt5/pjog3jqt.midi"><img src="//upload.wikimedia.org/score/p/j/pjog3jqt8hf2uhlo7x2zlksj1ya2bt5/pjog3jqt.png" width="447" height="57" alt="
\relative c' {
 \key gis \major
\set Staff.printKeyCancellation = ##f
 <gis' bis dis>
\bar "||"
 \key dis \major
 <dis fisis ais>
\bar "||"
 \key fes \major
 <fes as ces>
\bar "||"
 \key beses \major
 <beses des fes>
}
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/p/j/pjog3jqt8hf2uhlo7x2zlksj1ya2bt5/pjog3jqt.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/p/j/pjog3jqt8hf2uhlo7x2zlksj1ya2bt5/pjog3jqt.mp3">download the audio file</a>.</div></audio></div></div> <p>The default behaviour of <a href="/wiki/LilyPond" title="LilyPond">LilyPond</a> (pictured above) writes single sharps or flats in the circle-of-fifths order, before proceeding to double sharps or flats. This is the format used in <a href="/wiki/John_Foulds" title="John Foulds">John Foulds</a>' <i>A World Requiem</i>, Op. 60,<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> which ends with the key signature of G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> major, as displayed above. The sharps in the key signature of G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> major here proceed C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:DoubleSharp.svg" class="mw-file-description" title="double sharp"><img alt="double sharp" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/DoubleSharp.svg/7px-DoubleSharp.svg.png" decoding="async" width="7" height="8" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/DoubleSharp.svg/10px-DoubleSharp.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/DoubleSharp.svg/14px-DoubleSharp.svg.png 2x" data-file-width="6" data-file-height="7" /></a></span></span>. </p><p>Single sharps or flats in the key signature are sometimes repeated as a courtesy, e.g. <a href="/wiki/Max_Reger" title="Max Reger">Max Reger</a>'s <i>Supplement to the Theory of Modulation</i>, which contains D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> minor key signatures on <a rel="nofollow" class="external text" href="https://archive.org/details/supplementtotheo00rege/page/42/mode/2up">pp. 42–45</a>. These have a B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> at the start and also a B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Doubleflat.svg" class="mw-file-description" title="double flat"><img alt="double flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></span> at the end (with a double-flat symbol), going B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Doubleflat.svg" class="mw-file-description" title="double flat"><img alt="double flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></span>. The convention of LilyPond and Foulds would suppress the initial B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>. Sometimes the double signs are written at the beginning of the key signature, followed by the single signs. For example, the F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> key signature is notated as B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Doubleflat.svg" class="mw-file-description" title="double flat"><img alt="double flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></span>, E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>. This convention is used by Victor Ewald,<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> by the program <a href="/wiki/Finale_(scorewriter)" title="Finale (scorewriter)">Finale</a>, and by some theoretical works. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=17" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Approach_chord" title="Approach chord">Approach chord</a></li> <li><a href="/wiki/Sonata_form" title="Sonata form">Sonata form</a></li> <li><a href="/wiki/Well_temperament" title="Well temperament">Well temperament</a></li> <li><a href="/wiki/Circle_of_fifths_text_table" title="Circle of fifths text table">Circle of fifths text table</a></li> <li><a href="/wiki/Pitch_constellation" class="mw-redirect" title="Pitch constellation">Pitch constellation</a></li> <li><a href="/wiki/Multiplicative_group_of_integers_modulo_n" title="Multiplicative group of