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class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Voorkoms"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Voorkoms" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Voorkoms</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_af.wikipedia.org&uselang=af" class=""><span>Skenkings</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesiaal:SkepRekening&returnto=Diatoniese+toonleer" title="U word aangemoedig om 'n gebruiker te skep en aan te meld, hoewel dit nie verpligtend is nie." class=""><span>Skep gebruiker</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesiaal:Teken_in&returnto=Diatoniese+toonleer" title="U word aangemoedig om aan te meld. Dit is egter nie verpligtend nie. [o]" accesskey="o" class=""><span>Meld aan</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Meer opsies" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Persoonlike gereedskap" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Persoonlike gereedskap</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_af.wikipedia.org&uselang=af"><span>Skenkings</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesiaal:SkepRekening&returnto=Diatoniese+toonleer" title="U word aangemoedig om 'n gebruiker te skep en aan te meld, hoewel dit nie verpligtend is nie."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Skep gebruiker</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesiaal:Teken_in&returnto=Diatoniese+toonleer" title="U word aangemoedig om aan te meld. 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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Meld aan</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Bladsye vir uitgemelde redakteurs <a href="/wiki/Hulp:Inleiding" aria-label="Leer meer oor redigering"><span>leer meer</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Spesiaal:Mybydrae" title="A list of edits made from this IP address [y]" accesskey="y"><span>Bydraes</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spesiaal:Mybespreking" title="Bespreking oor bydraes van hierdie IP-adres [n]" accesskey="n"><span>Bespreking</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Werf"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Inhoud" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Inhoud</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">versteek</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inleiding</div> </a> </li> <li id="toc-Geskiedenis" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geskiedenis"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Geskiedenis</span> </div> </a> <button aria-controls="toc-Geskiedenis-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>Wissel Geskiedenis subafdeling</span> </button> <ul id="toc-Geskiedenis-sublist" class="vector-toc-list"> <li id="toc-Voorgeskiedenis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Voorgeskiedenis"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Voorgeskiedenis</span> </div> </a> <ul id="toc-Voorgeskiedenis-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Teorie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Teorie"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Teorie</span> </div> </a> <ul id="toc-Teorie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ontleding" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ontleding"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Ontleding</span> </div> </a> <button aria-controls="toc-Ontleding-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>Wissel Ontleding subafdeling</span> </button> <ul id="toc-Ontleding-sublist" class="vector-toc-list"> <li id="toc-Majeurtoonleer" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Majeurtoonleer"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Majeurtoonleer</span> </div> </a> <ul id="toc-Majeurtoonleer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Natuurlike_mineurtoonleer" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Natuurlike_mineurtoonleer"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Natuurlike mineurtoonleer</span> </div> </a> <ul id="toc-Natuurlike_mineurtoonleer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modusse" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Modusse"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Modusse</span> </div> </a> <ul id="toc-Modusse-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Diatoniese_toonlere_en_tetrachorde" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diatoniese_toonlere_en_tetrachorde"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Diatoniese toonlere en tetrachorde</span> </div> </a> <ul id="toc-Diatoniese_toonlere_en_tetrachorde-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Eienskappe" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eienskappe"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Eienskappe</span> </div> </a> <ul id="toc-Eienskappe-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stemming" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Stemming"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Stemming</span> </div> </a> <ul id="toc-Stemming-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sien_ook" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sien_ook"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Sien ook</span> </div> </a> <ul id="toc-Sien_ook-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Verwysings" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Verwysings"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Verwysings</span> </div> </a> <ul