User:Fitzgerald Lee/15edo Chord Names: Difference between revisions

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==Chord Names==
==Chord Names==
Triads shown here are the ones built from thirds, or from a second or fourth with a [[3/2]] fifth.
{| class="wikitable"
{| class="wikitable"
|+ style="font-size: 120%;" |
|+ style="font-size: 120%;" |
Secundal, Tertial and Quartal Triads
Triads
|-
|-
! Triad !! Approx. JI !! Shorthand !! Name
! Triad !! Approx. JI !! Shorthand !! Name
|-
| [0,2,9] || 18:20:27 || C2 || Suspended Second
|-
|-
| [0,3,6] || 21:24:28 || Cf || Semaphore
| [0,3,6] || 21:24:28 || Cf || Semaphore
|-
|-
| [0,3,7] || 7/6/5 || Cu || Utonal Diminished
| [0,3,7] || 7/6/5 || Cu || Utonal Diminished
|-
| [0,4,7] || 5:6:7 || Co || Otonal Diminished
|-
|-
| [0,3,8] || 7:8:10 || Ct || Triforce
| [0,3,8] || 7:8:10 || Ct || Triforce
|-
|-
| [0,3,9] || 6:7:9 || Cs || Subminor
| [0,4,8] || 35:42:50 || Cd || Diminished
|-
|-
| [0,4,7] || 5:6:7 || Co || Otonal Diminished
| [0,5,8] || 10/8/7 || Cw || Wolf
|-
|-
| [0,4,8] || 35:42:50 || Cd || Diminished
| [0,2,9] || 18:20:27 || C2 || Suspended Second
|-
|-
| [0,4,9] || 6/5/4 || c || Minor
| [0,3,9] || 6:7:9 || Cs || Subminor
|-
|-
| [0,5,8] || 10/8/7 || Cw || Wolf
| [0,4,9] || 6/5/4 || Cm || Minor
|-
|-
| [0,5,9] || 4:5:6 || C || Major
| [0,5,9] || 4:5:6 || C || Major
|-
| [0,6,9] || 6:8:9 || C4 || Suspended Fourth
|-
|-
| [0,5,10] || 20:25:32 || Ca || Augmented
| [0,5,10] || 20:25:32 || Ca || Augmented
|}
Tetradic and pentadic extensions have different intervals to use, depending on the top note of the triad in root position. Extensions shown below are assuming that tetradic and pentadic extensions extend by thirds (except 6th chords, which usually only extends by a fourth to a 6/9 chord but is still notatable in this system).
{| class="wikitable"
|+ style="font-size: 102%;" |
Tetradic and pentadic extensions (top note 6\15)
|-
|-
| [0,6,9] || 6:8:9 || C4 || Suspended Fourth
! Interval !! Approx. JI !! Shorthand !! Name
|-
| 8\15 || 10/7 || d || Diminished Fifth
|-
| 9\15 || 3/2 || 5 || Perfect Fifth
|-
| 10\15 || 8/5 || m || Minor Sixth
|-
| 11\15 || 5/3 || 6 || Major Sixth
|-
| 12\15 || 7/4 || h || Harmonic Seventh
|-
| 13\15 || 9/5 || n || Neutral Seventh
|-
| 14\15 || 15/8 || M || Major Seventh