integers modulo n">Multiplicative group of integers modulo n</a></li> <li><a href="/wiki/Multiplication_(music)" title="Multiplication (music)">Multiplication (music)</a></li> <li><a href="/wiki/Circle_of_thirds" title="Circle of thirds">Circle of thirds</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=18" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=19" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Michael Pilhofer and Holly Day (23 Feb 2009). <a rel="nofollow" class="external text" href="http://www.dummies.com/how-to/content/the-circle-of-fifths-a-brief-history.html">"The Circle of Fifths: A Brief History"</a>, www.dummies.com.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBroekhuis2022" class="citation web cs1">Broekhuis, Rogier (2022-10-11). <a rel="nofollow" class="external text" href="https://www.wheelof5ths.com/en-us/blogs/music-theory-lessons/harmonic-function">"Wheel of Fifths – Harmonic Function"</a>. <i>Wheel of Fifths</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-10-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Wheel+of+Fifths&rft.atitle=Wheel+of+Fifths+%E2%80%93+Harmonic+Function&rft.date=2022-10-11&rft.aulast=Broekhuis&rft.aufirst=Rogier&rft_id=https%3A%2F%2Fwww.wheelof5ths.com%2Fen-us%2Fblogs%2Fmusic-theory-lessons%2Fharmonic-function&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTENattiez1990225-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTENattiez1990225_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFNattiez1990">Nattiez 1990</a>, p. 225.</span> </li> <li id="cite_note-FOOTNOTEGoldman196568-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGoldman196568_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGoldman1965">Goldman 1965</a>, p. 68.</span> </li> <li id="cite_note-FOOTNOTEGoldman1965chapter_3-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGoldman1965chapter_3_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGoldman1965">Goldman 1965</a>, chapter 3.</span> </li> <li id="cite_note-FOOTNOTENattiez1990226-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTENattiez1990226_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFNattiez1990">Nattiez 1990</a>, p. 226.</span> </li> <li id="cite_note-Jensen-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Jensen_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFJensen1992">Jensen 1992</a>, pp. 306–307</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Johann David Heinichen, <i>Neu erfundene und gründliche Anweisung</i> (1711), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=4O1CAAAAcAAJ&pg=PA260-IA1">p. 261</a></span> </li> <li id="cite_note-FOOTNOTEBarnett2002444-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBarnett2002444_9-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBarnett2002">Barnett 2002</a>, p. 444.</span> </li> <li id="cite_note-FOOTNOTELester1989110–112-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTELester1989110–112_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLester1989">Lester 1989</a>, pp. 110–112.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLerdahl2005" class="citation book cs1">Lerdahl, Fred (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6bxFrgVMDpsC&pg=PA42"><i>Tonal Pitch Space</i></a>. New York: Oxford University Press. p. 42. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0195178297" title="Special:BookSources/0195178297"><bdi>0195178297</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Tonal+Pitch+Space.&rft.place=New+York&rft.pages=42&rft.pub=Oxford+University+Press&rft.date=2005&rft.isbn=0195178297&rft.aulast=Lerdahl&rft.aufirst=Fred&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D6bxFrgVMDpsC%26pg%3DPA42&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://jadebultitude.com/the-circle-of-fifths-complete-guide/#:~:text=From%20what%20we%20can%20see,known%20as%20the%20Pythagorean%20circle.">"The Circle of Fifths Complete Guide!"</a>. 17 January 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Circle+of+Fifths+Complete+Guide%21&rft.date=2021-01-17&rft_id=https%3A%2F%2Fjadebultitude.com%2Fthe-circle-of-fifths-complete-guide%2F%23%3A~%3Atext%3DFrom%2520what%2520we%2520can%2520see%2Cknown%2520as%2520the%2520Pythagorean%2520circle.