id="toc-Verwysings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Verdere_leeswerk" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Verdere_leeswerk"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Verdere leeswerk</span> </div> </a> <ul id="toc-Verdere_leeswerk-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="Inhoud" 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="Wissel die inhoudsopgawe" > <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">Wissel die inhoudsopgawe</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">Diatoniese toonleer</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="Gaan na 'n artikel in 'n ander taal. Beskikbaar in 43 tale" > <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-43" 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">43 tale</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%95%E0%A7%83%E0%A6%A4_%E0%A6%B8%E0%A7%8D%E0%A6%AC%E0%A6%B0%E0%A6%97%E0%A7%8D%E0%A6%B0%E0%A6%BE%E0%A6%AE" title="প্রকৃত স্বরগ্রাম – Bengaals" lang="bn" hreflang="bn" data-title="প্রকৃত স্বরগ্রাম" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Escala_diat%C3%B2nica" title="Escala diatònica – Katalaans" lang="ca" hreflang="ca" data-title="Escala diatònica" data-language-autonym="Català" data-language-local-name="Katalaans" 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/Diatonick%C3%A1_stupnice" title="Diatonická stupnice – Tsjeggies" lang="cs" hreflang="cs" data-title="Diatonická stupnice" data-language-autonym="Čeština" data-language-local-name="Tsjeggies" 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/Diatonisk_skala" title="Diatonisk skala – Deens" lang="da" hreflang="da" data-title="Diatonisk skala" data-language-autonym="Dansk" data-language-local-name="Deens" 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/Diatonik" title="Diatonik – Duits" lang="de" hreflang="de" data-title="Diatonik" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CF%84%CE%BF%CE%BD%CE%B9%CE%BA%CE%AE_%CE%BA%CE%BB%CE%AF%CE%BC%CE%B1%CE%BA%CE%B1" title="Διατονική κλίμακα – Grieks" lang="el" hreflang="el" data-title="Διατονική κλίμακα" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Diatonic_scale" title="Diatonic scale – Engels" lang="en" hreflang="en" data-title="Diatonic scale" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Diatona_gamo" title="Diatona gamo – Esperanto" lang="eo" hreflang="eo" data-title="Diatona gamo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Escala_diat%C3%B3nica" title="Escala diatónica – Spaans" lang="es" hreflang="es" data-title="Escala diatónica" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Diatooniline_helirida" title="Diatooniline helirida – Estnies" lang="et" hreflang="et" data-title="Diatooniline helirida" data-language-autonym="Eesti" data-language-local-name="Estnies" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Eskala_diatoniko" title="Eskala diatoniko – Baskies" lang="eu" hreflang="eu" data-title="Eskala diatoniko" data-language-autonym="Euskara" data-language-local-name="Baskies" 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/%DA%AF%D8%A7%D9%85_%D8%AF%DB%8C%D8%A7%D8%AA%D9%88%D9%86%DB%8C%DA%A9" title="گام دیاتونیک – Persies" lang="fa" hreflang="fa" data-title="گام دیاتونیک" data-language-autonym="فارسی" data-language-local-name="Persies" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Diatoninen_asteikko" title="Diatoninen asteikko – Fins" lang="fi" hreflang="fi" data-title="Diatoninen asteikko" data-language-autonym="Suomi" data-language-local-name="Fins" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89chelle_diatonique" title="Échelle diatonique – Frans" lang="fr" hreflang="fr" data-title="Échelle diatonique" data-language-autonym="Français" data-language-local-name="Frans" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Diatonacht" title="Diatonacht – Iers" lang="ga" hreflang="ga" data-title="Diatonacht" data-language-autonym="Gaeilge" data-language-local-name="Iers" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Diat%C3%B3nica" title="Diatónica – Galisies" lang="gl" hreflang="gl" data-title="Diatónica" data-language-autonym="Galego" data-language-local-name="Galisies" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%95%D7%9C%D7%9D_%D7%93%D7%99%D7%90%D7%98%D7%95%D7%A0%D7%99" title="סולם דיאטוני – Hebreeus" lang="he" hreflang="he" data-title="סולם דיאטוני" data-language-autonym="עברית" data-language-local-name="Hebreeus" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Diatonikus_hangsor" title="Diatonikus hangsor – Hongaars" lang="hu" hreflang="hu" data-title="Diatonikus hangsor" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%AB%D5%A1%D5%BF%D5%B8%D5%B6%D5%AB%D5%AF%D5%A1" title="Դիատոնիկա – Armeens" lang="hy" hreflang="hy" data-title="Դիատոնիկա" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Tangga_nada_diatonik" title="Tangga nada diatonik – Indonesies" lang="id" hreflang="id" data-title="Tangga nada diatonik" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesies" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Scala_diatonica" title="Scala diatonica – Italiaans" lang="it" hreflang="it" data-title="Scala diatonica" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%85%A8%E9%9F%B3%E9%9A%8E" title="全音階 – Japannees" lang="ja" hreflang="ja" data-title="全音階" data-language-autonym="日本語" data-language-local-name="Japannees" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Tangga_nada_diatonik" title="Tangga nada diatonik – Javaans" lang="jv" hreflang="jv" data-title="Tangga