|-
| 16\15 || 32/15 || m || Minor Ninth
|}
|}
{| class="wikitable"
{| class="wikitable"
|+ style="font-size: 120%;" |
|+ style="font-size: 102%;" |
Tetradic Extensions
Tetradic and pentadic extensions (top note 7\15)
|-
|-
! Interval !! Approx. JI !! Shorthand !! Name
! Interval !! Approx. JI !! Shorthand !! Name
Line 46: Line 70:
| 13\15 || 9/5 || n || Neutral Seventh
| 13\15 || 9/5 || n || Neutral Seventh
|-
|-
| 14\15 || 15/8 || 7 || Major Seventh
| 14\15 || 15/8 || M || Major Seventh
|-
| 16\15 || 32/15 || m || Minor Ninth
|-
| 17\15 || 20/9 || 9 || Major Ninth
|}
{| class="wikitable"
|+ style="font-size: 102%;" |
Tetradic and pentadic extensions (top note 8\15)
|-
! Interval !! Approx. JI !! Shorthand !! Name
|-
| 10\15 || 8/5 || m || Minor Sixth
|-
| 11\15 || 5/3 || 6 || Major Sixth
|-
| 12\15 || 7/4 || h || Harmonic Seventh
|-
| 13\15 || 9/5 || n || Neutral Seventh
|-
| 14\15 || 15/8 || M || Major Seventh
|-
| X || X || 7 || Seventh
|-
| 16\15 || 32/15 || m || Minor Ninth
|-
| 17\15 || 20/9 || 9 || Major Ninth
|-
| 18\15 || 16/7 || s || Subminor Tenth
|}
X: The seventh which is derived from going the corresponding third up from the fifth (only applicable to Triforce, Diminished and Wolf chords).
{| class="wikitable"
|+ style="font-size: 102%;" |
Tetradic and pentadic extensions (top note 9\15)
|-
! Interval !! Approx. JI !! Shorthand !! Name
|-
| 11\15 || 5/3 || 6 || Sixth
|-
| 12\15 || 7/4 || h || Harmonic Seventh
|-
| 13\15 || 9/5 || n || Neutral Seventh
|-
| 14\15 || 15/8 || M || Major Seventh
|-
| X || X || 7 || Seventh
|-
| 16\15 || 32/15 || m || Minor Ninth
|-
| 17\15 || 20/9 || M || Major Ninth
|-
| 18\15 || 16/7 || s || Subminor Tenth
|-
| 19\15 || 12/5 || m || Minor Tenth
|-
|}
X: The seventh which is derived from going the corresponding third up from the fifth (only applicable to subminor, minor and major chords).
{| class="wikitable"
|+ style="font-size: 102%;" |
Tetradic and pentadic extensions (top note 10\15)
|-
! Interval !! Approx. JI !! Shorthand !! Name
|-
| 12\15 || 7/4 || 6 || Sixth
|-
| 13\15 || 9/5 || n || Neutral Seventh
|-
| 14\15 || 15/8 || 7 || (Major) Seventh
|-
| 16\15 || 32/15 || m || Minor Ninth
|-
| 17\15 || 20/9 || 9 || Major Ninth
|-
| 18\15 || 16/7 || s || Subminor Tenth
|-
| 19\15 || 12/5 || m || Minor Tenth
|}
|}


