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

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==2\15 vs 3\15 ==
==Chord Names==
Which one be used as a major second? Both are equally away from [[12edo]]’s major second after all, and opinions differ on which one sounds more like a major second. Well, while 3\15 is also used as a kind of minor third in Nice-Ionian, 3\15 is 2 3/2s stacked and reduced by an octave. These two points will come into play in comparing 15edo’s two possible major scales in the next section.
Triads shown here are the ones built from thirds, or from a second or fourth with a [[3/2]] fifth.
==LH Nice-Ionian vs RH Nice-Ionian==
{| class="wikitable"
|+ style="font-size: 120%;" |
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).
{| class="wikitable"
|+ style="font-size: 102%;" |
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
|}
{| class="wikitable"
|+ style="font-size: 102%;" |
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
|}
{| 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==
Assuming the root note is C,
<br>
[0,3,8,11] &rarr; Ct6
<br>
[0,4,8,12] &rarr; Cd7
<br>
[0,5,9,13] &rarr; Cn
<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.
 
==Links==
[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]
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