nada diatonik" data-language-autonym="Jawa" data-language-local-name="Javaans" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%93%E1%83%98%E1%83%90%E1%83%A2%E1%83%9D%E1%83%9C%E1%83%98%E1%83%99%E1%83%90" title="დიატონიკა – Georgies" lang="ka" hreflang="ka" data-title="დიატონიკა" data-language-autonym="ქართული" data-language-local-name="Georgies" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%B8%D0%B0%D1%82%D0%BE%D0%BD%D0%B8%D0%BA%D0%B0" title="Диатоника – Kazaks" lang="kk" hreflang="kk" data-title="Диатоника" data-language-autonym="Қазақша" data-language-local-name="Kazaks" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%98%A8%EC%9D%8C%EA%B3%84" title="온음계 – Koreaans" lang="ko" hreflang="ko" data-title="온음계" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%94%D0%B8%D0%B0%D1%82%D0%BE%D0%BD%D0%B8%D0%BA%D0%B0" title="Диатоника – Kirgisies" lang="ky" hreflang="ky" data-title="Диатоника" data-language-autonym="Кыргызча" data-language-local-name="Kirgisies" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Derm%C4%97" title="Dermė – Litaus" lang="lt" hreflang="lt" data-title="Dermė" data-language-autonym="Lietuvių" data-language-local-name="Litaus" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Diatoniek" title="Diatoniek – Nederlands" lang="nl" hreflang="nl" data-title="Diatoniek" data-language-autonym="Nederlands" data-language-local-name="Nederlands" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Diatonisk_skala" title="Diatonisk skala – Nuwe Noors" lang="nn" hreflang="nn" data-title="Diatonisk skala" data-language-autonym="Norsk nynorsk" data-language-local-name="Nuwe Noors" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Diatonisk_skala" title="Diatonisk skala – Boeknoors" lang="nb" hreflang="nb" data-title="Diatonisk skala" data-language-autonym="Norsk bokmål" data-language-local-name="Boeknoors" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Escala_diatonica" title="Escala diatonica – Oksitaans" lang="oc" hreflang="oc" data-title="Escala diatonica" data-language-autonym="Occitan" data-language-local-name="Oksitaans" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Skala_diatoniczna" title="Skala diatoniczna – Pools" lang="pl" hreflang="pl" data-title="Skala diatoniczna" data-language-autonym="Polski" data-language-local-name="Pools" 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/Escala_diat%C3%B4nica" title="Escala diatônica – Portugees" lang="pt" hreflang="pt" data-title="Escala diatônica" data-language-autonym="Português" data-language-local-name="Portugees" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B8%D0%B0%D1%82%D0%BE%D0%BD%D0%B8%D0%BA%D0%B0" title="Диатоника – Russies" lang="ru" hreflang="ru" data-title="Диатоника" data-language-autonym="Русский" data-language-local-name="Russies" 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/Diatonic_scale" title="Diatonic scale – Simple English" lang="en-simple" hreflang="en-simple" data-title="Diatonic scale" 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/Diatonick%C3%A1_stupnica" title="Diatonická stupnica – Slowaaks" lang="sk" hreflang="sk" data-title="Diatonická stupnica" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Diatonik_(musik)" title="Diatonik (musik) – Sweeds" lang="sv" hreflang="sv" data-title="Diatonik (musik)" data-language-autonym="Svenska" data-language-local-name="Sweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D1%96%D0%B0%D1%82%D0%BE%D0%BD%D1%96%D0%BA%D0%B0" title="Діатоніка – Oekraïens" lang="uk" hreflang="uk" data-title="Діатоніка" data-language-autonym="Українська" data-language-local-name="Oekraïens" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Diatonika" title="Diatonika – Oezbeeks" lang="uz" hreflang="uz" data-title="Diatonika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Thang_%C3%A2m_nguy%C3%AAn" title="Thang âm nguyên – Viëtnamees" lang="vi" hreflang="vi" data-title="Thang âm nguyên" data-language-autonym="Tiếng Việt" data-language-local-name="Viëtnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E9%9F%B3%E9%98%B6" title="自然音阶 – Wu-Sjinees" lang="wuu" hreflang="wuu" data-title="自然音阶" data-language-autonym="吴语" data-language-local-name="Wu-Sjinees" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E9%9F%B3%E9%98%B6" title="自然音阶 – Chinees" lang="zh" hreflang="zh" data-title="自然音阶" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q23702413#sitelinks-wikipedia" title="Wysig skakels tussen tale" class="wbc-editpage">Wysig skakels</a></span></div> </div> </div> </div> </header> <div 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Diatonic_scale_on_C.png/495px-Diatonic_scale_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Diatonic_scale_on_C.png/660px-Diatonic_scale_on_C.png 2x" data-file-width="1071" data-file-height="256" /></a><figcaption>Diatoniese toonleer op C, gelykswewende stemming <span class="unicode haudio"><span class="fn"><span typeof="mw:File"><a href="/wiki/L%C3%AAer:Diatonic_scale_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span> Play</span> <small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Mediahulp" title="Wikipedia:Mediahulp">help</a>·info)</small></span> and just <span class="unicode haudio"><span class="fn"><span typeof="mw:File"><a href="/wiki/L%C3%AAer:Just_diatonic_scale_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span> Play</span> <small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Mediahulp" title="Wikipedia:Mediahulp">help</a>·info)</small></span>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/L%C3%AAer:Pythagorean_diatonic_scale_on_C.