Circle of thirds

<h2 id="history">History</h2>
<p class="note">Further information: <a href="/facts/Coltrane_changes/5EPuHaMt">Coltrane changes</a> and <a href="/facts/John_Coltrane/IhSaHEEQ">John Coltrane</a></p>
<h3>Origins</h3>

<p>The concept of a "circle of thirds" is relatively new in the history of music. Although certainly not the first to use it, a popular American <a href="/facts/Jazz/lmUzXGq8">jazz</a> musician named <a href="/facts/John_Coltrane/IhSaHEEQ">John Coltrane</a> often used a cycle composed of a sequence of <a href="/facts/Major_third/7CPRURg4">major thirds</a> for his unique <a href="/facts/Key_change/qF2kCACj">key changes</a>, hence the namesake for "<a href="/facts/Coltrane_changes/5EPuHaMt">coltrane changes</a>". His popularity during the 1960s and in the ensuing decades, brought a lot of attention to the <a href="/facts/Augmented_triad/2R7MpG0C">augmented triads</a>, and at the same time, the concept of a cycle of thirds, which was mainly inspired by the "<a href="/facts/Coltrane_changes/5EPuHaMt">coltrane changes</a>".<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a>
</p><p>Although the exact date when the term "circle of thirds" was coined is not known, the circle of thirds and the coltrane changes continue to be used in many jazz compositions to this day, and has extended its reach into other musical genres, such as <a href="/facts/Rock_music/zBM2guyQ">rock</a>, <a href="/facts/Pop_music/kgshFE5B">pop</a>, and other forms of <a href="/facts/Popular_music/Q5yhxIwY">popular music</a>.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a>
</p><p>The circle of thirds is also mentioned in relation to tonal music, but more rarely.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a>
</p>
<h2 id="structure-and-modern-usage">Structure and modern usage</h2>

<h3>Chord construction</h3>
<p class="note">Further information: <a href="/facts/Chord_theory/hJBCHCSB">Chord theory</a></p><p>In music, <a href="/facts/Triad_(chord)/Uqq9WYD4">triads</a> are primarily built on the circle of thirds. In fact, by going progressively forward in the repeating 24 note <a href="/facts/Sequence/gV2S4uqp">sequence</a> of the circle of thirds, many chords can be constructed. 
</p><p>F#/G♭–b♭–D♭–f–A♭–c–E♭–g–B♭–d–F–a–C–e–G–b–D–f#–A–c#–E–g#–B–d#–F#/G♭
</p><p>For example, in <a href="/facts/A_major/30sVcrBo">A major</a>, the first notes in the cycle of thirds are A, C♯, and E, which is also the three notes present in the A major triad.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> But this rule not only applies to <a href="/facts/Major_chord/RwuuqKYS">major</a> or <a href="/facts/Minor_chord/XdLGImHS">minor chords</a>, but also to <a href="/facts/Seventh_chord/XeWsnNrL">seventh chords</a>. For example, in the key in <a href="/facts/E_minor/TxmUV3NP">E minor</a>, the <a href="/facts/Tonic_chord/3YWh9zFV">tonic chord</a> (E, G, B) becomes an E minor seventh chord (E, G, B, D), if the fourth note (D) is added to the triad. This applies to all other chords in the scale.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> 
</p><p>A mnemonic also exists in the circle of thirds. The sequence DFACEGB appears three times.
</p><p>[D♭, F, A♭, C, E♭, G, B♭], [D, F, A, C, E, G, B], [D, F#, A, C#, E, G#, B]
</p><p>The first sequence of DFACEGB is associated with the major scales and chords commonly notated with flatted notes (D♭, A♭, E♭, B♭) and the third sequence of DFACEGB is associated with the scales and chords that contain sharp notes (D, A, E, B).
</p>
<h2 id="relationship-to-other-scales">Relationship to other scales</h2>
<p>The circle of thirds is closely tied to the diatonic scale. Every note on the circle of thirds that starts a minor triad or minor 7th chord starts a sequence of 7 notes that belong to a Dorian scale. For example the sequence DFACEGB in the circle of thirds contains all the notes in D Dorian and D Dorian's associated modes.
</p>
Modes Associated with D Dorian<table><tbody><tr><th>Mode</th><th>Notes</th></tr><tr><td>D Dorian</td><td>D, E, F, G, A, B, C</td></tr><tr><td>E Phrygian</td><td>E, F, G, A, B, C, D</td></tr><tr><td>F Lydian</td><td>F, G, A, B, C, D, E</td></tr><tr><td>G Mixolydian</td><td>G, A, B, C, D, E, F</td></tr><tr><td>A Aeolian</td><td>A, B, C, D, E, F, G</td></tr><tr><td>B Locrian</td><td>B, C, D, E, F, G, A</td></tr><tr><td>C Ionian</td><td>C, D, E, F, G, A, B</td></tr></tbody></table>
<h2 id="relationship-to-other-circles">Relationship to other circles</h2>
<p>The circle of thirds is related to the <a href="/facts/Circle_of_fifths/0aE2lkVq">Circle of fifths</a>. The circle of fifths is composed of the twelve Major keys in the order (C, G, D, A, E, B, F#/G♭, D♭, A♭, E♭, B♭, F) going clockwise. The circle of fifths can also be drawn as a circle of the associated minor keys in the order (Am, Em, Bm, F#m, C#m, G#m, D#m, B♭m, Fm, Cm, Gm, Dm). The circle of thirds is the circle of fifths' Major keys, preceded by each associated minor key.
</p>