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.linkedin.com/pulse/circle-fifths-made-clear-mark-newman">"The Circle of Fifths made clear"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Circle+of+Fifths+made+clear&rft_id=https%3A%2F%2Fwww.linkedin.com%2Fpulse%2Fcircle-fifths-made-clear-mark-newman&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.dummies.com/article/academics-the-arts/music/music-theory/the-circle-of-fifths-a-brief-history-201561">"Dummies - Learning Made Easy"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Dummies+-+Learning+Made+Easy&rft_id=https%3A%2F%2Fwww.dummies.com%2Farticle%2Facademics-the-arts%2Fmusic%2Fmusic-theory%2Fthe-circle-of-fifths-a-brief-history-201561&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrazer2001" class="citation cs2">Frazer, Peter A. (2001), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130701202500/http://www.midicode.com/tunings/Tuning10102004.pdf"><i>The Development of Musical Tuning Systems</i></a> <span class="cs1-format">(PDF)</span>, pp. 9, 13, archived from <a rel="nofollow" class="external text" href="http://www.midicode.com/tunings/Tuning10102004.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 1 July 2013<span class="reference-accessdate">, retrieved <span class="nowrap">24 May</span> 2020</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Development+of+Musical+Tuning+Systems&rft.pages=9%2C+13&rft.date=2001&rft.aulast=Frazer&rft.aufirst=Peter+A.&rft_id=http%3A%2F%2Fwww.midicode.com%2Ftunings%2FTuning10102004.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDumbrill2005" class="citation book cs1">Dumbrill, Richard J. 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Hal Leonard.</span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOakes1980" class="citation web cs1">Oakes, Tim (June 1980). <a rel="nofollow" class="external text" href="https://tubular.net/articles/1980_06/Mike-Oldfield-by-Tim-Oakes">"Mike Oldfield"</a>. <i>International Musician and Recording World</i><span class="reference-accessdate">. Retrieved <span class="nowrap">19 February</span> 2021</span> – via Tubular.net.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=International+Musician+and+Recording+World&rft.atitle=Mike+Oldfield&rft.date=1980-06&rft.aulast=Oakes&rft.aufirst=Tim&rft_id=https%3A%2F%2Ftubular.net%2Farticles%2F1980_06%2FMike-Oldfield-by-Tim-Oakes&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text">Fekaris, D. and Perren, F. J. (1978) "I Will Survive". Polygram International Publishing.</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text">Tennant, N. and Lowe, C. (1987, bars 1–8) "It's a Sin." Sony/ATV Music Publishing (UK) Ltd.</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><a href="/wiki/Giorgio_Moroder" title="Giorgio Moroder">Moroder, G.</a>, <a href="/wiki/Pete_Bellotte" title="Pete Bellotte">Bellote, P.</a> and <a href="/wiki/Donna_Summer" title="Donna Summer">Summer, D.</a> (1975, bars 11–14) "Love to Love you, Baby" 1976, Bulle Music</span> </li> <li id="cite_note-FOOTNOTEMcCartin1998364-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMcCartin1998364_30-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMcCartin1998">McCartin 1998</a>, p. 364.</span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://imslp.org/wiki/A_World_Requiem%2C_Op.60_(Foulds%2C_John)">"Foulds, John, <i>A World Requiem</i>, Op. 60, pp. 153ff"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Foulds%2C+John%2C+A+World+Requiem%2C+Op.+60%2C+pp.+153ff.&rft_id=https%3A%2F%2Fimslp.org%2Fwiki%2FA_World_Requiem%252C_Op.60_%28Foulds%252C_John%29&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.hickeys.com/music/brass/brass_ensembles/brass_quintets/products/sku035994-ewald-victor-quintet-no-4-in-ab-op-8.php">"Ewald, Victor, <i>Quintet No 4 in A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></i>, Op. 8 for Brass Quintet [211.01]"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Ewald%2C+Victor%2C+Quintet+No+4+in+A%3Cspan+class%3D%22music-symbol%22+style%3D%22font-family%3A+Arial+Unicode+MS%2C+Lucida+Sans+Unicode%3B%22%3E%3Cspan+class%3D%22music-flat%22%3E%26%23x266d%3B%3C%2Fspan%3E%3C%2Fspan%3E%2C+Op.