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Pythagorean_diatonic_scale_on_C.png/330px-Pythagorean_diatonic_scale_on_C.png" decoding="async" width="330" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Pythagorean_diatonic_scale_on_C.png/495px-Pythagorean_diatonic_scale_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Pythagorean_diatonic_scale_on_C.png/660px-Pythagorean_diatonic_scale_on_C.png 2x" data-file-width="1071" data-file-height="256" /></a><figcaption>Pythagoreaanse diatoniese toonleer op C <span class="unicode haudio"><span class="fn"><span typeof="mw:File"><a href="/wiki/L%C3%AAer:Pythagorean_diatonic_scale_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span> Play</span> <small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Mediahulp" title="Wikipedia:Mediahulp">help</a>·info)</small></span>. ’n Plusteken (+) dui die sintoniese komma aan.</figcaption></figure> <p>In musiekteorie is ’n <b>diatoniese toonleer</b> 'n hepatoniese toonleer wat bestaan uit vyf heeltone en twee halftone vir elke oktaaf insluit, waarin die twee halftone deur óf twee óf drie heeltone geskei word, afhangende van hulle posisie in die toonleer. Hierdie patroon verseker dat, in ’n diatoniese toonleer wat verder as een oktaaf strek, al die halftone maksimaal van mekaar geskei is (d.w.s. deur ten minste twee heeltone geskei word). Die woord "diatonies" kom van die <a href="/wiki/Grieks" title="Grieks">Grieks</a> <span lang="el">διατονικός</span>, wat beteken om deur <a href="/wiki/Toonhoogte" title="Toonhoogte">tone</a> heen te beweeg.<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>Die sewe <a href="/wiki/Toonhoogte" title="Toonhoogte">toonhoogtes</a> van enige diatoniese toonleer kan verkry word deur middel van ’n reeks van ses rein kwinte (of volmaakte vyfdes). Byvoorbeeld die sewe natuurlike toonhoogtes waaruit die C <a href="/wiki/Majeurtoonleer" title="Majeurtoonleer">majeurtoonleer</a> bestaan, kan verkry word uit ’n reeks rein kwinte wat by F begin: </p> <dl><dd>F—C—G—D—A—E—B</dd></dl> <p>Hierdie eienskap van die diatoniese toonleer word Pythagoreaanse stemming genoem. Dit was geskiedkundig betekenisvol en het moontlik bygedra tot die wêreldwye verspreiding daarvan omdat dit musici eeue lank toegelaat het om musiekinstrumente maklik volgens gehoor te stem. </p><p>Enige reeks van sewe opeenvolgende natuurlike note, soos C-D-E-F-G-A-B, en enige transposisie daarvan, is ’n diatoniese toonleer. Klavierklawerborde is ontwerp om natuurlike note, en gevolglik diatoniese toonlere, met die wit note te speel. ’n Diatoniese toonleer kan ook beskryf word as twee tetrachorde (vier opeenvolgende tone) wat deur ’n heeltoon geskei word. </p><p>Die term <i>diatonies</i> het oorspronklik verwys na die diatoniese genus, een van die drie genusse van die antieke Grieke. In musikale reeksteorie klassifiseer Allen Forte diatoniese toonlere as reeksvorm 7–35. </p><p>Hierdie artikel sluit nie alternatiewe sewenoot-diatoniese toonlere soos die harmoniese mineur of die melodiese mineur in nie. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Geskiedenis">Geskiedenis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=1" title="Wysig afdeling: Geskiedenis" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=1" title="Edit section's source code: Geskiedenis"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Westerse <a href="/wiki/Harmonie" title="Harmonie">harmonie</a> uit die Renaissance tot die laat-<a href="/wiki/19de_eeu" title="19de eeu">19de eeu</a> is gegrond op die diatoniese toonleer en die unieke hiërargiese verhoudings, of diatoniese funksionaliteit, wat geskep word deur hierdie organisasie van sewe note. </p><p>Die moderne <a href="/wiki/Majeurtoonleer" title="Majeurtoonleer">majeur</a>- en mineurtoonlere is diatonies, net soos al die 'kerkmodusse' was. Wat nou majeur en mineur genoem word, was in werklikheid – gedurende die Middeleue en die Renaissance – net twee van agt modusse ('kerkmodusse') wat gegrond was op dieselfde diatoniese note (maar wat verskillende toonlere gevorm het wanneer die aanvangsnoot verander is). Na gelang van watter noot as die eerste noot gebruik is, val die posisies van die intervalle, die halftone, op verskillende afstande van die eerste noot, waardeur sewe verskillende toonlere of modusse verkry word wat, soos reeds genoem is, van die diatoniese toonleer afgelei is. Teen die einde van die <a href="/wiki/Barokmusiek" title="Barokmusiek">Baroktydperk</a> is die konsep van ’n musikale toonsoort gevestig – gebaseer op ’n sentrale drieklank eerder as ’n sentrale toon. Majeur- en mineurtoonlere het tot ten minste die begin van die 20e eeu oorheers, gedeeltelik omdat hulle intervalpatrone geskik is vir die versterking van die sentrale drieklank. Party kerkmodusse het tot in die vroeë <a href="/wiki/18de_eeu" title="18de eeu">18de eeu</a> oorleef, en het ook soms in klassieke en 20de eeuse musiek voorgekom, en later in modale jazz. </p> <div class="mw-heading mw-heading3"><h3 id="Voorgeskiedenis">Voorgeskiedenis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=2" title="Wysig afdeling: Voorgeskiedenis" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=2" title="Edit section's source code: Voorgeskiedenis"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Daar word soms beweer dat die 45 000 jaar oue Divje Babe-fluit ’n diatoniese toonleer gebruik, maar daar bestaan geen bewys of konsensus dat dit eers ’n musiekinstrument is nie.