<p>The jump pattern 15263748... repeating around the circle of thirds will generate a 48 note cycle of modular arithmetic (modulo 12) that groups common tones together.
</p><p>C, D, E, F, G, A, B, C, D, E, F#, G, A, B, C#, D, E, F#, G#, A, B, C#, D#, E, G♭, A♭, B♭, B, D♭, E♭, F, G♭, A♭, B♭, C, D♭, E♭, F, G, A♭, B♭, C, D, E♭, F, G, A, B♭
</p><p>This cycle of 48 notes is a sequence of the first four notes of each major scale in the order of fifths from the circle of fifths. This cycle also contains all the Major/Ionian scales (overlapping) in the order of fifths with Dorian, Phrygian and Lydian modes also included for each Major group (e.g. C Ionian, D Dorian, E Phrygian, F Lydian).
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Circle_of_fifths/0aE2lkVq">Circle of fifths</a></li>
<li><a href="/facts/Triad_(music)/YIA2T6Y6">Triads</a></li>
<li><a href="/facts/Coltrane_changes/5EPuHaMt">Coltrane changes</a></li>
<li><a href="/facts/Major_third/7CPRURg4">Major third</a></li>
<li><a href="/facts/Minor_third/4y8zBxwY">Minor third</a></li></ul>

<h3>Citations</h3>

<h3>Notes</h3>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>"Circle of Thirds: Visual Tool for Chords in Major or Minor Scales". muted.io. Retrieved 2024-08-28. <a href="https://muted.io/circle-of-thirds/#:~:text=The%20circle%20is%20formed%20by,-2-4-6." target="_blank">https://muted.io/circle-of-thirds/#:~:text=The%20circle%20is%20formed%20by,-2-4-6.</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Bleu, Nicola. "Basic Music Theory: The Complete Beginner's Guide". Your Creative Aura. Retrieved 2024-09-11. <a href="https://yourcreativeaura.com/basic-music-theory/" target="_blank">https://yourcreativeaura.com/basic-music-theory/</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>"Circle of Thirds: Visual Tool for Chords in Major or Minor Scales". muted.io. Retrieved 2024-08-28. <a href="https://muted.io/circle-of-thirds/#:~:text=The%20circle%20is%20formed%20by,-2-4-6." target="_blank">https://muted.io/circle-of-thirds/#:~:text=The%20circle%20is%20formed%20by,-2-4-6.</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Marie, Yona (August 9, 2021). "Circle of Thirds - Is it a Thing?". Yona Marie Music. <a href="https://yonamariemusic.com/yona/blog/103/circle-of-thirds-is-it-a-thing" target="_blank">https://yonamariemusic.com/yona/blog/103/circle-of-thirds-is-it-a-thing</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>"Coltrane Changes Explained". TJPS. Retrieved 2024-01-31. <a href="https://www.thejazzpianosite.com/jazz-piano-lessons/jazz-chord-progressions/coltrane-changes/" target="_blank">https://www.thejazzpianosite.com/jazz-piano-lessons/jazz-chord-progressions/coltrane-changes/</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>"Coltrane Changes Explained". TJPS. Retrieved 2024-01-31. <a href="https://www.thejazzpianosite.com/jazz-piano-lessons/jazz-chord-progressions/coltrane-changes/" target="_blank">https://www.thejazzpianosite.com/jazz-piano-lessons/jazz-chord-progressions/coltrane-changes/</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Meeùs, Nicolas, "Tonal and 'Modal' Harmony: A Transformational Perspective", Keynote address at the Dublin International Conference on Music Analysis, 23 June 2005, online <a href="https://nmeeus.ovh/NMVecteurs/VHDublinEn.pdf" target="_blank">https://nmeeus.ovh/NMVecteurs/VHDublinEn.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>Bleu, Nicola. "Basic Music Theory: The Complete Beginner's Guide". Your Creative Aura. Retrieved 2024-09-11. <a href="https://yourcreativeaura.com/basic-music-theory/" target="_blank">https://yourcreativeaura.com/basic-music-theory/</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
<li id="fn:9"><p>"Circle of Thirds: Visual Tool for Chords in Major or Minor Scales". muted.io. Retrieved 2024-08-28. <a href="https://muted.io/circle-of-thirds/#:~:text=The%20circle%20is%20formed%20by,-2-4-6." target="_blank">https://muted.io/circle-of-thirds/#:~:text=The%20circle%20is%20formed%20by,-2-4-6.</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li>
</ol>

Circle of thirds open-in-new

Circle of thirds