Kite's ups and downs notation: Difference between revisions

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-07-23 00:50:09 UTC</tt>.<br>

: The original revision id was <tt>587608403</tt>.<br>

P1 ^P1 vm2 m2 vM2 M2 ^M2 vm3 m3 vM3 M3 ^M3 vP4 P4 ^P4 A4 d5 vP5 P5 etc.

The name "major" refers not to the sound but to the function of the chord. If you want to play a I - VIm - IIm - V - I progression without pitch shifts or tonic drift, you can do that in any edo, as long as you use major and minor chords. The notation tells you what kind of chord can be used to play that progression. In 22edo, the chord that you need sounds like a red chord.

Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in the above diagram, they are the ones to the left of the central line in the light blue region, plus the ones to the right of the central line in the orange region. The ones on the left edge of the blue region are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.

There are two strategies for notating these "oddball" EDOs, besides heptatonic fifth-based notation with ups and downs. One is to switch from heptatonic notation to some other type. The orange region contains edos for which pentatonic notation is a natural fit, in the sense that no ups or downs are needed. This includes 8edo, 13edo and 18edo.

The other approach is to use some interval other than the fifth to generate the notation. Above I said notating 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C was a bad idea because the G-D and the A-E fifths looked perfect but were actually diminished. The reasoning is that 3/2 is an important ratio, and any decent approximation of 3/2 should look like a perfect fifth. But these EDOs don't approximate 3/2 well, so they can be thought of as having both a major fifth and a minor fifth. This negates any expectations of what a fifth should look like.

The genspan for the up symbol in 22-tone can be found from the Tree of Kites. Or it can be calculated from the keyspans:

P1 ^P1 vm2 m2 vM2 M2 ^M2 vm3 m3 vM3 M3 ^M3 vP4 P4 ^P4 A4 d5 vP5 P5 etc.&lt;br /&gt;

The name &amp;quot;major&amp;quot; refers not to the sound but to the function of the chord. If you want to play a I - VIm - IIm - V - I progression without pitch shifts or tonic drift, you can do that in any edo, as long as you use major and minor chords. The notation tells you what kind of chord can be used to play that progression. In 22edo, the chord that you need sounds like a red chord.&lt;br /&gt;

Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in the above diagram, they are the ones to the left of the central line in the light blue region, plus the ones to the right of the central line in the orange region. The ones on the left edge of the blue region are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.&lt;br /&gt;

There are two strategies for notating these &amp;quot;oddball&amp;quot; EDOs, besides heptatonic fifth-based notation with ups and downs. One is to switch from heptatonic notation to some other type. The orange region contains edos for which pentatonic notation is a natural fit, in the sense that no ups or downs are needed. This includes 8edo, 13edo and 18edo.&lt;br /&gt;

The other approach is to use some interval other than the fifth to generate the notation. Above I said notating 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C was a bad idea because the G-D and the A-E fifths looked perfect but were actually diminished. The reasoning is that 3/2 is an important ratio, and any decent approximation of 3/2 should look like a perfect fifth. But these EDOs don't approximate 3/2 well, so they can be thought of as having both a major fifth and a minor fifth. This negates any expectations of what a fifth should look like.&lt;br /&gt;

The genspan for the up symbol in 22-tone can be found from the Tree of Kites. Or it can be calculated from the keyspans:&lt;br /&gt;