<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> </p><p>Daar is getuienis dat die <a href="/wiki/Sumer" title="Sumer">Sumeriërs</a> en <a href="/wiki/Babiloni%C3%AB" title="Babilonië">Babiloniërs</a> die een of ander vorm van die diatoniese toonleer gebruik het.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Dit word afgelei uit bestaande inskripsies wat ’n stemmingstelsel en musikale komposisies bevat. Ten spyte van die onsekere aard van rekonstruksies van die stuk gegrond op die oorblywende teks van wat as die Hurritiese liedere bekend staan, is die getuienis dat dit die diatoniese toonleer gebruik het, baie meer gevestig. Dit is omdat instruksies om die toonleer te stem, ’n reeks van ses kwinte behels, sodat die ooreenstemmende kring van sewe majeur- en mineurderdes almal gelykluidend is, en dit is ’n resep om ’n diatoniese toonleer te stem. </p><p>Fluite 9 000 jaar oud is in Jiahu, China, gevind en dui op die evolusie, oor ’n tydperk van 1 200 jaar, van fluite wat 4, 5 en 6 gate het tot 7 en 8 gate, waarvan laasgenoemde treffende ooreenkomste toon met die diatoniese spasiëring van gate en klanke.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Teorie">Teorie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=3" title="Wysig afdeling: Teorie" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=3" title="Edit section's source code: Teorie"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Deur die twaalf note van die <a href="/wiki/Chromatiese_toonleer" title="Chromatiese toonleer">chromatiese toonleer</a> te gebruik, kan twaalf van elk van die drie majeurtoonlere (dié met ’n majeurderde/drieklankː Ionies, Lidies en Mixolidies), twaalf van elk van die drie mineurtoonlere (dié met ’n mineurderde/drieklank: Dories, Frigies en Eolies), en twaalf Lokriese toonlere gespeel word, wat altesaam vier-en-tagtig diatoniese toonlere uitmaak. Die moderne musikale klawerbord, met sy swart note wat in twees en dries gegroepeer is, is in wese diatonies. Hierdie rangskikking help musici nie net om hulle voor die klawerbord te oriënteer nie, maar vereenvoudig ook  die stelsel van toonsoorttekens in vergelyking met wat nodig sou wees vir ’n voortdurende afwisseling van swart en wit note. Die swart (of "kort") sleutels was ’n innovasie wat toegelaat het dat die meeste van die diatoniese heeltone (almal in die geval van C-majeur) langs mekaar geplaas word, met betekenisvolle fisiese en konseptuele voordele. </p> <div class="mw-heading mw-heading2"><h2 id="Ontleding">Ontleding</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=4" title="Wysig afdeling: Ontleding" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=4" title="Edit section's source code: Ontleding"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/L%C3%AAer:Piano-keyboard.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Piano-keyboard.jpg/300px-Piano-keyboard.jpg" decoding="async" width="300" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Piano-keyboard.jpg/450px-Piano-keyboard.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Piano-keyboard.jpg/600px-Piano-keyboard.jpg 2x" data-file-width="800" data-file-height="561" /></a><figcaption>Die moderne klavierklawerbord is gebaseer op die intervalpatrone van die diatoniese toonleer. Enige opeenvolging van sewe agtereenvolgende wit note is ’n diatoniese toonleer.</figcaption></figure> <p>In musiek van die algemene Westerse klassieke tradisie kan die patroon van sewe intervalle waarin die agt note van ’n oktaaf voorkom, op drie maniere voorgestel word, wat ekwivalent aan mekaar is. Byvoorbeeld, vir ’n majeurtoonleer, is hierdie intervalleː </p> <ul><li><i>T–T–H–T–T–T–H</i>: waar <i>H</i> ’n halftoon beteken; <i>T</i> beteken heeltoon</li> <li><i>2–2–1–2–2–2–1</i>: waar <i>1</i> ’n halftoon beteken; <i>2</i> beteken heeltoon (2 halftone)</li> <li><i>heel-heel-half-heel-heel-heel-half</i>: waar <i>half</i> ’n halftoon beteken; <i>heel</i> beteken heeltoon.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Majeurtoonleer">Majeurtoonleer</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=5" title="Wysig afdeling: Majeurtoonleer" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=5" title="Edit section's source code: Majeurtoonleer"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Die <a href="/wiki/Majeurtoonleer" title="Majeurtoonleer">majeurtoonleer</a> of Ioniese toonleer is een van die diatoniese toonlere. Dit bestaan uit sewe afsonderlike note, plus ’n agtste wat dieselfde is as die eerste, maar ’n oktaaf hoër. Die patroon van sewe intervalle wat die agt note skei, is T-T-H-T-T-T-H. In solfège, is die name van elke <a href="/wiki/Trap_(musiek)" title="Trap (musiek)">trap</a> van die toonleer  "Do–Re–Mi–Fa–Sol–La–Ti–Do". ’n Opeenvolging van natuurlike note wat by C begin, is ’n voorbeeld van ’n majeurtoonleer, naamlik die C-majeurtoonleer. </p> <table border="0" cellpadding="3" cellspacing="0" style="margin-bottom: 10px;"> <tbody><tr> <td>Note in C-majeur: </td> <td>C </td> <td>D </td> <td>E </td> <td>F </td> <td>G </td> <td>A </td> <td>B </td> <td>C </td></tr> <tr> <td>Trappe in solfege: </td> <td>Do </td> <td>Re </td> <td>Mi </td> <td>Fa </td> <td>Sol </td> <td>La </td> <td>Ti </td> <td>Do </td></tr> <tr> <td>Intervalopeenvolging: </td> <td>T </td> <td>T </td> <td>H </td> <td>T </td> <td>T </td> <td>T </td> <td>H </td></tr></tbody></table> <p>Die agt trappe van die toonleer se tradisionele name is: </p> <dl><dd><ul><li>1e – <a href="/wiki/Tonika" title="Tonika">Tonika</a></li> <li>2e – <a href="/wiki/Supertonika" title="Supertonika">Supertonika</a></li> <li>3e – <a href="/wiki/Mediant" title="Mediant">Mediant</a></li> <li>4e – Subdominant</li> <li>5e – Dominant</li> <li>6e – Submediant</li> <li>7e – Leitoon</li> <li>8e – <a href="/wiki/Tonika" title="Tonika">Tonika</a> (Oktaaf)</li></ul></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Natuurlike_mineurtoonleer">Natuurlike mineurtoonleer</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=6" title="Wysig afdeling: Natuurlike mineurtoonleer" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=6" title="Edit section's source code: Natuurlike mineurtoonleer"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Vir elke majeurtoonleer, is daar ’n ooreenstemmende natuurlike mineurtoonleer, wat soms sy verwante mineur genoem word. Dit gebruik dieselfde opeenvolging van note as die ooreenstemmende majeurtoonleer, maar begin op ’n ander noot. Dit begin op die sesde trap van die majeurtoonleer en gaan stap vir stap verder tot by die eerste oktaaf van die sesde trap. ’n Reeks van opeenvolgende natuurlike note wat by A begin, is ’n voorbeeld van ’n nartuurlike mineurtoonleer, wat die A-mineurtoonleer genoem word. </p> <table border="0" cellpadding="3" cellspacing="0" style="margin-bottom: 10px;"> <tbody><tr> <td>Note in A-mineur: </td> <td>A </td> <td>B </td> <td>C </td> <td>D </td> <td>E </td> <td>F </td> <td>G </td> <td>A </td></tr> <tr> <td>Intervalopeenvolging: </td> <td>T </td> <td>H </td> <td>T </td> <td>T </td> <td>H </td> <td>T </td> <td>T </td></tr></tbody></table> <p>Die trappe van die natuurlike mineurtoonleer het dieselfde name as dié van die majeurtoonleer, behalwe die sewende trap, wat as die subtonika bekend staan omdat dit ’n heeltoon onder die tonika is. Die term leitoon word oor die algemeen gehou vir sewende trappe wat ’n halftoon van die tonikaaf  is, soos in die geval van ’n majeurtoonleer of die harmoniese mineurtoonleer (en die melodiese mineur, opgaande). In solfège word die trappe van die toonleer op verskillende maniere benoem, naamlik "La–Ti–Do–Re–Mi–Fa–So–La" of "Do–Re–Me–Fa–So–La–Ti–Do." </p><p>Buiten die natuurlike mineurtoonleer kan vyf ander soorte of modusse van toonlere uit die note van die majeurtoonleer verkry word, deur eenvoudig ’n ander noot as die beginpunt of tonika te kies. Al hierdie toonlere voldoen aan die vereistes van ’n diatoniese toonleer. </p> <div class="mw-heading mw-heading3"><h3 id="Modusse">Modusse</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=7" title="Wysig afdeling: Modusse" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=7" title="Edit section's source code: Modusse"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Die hele versameling diatoniese toonlere soos hierbo omskryf kan in sewe verskillende modusse ingedeel word. </p><p>Soos hierbo verduidelik is, gebruik alle <a href="/wiki/Majeurtoonleer" title="Majeurtoonleer">majeurtoonlere</a> dieselfde intervalopeenvolging T-T-h-T-T-T-h. Vanuit die modale oogpunt word hierdie intervalopeenvolging die <i>Ioniese modus </i>genoem. Dit is een van die sewe moderne modusse. In enige majeurtoonleer word ’n nuwe toonleer voortgebring deur ’n ander trap van die majeurtoonleer as die tonika te gebruik. Deur middel van hierdie metode is dit moontlik om ses ander toonlere of modusse uit elke majeurtoonleer voort te bring, waarvan elk deur ’n ander intervalopeenvolging gekenmerk word: </p> <table class="wikitable" style="margin-bottom: 10px;"> <tbody><tr> <th>Modus </th> <th>Ook bekend as </th> <th>Tonika in verhouding tot majeurtoonleer </th> <th><a href="/w/index.php?title=Interval_(musiek)&action=edit&redlink=1" class="new" title="Interval (musiek) (bladsy bestaan nie)">Interval</a>-opeenvolging </th> <th>Voorbeeld </th></tr> <tr> <td>Ionies </td> <td>Majeurtoonleer </td> <td>I </td> <td align="center">T-T-h-T-T-T-h </td> <td>C-D-E-F-G-A-B-C </td></tr> <tr> <td>Dories </td> <td>II </td> <td align="center">T-h-T-T-T-h-T </td> <td>D-E-F-G-A-B-C-D </td></tr> <tr> <td>Frigies </td> <td>III </td> <td align="center">h-T-T-T-h-T-T </td> <td>E-F-G-A-B-C-D-E </td></tr> <tr> <td>Lidies </td> <td>IV </td> <td align="center">T-T-T-h-T-T-h </td> <td>F-G-A-B-C-D-E-F </td></tr> <tr> <td>Mixolidies </td> <td>Dominant toonleer </td> <td>V </td> <td align="center">T-T-h-T-T-h-T </td> <td>G-A-B-C-D-E-F-G </td></tr> <tr> <td>Eolies </td> <td>Natuurlike mineurtoonleer </td> <td>VI </td> <td align="center">T-h-T-T-h-T-T </td> <td>A-B-C-D-E-F-G-A </td></tr> <tr> <td>Lokries </td> <td>VII </td> <td align="center">h-T-T-h-T-T-T </td> <td>B-C-D-E-F-G-A-B </td></tr></tbody></table> <p>Eenvoudigheidshalwe word die voorbeelde hierbo gevorm deur natuurlike note (ook "wit note" genoem omdat hulle gespeel kan word deur die wit note van ’n klavier te gebruik). Enige transposisie van elkeen van hierdie toonlere is egter ’n geldige voorbeeld van die ooreenstemmende modus. Met ander woorde, transposie behou die modus. </p><p>Die hele stel diatoniese toonlere word oor die algemeen gedefineer as die stel wat bestaan uit hierdie sewe toonlere met natuurlike note, saam met al hulle moontlike transposisies. Soos elders bespreek, word ander definisies van hierdie stel soms in die literatuur gebruik. </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/L%C3%AAer:Modes.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Modes.svg/700px-Modes.svg.png" decoding="async" width="700" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Modes.svg/1050px-Modes.