+8+for+Brass+Quintet+%26%2391%3B211.01%26%2393%3B&rft_id=https%3A%2F%2Fwww.hickeys.com%2Fmusic%2Fbrass%2Fbrass_ensembles%2Fbrass_quintets%2Fproducts%2Fsku035994-ewald-victor-quintet-no-4-in-ab-op-8.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=20" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarnett2002" class="citation book cs1">Barnett, Gregory (2002). "Tonal Organization in Seventeenth-century Music Theory.". In Thomas Christensen (ed.). <i>The Cambridge History of Western Music Theory</i>. Cambridge: Cambridge University Press. pp. 407–455.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Tonal+Organization+in+Seventeenth-century+Music+Theory.&rft.btitle=The+Cambridge+History+of+Western+Music+Theory&rft.place=Cambridge&rft.pages=407-455&rft.pub=Cambridge+University+Press&rft.date=2002&rft.aulast=Barnett&rft.aufirst=Gregory&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGioia2012" class="citation book cs1"><a href="/wiki/Ted_Gioia" title="Ted Gioia">Gioia, Ted</a> (2012). <i><a href="/wiki/The_Jazz_Standards:_A_Guide_to_the_Repertoire" title="The Jazz Standards: A Guide to the Repertoire">The Jazz Standards: A Guide to the Repertoire</a></i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780199769155" title="Special:BookSources/9780199769155"><bdi>9780199769155</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Jazz+Standards%3A+A+Guide+to+the+Repertoire&rft.pub=Oxford+University+Press&rft.date=2012&rft.isbn=9780199769155&rft.aulast=Gioia&rft.aufirst=Ted&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoldman1965" class="citation book cs1"><a href="/wiki/Richard_Franko_Goldman" title="Richard Franko Goldman">Goldman, Richard Franko</a> (1965). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/harmonyinwestern00gold"><i>Harmony in Western Music</i></a></span>. New York: W. W. Norton.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Harmony+in+Western+Music&rft.place=New+York&rft.pub=W.+W.+Norton&rft.date=1965&rft.aulast=Goldman&rft.aufirst=Richard+Franko&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fharmonyinwestern00gold&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJensen1992" class="citation journal cs1">Jensen, Claudia R. (Summer 1992). "A Theoretical Work of Late Seventeenth-Century Muscovy: Nikolai Diletskii's "Grammatika" and the Earliest Circle of Fifths". <i><a href="/wiki/Journal_of_the_American_Musicological_Society" title="Journal of the American Musicological Society">Journal of the American Musicological Society</a></i>. <b>45</b> (2): 305–331. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F831450">10.2307/831450</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/831450">831450</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Musicological+Society&rft.atitle=A+Theoretical+Work+of+Late+Seventeenth-Century+Muscovy%3A+Nikolai+Diletskii%27s+%22Grammatika%22+and+the+Earliest+Circle+of+Fifths&rft.ssn=summer&rft.volume=45&rft.issue=2&rft.pages=305-331&rft.date=1992&rft_id=info%3Adoi%2F10.2307%2F831450&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F831450%23id-name%3DJSTOR&rft.aulast=Jensen&rft.aufirst=Claudia+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLester1989" class="citation book cs1">Lester, Joel (1989). <i>Between Modes and Keys: German theory 1592–1802</i>. Stuyvesant: Pendragon Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Between+Modes+and+Keys%3A+German+theory+1592%E2%80%931802&rft.place=Stuyvesant&rft.pub=Pendragon+Press&rft.date=1989&rft.aulast=Lester&rft.aufirst=Joel&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcCartin1998" class="citation journal cs1">McCartin, Brian J. (November 1998). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080517071420/http://www.maa.org/pubs/cmj_Nov98.html">"Prelude to Musical Geometry"</a>. <i><a href="/wiki/The_College_Mathematics_Journal" title="The College Mathematics Journal">The College Mathematics Journal</a></i>. <b>29</b> (5): 354–370. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F07468342.1998.11973971">10.1080/07468342.1998.11973971</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2687250">2687250</a>. Archived from <a rel="nofollow" class="external text" href="http://www.maa.org/pubs/cmj_Nov98.html">the original</a> on 2008-05-17<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-07-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+College+Mathematics+Journal&rft.atitle=Prelude+to+Musical+Geometry&rft.volume=29&rft.issue=5&rft.pages=354-370&rft.date=1998-11&rft_id=info%3Adoi%2F10.1080%2F07468342.1998.11973971&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2687250%23id-name%3DJSTOR&rft.aulast=McCartin&rft.aufirst=Brian+J.&rft_id=http%3A%2F%2Fwww.maa.org%2Fpubs%2Fcmj_Nov98.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></li> <li><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><cite class="citation wikicite" id="CITEREFNattiez1990"><a href="/wiki/Jean-Jacques_Nattiez" title="Jean-Jacques Nattiez">Nattiez, Jean-Jacques</a> (1990). <i>Music and Discourse: Toward a Semiology of Music</i>, translated by Carolyn Abbate. Princeton, New Jersey: Princeton University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-02714-5" title="Special:BookSources/0-691-02714-5">0-691-02714-5</a>. (Originally published in French, as <i>Musicologie générale et sémiologie</i>. Paris: C. Bourgois, 1987. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/2-267-00500-X" title="Special:BookSources/2-267-00500-X">2-267-00500-X</a>).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaruskin2010" class="citation book cs1"><a href="/wiki/Richard_Taruskin" title="Richard Taruskin">Taruskin, Richard</a> (2010). <i>The Oxford History of Western Music: Music in the Seventeenth and Eighteenth Centuries</i>. Oxford University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Oxford+History+of+Western+Music%3A+Music+in+the+Seventeenth+and+Eighteenth+Centuries&rft.pub=Oxford+University+Press&rft.date=2010&rft.aulast=Taruskin&rft.aufirst=Richard&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACircle+of+fifths" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=21" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Vincent_d%27Indy" title="Vincent d'Indy">D'Indy, Vincent</a> (1903). <i>Cours de composition musicale</i>. Paris: A. Durand et fils.</li> <li>Lester, Joel. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=t2xAAIK7jd0C&q=heinichen&pg=PA110"><i>Between Modes and Keys: German Theory, 1592–1802</i></a>. 1990.</li> <li>Miller, Michael. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=sTMbuSQdqPMC"><i>The Complete Idiot's Guide to Music Theory, 2nd ed</i></a>. [Indianapolis, IN]: Alpha, 2005. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-59257-437-8" title="Special:BookSources/1-59257-437-8">1-59257-437-8</a>.</li> <li>Purwins, Hendrik (2005)."<a rel="nofollow" class="external text" href="http://ccrma.stanford.edu/~purwins/purwinsPhD.pdf">Profiles of Pitch Classes: Circularity of Relative Pitch and Key—Experiments, Models, Computational Music Analysis, and Perspectives</a>". Ph.D. thesis. Berlin: <a href="/wiki/Berlin_Institute_of_Technology" class="mw-redirect" title="Berlin Institute of Technology">Technische Universität Berlin</a>.</li> <li>Purwins, Hendrik, Benjamin Blankertz, and Klaus Obermayer (2007). "<a rel="nofollow" class="external text" href="http://www.ccarh.org/publications/cm/15/cm15-05-purwins.pdf">Toroidal Models in Tonal Theory and Pitch-Class Analysis</a>". in: <i>Computing in Musicology</i> 15 ("Tonal Theory for the Digital Age"): 73–98.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circle_of_fifths&action=edit&section=22" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://mdecks.com/graphs/mcircle.php">Decoding the Circle of Vths</a></li> <li><a rel="nofollow" class="external text" href="https://randscullard.com/CircleOfFifths/">Interactive Circle of Fifths</a></li> <li><a rel="nofollow" class="external text" href="https://www.mindfulharmony.app/write/">Interactive Circle of Fifths Composing Tool</a></li> <li><a rel="nofollow" class="external text" href="https://guitardashboard.com/">Interactive circle of fifths for guitarists</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist 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