==Examples==
==Examples==
Assuming the root note is C,
Assuming the root note is C,
</br>
<br>
[0,3,8,11] &rarr; Ct6
[0,3,8,11] &rarr; Ct6
</br>
<br>
[0,4,8,12] &rarr; Cdh
[0,4,8,12] &rarr; Cd7
</br>
<br>
[0,5,9,13] &rarr; Cn
[0,5,9,13] &rarr; Cn
</br>
<br>
[0,3,6,9,13] &rarr; Cf5n
<br>
[0,4,9,14,19] &rarr; CmMm
<br>
[0,5,9,12,17] &rarr; Ch9
<br>
Etc.
Etc.


==Links==
==Links==
[https://luphoria.com/xenpaper/#%7B15edo%7D(bpm%3A10)%0A%5B0%2C2%2C9%5D_%23C2_(suspended_second)_18%3A20%3A27%0A%5B0%2C3%2C6%5D_%23Cf_(semaphore)_21%3A24%3A28%0A%5B0%2C3%2C7%5D_%23Cu_(utonal_diminished)_7%2F6%2F5%0A%5B0%2C3%2C8%5D_%23Ct_(triforce)_7%3A8%3A10%0A%5B0%2C3%2C9%5D_%23Cs_(subminor)_6%3A7%3A9%0A%5B0%2C4%2C7%5D_%23Co_(otonal_diminished)_5%3A6%3A7%0A%5B0%2C4%2C8%5D_%23Cd_(diminished)_35%3A42%3A50%0A%5B0%2C4%2C9%5D_%23c_(minor)_6%2F5%2F4%0A%5B0%2C5%2C8%5D_%23Cw_(wolf)_10%2F8%2F7%0A%5B0%2C5%2C9%5D_%23C_(major)_4%3A5%3A6%0A%5B0%2C5%2C10%5D_%23Ca_(augmented)_20%3A25%3A32%0A%5B0%2C6%2C9%5D_%23C4_(suspended_fourth)%0A%0A%5B0%2C2%2C9%2C12%5D_%23C2h%0A%5B0%2C2%2C9%2C13%5D_%23C2n%0A%5B0%2C2%2C9%2C14%5D_%23C27%0A%5B0%2C3%2C6%2C9%5D_%23Cf5%0A%5B0%2C3%2C6%2C10%5D_%23Cfm%0A%5B0%2C3%2C6%2C11%5D_%23Cf6%0A%5B0%2C3%2C7%2C10%5D_%23Cum%0A%5B0%2C3%2C7%2C11%5D_%23Cu6%0A%5B0%2C3%2C7%2C12%5D_%23Cuh%0A%5B0%2C3%2C8%2C11%5D_%23Ct6%0A%5B0%2C3%2C8%2C12%5D_%23Cth%0A%5B0%2C3%2C8%2C13%5D_%23Ctn%0A%5B0%2C3%2C9%2C12%5D_%23Csh%0A%5B0%2C3%2C9%2C13%5D_%23Csn%0A%5B0%2C3%2C9%2C14%5D_%23Cs7%0A%5B0%2C4%2C7%2C10%5D_%23Com%0A%5B0%2C4%2C7%2C11%5D_%23Co6%0A%5B0%2C4%2C7%2C12%5D_%23Coh%0A%5B0%2C4%2C8%2C11%5D_%23Cd6%0A%5B0%2C4%2C8%2C12%5D_%23Cdh%0A%5B0%2C4%2C8%2C13%5D_%23Cdn%0A%5B0%2C4%2C9%2C12%5D_%23Cmh%0A%5B0%2C4%2C9%2C13%5D_%23Cmn%0A%5B0%2C4%2C9%2C14%5D_%23Cm7%0A%5B0%2C5%2C8%2C11%5D_%23Cw6%0A%5B0%2C5%2C8%2C12%5D_%23Cwh%0A%5B0%2C5%2C8%2C13%5D_%23Cwn%0A%5B0%2C5%2C9%2C12%5D_%23Ch%0A%5B0%2C5%2C9%2C13%5D_%23Cn%0A%5B0%2C5%2C9%2C14%5D_%23C7%0A%5B0%2C5%2C10%2C13%5D_%23Can%0A%5B0%2C5%2C10%2C14%5D_%23Ca7%0A%5B0%2C5%2C10%2C15%5D_%23Ca8%0A%5B0%2C6%2C9%2C12%5D_%23C4h%0A%5B0%2C6%2C9%2C13%5D_%23C4n%0A%5B0%2C6%2C9%2C14%5D_%23C47 15edo Chord Names in Xenpaper]