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Modes.svg/1400px-Modes.svg.png 2x" data-file-width="1400" data-file-height="300" /></a><figcaption>Toonhoogtevoorstellings van die moderne musikale modusse</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Diatoniese_toonlere_en_tetrachorde">Diatoniese toonlere en tetrachorde</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=8" title="Wysig afdeling: Diatoniese toonlere en tetrachorde" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=8" title="Edit section's source code: Diatoniese toonlere en tetrachorde"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>’n Diatoniese toonleer kan ook beskryf word as twee tetrachorde wat deur ’n heeltoon geskei word. Byvoorbeeld, volgens hierdie beskouing sal die twee tetrachordstrukture van C-majeur die volgende wees: </p> <dl><dd>[C-D-E-F]-[G-A-B-C]</dd></dl> <p>en die natuurlike mineur, A, sou wees: </p> <dl><dd>[A-B-C-D]-[E-F-G-A].</dd></dl> <p>Die stel intervalle binne elke tetrachord bestaan uit twee heeltone en ’n halftoon. </p> <div class="mw-heading mw-heading2"><h2 id="Eienskappe">Eienskappe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=9" title="Wysig afdeling: Eienskappe" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=9" title="Edit section's source code: Eienskappe"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Die diatoniese toonleer, soos hierbo beskryf, het spesifieke eienskappe wat dit uniek onder sewenoottoonlere maak. Met ander woorde, geen ander soort toonleer het dieselfde eienskappe nie: </p> <ul><li>Dit word verkry uit ’n reeks van ses opeenvolgende rein kwinte. Byvoorbeeld, die sewe natuurlike note waaruit die C-majeurtoonleer bestaan, kan verkry word uit die reeks rein kwinte wat by F begin (F—C—G—D—A—E—B)</li> <li>Dit is óf ’n reeks van opeenvolgende natuurlike note (soos die C-majeurtoonleer, C-D-E-F-G-A-B, of die A-mineurtoonleer, A-B-C-D-E-F-G) of ’n transposisie daarvan.</li> <li>Dit kan geskryf word deur sewe opeenvolgende note sonder toevallige tekens op ’n balk met ’n konvensionele toonsoortteken, of met geen toonsoortteken nie. Dit is omdat die balk spesifiek ontwerp is om diatoniese toonlere voor te stel.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Stemming">Stemming</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=10" title="Wysig afdeling: Stemming" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=10" title="Edit section's source code: Stemming"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In natuurlike stemming word die diatoniese toonleer soos volg gestem: </p> <table class="wikitable"> <tbody><tr> <th>C </th> <th>D </th> <th>E </th> <th>F </th> <th>G </th> <th>A </th> <th>B </th> <th>C </th></tr> <tr> <td>1 </td> <td>9/8 </td> <td>5/4 </td> <td>4/3 </td> <td>3/2 </td> <td>5/3 </td> <td>15/8 </td> <td>2 </td></tr></tbody></table> <p>In Pythagoreaanse stemming is die diatoniese toonleer: </p> <table class="wikitable"> <tbody><tr> <th>C </th> <th>D </th> <th>E </th> <th>F </th> <th>G </th> <th>A </th> <th>B </th> <th>C </th></tr> <tr> <td>1 </td> <td>9/8 </td> <td>81/64 </td> <td>4/3 </td> <td>3/2 </td> <td>27/16 </td> <td>243/128 </td> <td>2 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Sien_ook">Sien ook</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=11" title="Wysig afdeling: Sien ook" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=11" title="Edit section's source code: Sien ook"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Oorsprong_van_musiek" title="Oorsprong van musiek">Oorsprong van musiek</a></li> <li>Diatonies en chromaties</li></ul> <div class="mw-heading mw-heading2"><h2 id="Verwysings">Verwysings</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=12" title="Wysig afdeling: Verwysings" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=12" title="Edit section's source code: Verwysings"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Ball, Philip (2010).</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">"Random Samples", <i>Science</i> April 1997, vol 276 no 5310 pp 203–205 (<a rel="nofollow" class="external text" href="http://www.sciencemag.org/cgi/content/short/276/5310/203g">aanlyn beskikbaar</a>).</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r2205490">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg");background-repeat:no-repeat;background-size:9px;background-position:right .1em center}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg");background-repeat:no-repeat;background-size:9px;background-position:right .1em center}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg");background-repeat:no-repeat;background-size:9px;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg");background-repeat:no-repeat;background-size:12px;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFKilmer1998" class="citation journal cs1">Kilmer, Anne Draffkorn (1998). <a rel="nofollow" class="external text" href="http://www.penn.museum/sites/expedition/?p=5425">"The Musical Instruments from Ur and Ancient Mesopotamian Music"</a>. <i>Expedition Magazine</i>. <b>40</b> (2): 12–19<span class="reference-accessdate">. Besoek op <span class="nowrap">29 Desember</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Expedition+Magazine&rft.atitle=The+Musical+Instruments+from+Ur+and+Ancient+Mesopotamian+Music&rft.volume=40&rft.issue=2&rft.pages=12-19&rft.date=1998&rft.aulast=Kilmer&rft.aufirst=Anne+Draffkorn&rft_id=http%3A%2F%2Fwww.penn.museum%2Fsites%2Fexpedition%2F%3Fp%3D5425&rfr_id=info%3Asid%2Faf.wikipedia.org%3ADiatoniese+toonleer" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2205490"><cite id="CITEREFCrickmore2010" class="citation book cs1">Crickmore, Leon (2010). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160113110832/http://xa.yimg.com/kq/groups/10599417/281241773/name/Crickmore-Iconea2008.pdf">"New Light on the Babylonian Tonal System"</a> <span class="cs1-format">(PDF)</span>. In Dumbrill, Richard; Finkel, Irving (reds.). <i>ICONEA 2008: Proceedings of the International Conference of Near Eastern Archaeomusicology</i>. Vol. 24. London: Iconea Publications. pp. 11–22. Geargiveer vanaf <a rel="nofollow" class="external text" href="http://xa.yimg.com/kq/groups/10599417/281241773/name/Crickmore-Iconea2008.pdf">die oorspronklike</a> <span class="cs1-format">(PDF)</span> op 13 Januarie 2016<span class="reference-accessdate">. Besoek op <span class="nowrap">29 Desember</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=New+Light+on+the+Babylonian+Tonal+System&rft.btitle=ICONEA+2008%3A+Proceedings+of+the+International+Conference+of+Near+Eastern+Archaeomusicology&rft.place=London&rft.pages=11-22&rft.pub=Iconea+Publications&rft.date=2010&rft.aulast=Crickmore&rft.aufirst=Leon&rft_id=http%3A%2F%2Fxa.yimg.com%2Fkq%2Fgroups%2F10599417%2F281241773%2Fname%2FCrickmore-Iconea2008.pdf&rfr_id=info%3Asid%2Faf.wikipedia.org%3ADiatoniese+toonleer" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2205490"><cite id="CITEREFZhangHarbottleWangKong1999" class="citation journal cs1">Zhang, Juzhong; Harbottle, Garman; Wang, Changsui; Kong, Zhaochen (23 September 1999). <a rel="nofollow" class="external text" href="http://www.nature.com/nature/journal/v401/n6751/full/401366a0.html">"Oldest playable musical instruments found at Jiahu early Neolithic site in China"</a>. <i>Nature</i>. <b>401</b>: 366–368.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Oldest+playable+musical+instruments+found+at+Jiahu+early+Neolithic+site+in+China&rft.volume=401&rft.pages=366-368&rft.date=1999-09-23&rft.aulast=Zhang&rft.aufirst=Juzhong&rft.au=Harbottle%2C+Garman&rft.au=Wang%2C+Changsui&rft.au=Kong%2C+Zhaochen&rft_id=http%3A%2F%2Fwww.nature.com%2Fnature%2Fjournal%2Fv401%2Fn6751%2Ffull%2F401366a0.html&rfr_id=info%3Asid%2Faf.wikipedia.org%3ADiatoniese+toonleer" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Verdere_leeswerk">Verdere leeswerk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diatoniese_toonleer&veaction=edit&section=13" title="Wysig afdeling: Verdere leeswerk" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diatoniese_toonleer&action=edit&section=13" title="Edit section's source code: Verdere leeswerk"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Balzano, Gerald J. (1980). "The Group Theoretic Description of 12-fold and Microtonal Pitch Systems", <i>Computer Music Journal</i> <b>4</b>:66–84.</li> <li>Balzano, Gerald J. (1982). "The Pitch Set as a Level of Description for Studying Musical Pitch Perception", <i>Music, Mind, and Brain</i>, Manfred Clynes, red., Plenum press.</li> <li>Clough, John (1979). "Aspects of Diatonic Sets", <i>Journal of Music Theory</i> <b>23</b>:45–61.</li> <li>Ellen Hickmann, Anne D. Kilmer and Ricardo Eichmann, (red.) <i>Studies in Music Archaeology III</i>, 2001, VML Verlag Marie Leidorf GmbH., Duitsland <a href="/wiki/Spesiaal:Boekbronne/3896466402" class="internal mw-magiclink-isbn">ISBN 3-89646-640-2</a>.</li> <li>Franklin, John C. (2002). "<a rel="nofollow" class="external text" href="http://www.kingmixers.com/Franklin%20PDF%20files%20copy/DiatonicmusicinGreece.pdf">Diatonic Music in Greece: a Reassessment of its Antiquity</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060624040706/http://www.kingmixers.com/Franklin%20PDF%20files%20copy/DiatonicmusicinGreece.pdf">Geargiveer</a> 24 Junie 2006 op <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>", <i>Mnemosyne</i> <b>56.1</b>:669–702</li> <li>Gould, Mark (2000). "Balzano and Zweifel: Another Look at Generalised Diatonic Scales", "Perspectives of New Music" <b>38/2</b>:88–105</li> <li>Johnson, Timothy (2003). <i>Foundations Of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals</i>. Key College Publishing. <a href="/wiki/Spesiaal:Boekbronne/1930190808" class="internal mw-magiclink-isbn">ISBN 1-930190-80-8</a>.</li> <li>Kilmer, A.D. (1971) "The Discovery of an Ancient Mesopotamian Theory of Music'". <i>Proceedings of the American Philosophical Society</i> <b>115</b>:131–149.</li> <li>Kilmer, Crocket, Brown: <i>Sounds from Silence</i> 1976, Bit Enki Publications, Berkeley, Calif. LC# 76-16729.</li> <li>David Rothenberg (1978). "<a rel="nofollow" class="external text" href="http://lumma.org/tuning/rothenberg/AModelForPatternPerception.pdf">A Model for Pattern Perception with Musical Applications Part I: Pitch Structures as order-preserving maps</a>", <i>Mathematical Systems Theory</i> <b>11</b>:199–234</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Ontsluit van "<a dir="ltr" href="https://af.wikipedia.org/w/index.php?title=Diatoniese_toonleer&oldid=2529320">https://af.wikipedia.org/w/index.php?title=Diatoniese_toonleer&oldid=2529320</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Spesiaal:Kategorie%C3%AB" title="Spesiaal:Kategorieë">Kategorie</a>: <ul><li><a href="/wiki/Kategorie:Musiekteorie" title="Kategorie:Musiekteorie">Musiekteorie</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Versteekte kategorie: <ul><li><a href="/wiki/Kategorie:Pages_using_ISBN_magic_links" title="Kategorie:Pages using ISBN magic links">Pages using ISBN magic links</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Die bladsy is laas op 10 Oktober 2022 om 15:44 bygewerk.</li> <li id="footer-info-copyright">Die teks is beskikbaar onder die lisensie <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Erkenning-Insgelyks Deel</a>. 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