[https://luphoria.com/xenpaper/#%7B15edo%7D(bpm%3A10)%0A%5B0%2C3%2C6%5D_%23Cf_(semaphore)_21%3A24%3A28%0A%5B0%2C3%2C7%5D_%23Cu_(utonal_diminished)_7%2F6%2F5%0A%5B0%2C4%2C7%5D_%23Co_(otonal_diminished)_5%3A6%3A7%0A%5B0%2C3%2C8%5D_%23Ct_(triforce)_7%3A8%3A10%0A%5B0%2C4%2C8%5D_%23Cd_(diminished)_35%3A42%3A50%0A%5B0%2C5%2C8%5D_%23Cw_(wolf)_10%2F8%2F7%0A%5B0%2C2%2C9%5D_%23C2_(suspended_second)_18%3A20%3A27%0A%5B0%2C3%2C9%5D_%23Cs_(subminor)_6%3A7%3A9%0A%5B0%2C4%2C9%5D_%23Cm_(minor)_6%2F5%2F4%0A%5B0%2C5%2C9%5D_%23C_(major)_4%3A5%3A6%0A%5B0%2C6%2C9%5D_%23C4_(suspended_fourth)_6%3A8%3A9%0A%5B0%2C5%2C10%5D_%23Ca_(augmented)_20%3A25%3A32%0A%0A%5B0%2C3%2C6%2C8%5D_%23Cfd%0A%5B0%2C3%2C6%2C9%5D_%23Cf5%0A%5B0%2C3%2C6%2C10%5D_%23Cfm%0A%5B0%2C3%2C6%2C11%5D_%23Cf6%0A%0A%5B0%2C3%2C7%2C9%5D_%23Cu5%0A%5B0%2C3%2C7%2C10%5D_%23Cum%0A%5B0%2C3%2C7%2C11%5D_%23Cu6%0A%5B0%2C3%2C7%2C12%5D_%23Cuh%0A%0A%5B0%2C4%2C7%2C9%5D_%23Co5%0A%5B0%2C4%2C7%2C10%5D_%23Com%0A%5B0%2C4%2C7%2C11%5D_%23Co6%0A%5B0%2C4%2C7%2C12%5D_%23Coh%0A%0A%5B0%2C3%2C8%2C10%5D_%23Ctm%0A%5B0%2C3%2C8%2C11%5D_%23Ct7%0A%5B0%2C3%2C8%2C12%5D_%23Cth%0A%5B0%2C3%2C8%2C13%5D_%23Ctn%0A%0A%5B0%2C4%2C8%2C10%5D_%23Cdm%0A%5B0%2C4%2C8%2C11%5D_%23Cd6%0A%5B0%2C4%2C8%2C12%5D_%23Cd7%0A%5B0%2C4%2C8%2C13%5D_%23Cdn%0A%0A%5B0%2C5%2C8%2C10%5D_%23Cwm%0A%5B0%2C5%2C8%2C11%5D_%23Cw6%0A%5B0%2C5%2C8%2C12%5D_%23Cwh%0A%5B0%2C5%2C8%2C13%5D_%23Cw7%0A%0A%5B0%2C2%2C9%2C11%5D_%23C26%0A%5B0%2C2%2C9%2C12%5D_%23C2h%0A%5B0%2C2%2C9%2C13%5D_%23C2n%0A%5B0%2C2%2C9%2C14%5D_%23C2M%0A%0A%5B0%2C3%2C9%2C11%5D_%23Cs6%0A%5B0%2C3%2C9%2C12%5D_%23Cs7%0A%5B0%2C3%2C9%2C13%5D_%23Csn%0A%5B0%2C3%2C9%2C14%5D_%23CsM%0A%0A%5B0%2C4%2C9%2C11%5D_%23Cm6%0A%5B0%2C4%2C9%2C12%5D_%23Cmh%0A%5B0%2C4%2C9%2C13%5D_%23Cm7%0A%5B0%2C4%2C9%2C14%5D_%23CmM%0A%0A%5B0%2C5%2C9%2C11%5D_%23C6%0A%5B0%2C5%2C9%2C12%5D_%23Ch%0A%5B0%2C5%2C9%2C13%5D_%23Cn%0A%5B0%2C5%2C9%2C14%5D_%23C7%0A%0A%5B0%2C6%2C9%2C11%5D_%23C46%0A%5B0%2C6%2C9%2C12%5D_%23C4h%0A%5B0%2C6%2C9%2C13%5D_%23C4n%0A%5B0%2C6%2C9%2C14%5D_%23C4M%0A%0A%5B0%2C5%2C10%2C12%5D_%23Cah%0A%5B0%2C5%2C10%2C13%5D_%23Can%0A%5B0%2C5%2C10%2C14%5D_%23Ca7 15edo Triad and Tetrad Names in Xenpaper]

Latest revision as of 02:23, 4 November 2025

Chord Names

Triads shown here are the ones built from thirds, or from a second or fourth with a 3/2 fifth.

Triads
Triad Approx. JI Shorthand Name
[0,3,6] 21:24:28 Cf Semaphore
[0,3,7] 7/6/5 Cu Utonal Diminished
[0,4,7] 5:6:7 Co Otonal Diminished
[0,3,8] 7:8:10 Ct Triforce
[0,4,8] 35:42:50 Cd Diminished
[0,5,8] 10/8/7 Cw Wolf
[0,2,9] 18:20:27 C2 Suspended Second
[0,3,9] 6:7:9 Cs Subminor
[0,4,9] 6/5/4 Cm Minor
[0,5,9] 4:5:6 C Major
[0,6,9] 6:8:9 C4 Suspended Fourth
[0,5,10] 20:25:32 Ca Augmented

Tetradic and pentadic extensions have different intervals to use, depending on the top note of the triad in root position. Extensions shown below are assuming that tetradic and pentadic extensions extend by thirds (except 6th chords, which usually only extends by a fourth to a 6/9 chord but is still notatable in this system).

Tetradic and pentadic extensions (top note 6\15)
Interval Approx. JI Shorthand Name
8\15 10/7 d Diminished Fifth
9\15 3/2 5 Perfect Fifth
10\15 8/5 m Minor Sixth
11\15 5/3 6 Major Sixth
12\15 7/4 h Harmonic Seventh
13\15 9/5 n Neutral Seventh
14\15 15/8 M Major Seventh
16\15 32/15 m Minor Ninth
Tetradic and pentadic extensions (top note 7\15)
Interval Approx. JI Shorthand Name
9\15 3/2 5 Fifth
10\15 8/5 m Minor Sixth
11\15 5/3 6 Major Sixth
12\15 7/4 h Harmonic Seventh
13\15 9/5 n Neutral Seventh
14\15 15/8 M Major Seventh
16\15 32/15 m Minor Ninth
17\15 20/9 9 Major Ninth
Tetradic and pentadic extensions (top note 8\15)
Interval Approx. JI Shorthand Name
10\15 8/5 m Minor Sixth
11\15 5/3 6 Major Sixth
12\15 7/4 h Harmonic Seventh
13\15 9/5 n Neutral Seventh
14\15 15/8 M Major Seventh
X X 7 Seventh
16\15 32/15 m Minor Ninth
17\15 20/9 9 Major Ninth
18\15 16/7 s Subminor Tenth

X: The seventh which is derived from going the corresponding third up from the fifth (only applicable to Triforce, Diminished and Wolf chords).

Tetradic and pentadic extensions (top note 9\15)
Interval Approx. JI Shorthand Name
11\15 5/3 6 Sixth
12\15 7/4 h Harmonic Seventh
13\15 9/5 n Neutral Seventh
14\15 15/8 M Major Seventh
X X 7 Seventh
16\15 32/15 m Minor Ninth
17\15 20/9 M Major Ninth
18\15 16/7 s Subminor Tenth
19\15 12/5 m Minor Tenth

X: The seventh which is derived from going the corresponding third up from the fifth (only applicable to subminor, minor and major chords).

Tetradic and pentadic extensions (top note 10\15)
Interval Approx. JI Shorthand Name
12\15 7/4 6 Sixth
13\15 9/5 n Neutral Seventh
14\15 15/8 7 (Major) Seventh
16\15 32/15 m Minor Ninth
17\15 20/9 9 Major Ninth
18\15 16/7 s Subminor Tenth
19\15 12/5 m Minor Tenth

Examples

Assuming the root note is C,
[0,3,8,11] → Ct6
[0,4,8,12] → Cd7
[0,5,9,13] → Cn
[0,3,6,9,13] → Cf5n
[0,4,9,14,19] → CmMm
[0,5,9,12,17] → Ch9
Etc.

Links

15edo Triad and Tetrad Names in Xenpaper

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