User:TromboneBoi9

Hello! My name is Andrew and I like screwing around with xenharmony, especially notation.

Currently experimenting with anti-diatonic stuff like EDOs 9, 11, 13, 16, and 23.

I have a website!!

An idea for notation I had

Something I noticed in regular EDO notation, using Pythagorean names, is that the major third in a lot of temperaments is no longer the closest the EDO has to the just major third 5/4. So, with some thought from Just Intonation notations, I came up with something that I think might be promising.

In essence, instead of solely relying on Pythaogrean names and arrows for edosteps in between (which can get unwieldy in larger EDOs), I considered making the arrow represent the syntonic comma instead. If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has syntonic comma that hasn't been tempered out. This won't change anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO.

For single edosteps, we can instead use a sort of slash-like symbol Bosanquet used in his notation, and perhaps stack them on top of each other to use less horizontal space.

Here's a full example in 37-EDO:

Steps	Pythagorean notation	Old notation	New notation
0	D	D	D
1	Eb	Eb	Eb
2	Fb	^Eb	^D
3	Gbb	^^Eb	^Eb
4	Bx	vvD#	vD#
5	Cx	vD#	vE
6	D#	D#	D#
7	E	E	E
8	F	F	F
9	Gb	Gb	Gb
10	Abb	^Gb	^F
11	Bbbb	^^Gb	^Gb
12	Dx	vvF#	vF#
13	E#	vF#	vG
14	F#	F#	F#
15	G	G	G
16	Ab	Ab	Ab
17	Bbb	^Ab	^G
18	Cbb	^^Ab	^Ab
19	Ex	vvG#	vG#
20	Fx	vG#	vA
21	G#	G#	G#
22	A	A	A
23	Bb	Bb	Bb
24	Cb	^Bb	^A
25	Dbb	^^Bb	vBb
26	F#x	vvA#	^A#
27	Gx	vA#	vB
28	A#	A#	A#
29	B	B	B
30	C	C	C
31	Db	Db	Db
32	Ebb	^Db	^C
33	Fbb	^^Db	^Db
34	Ax	vvC#	vC#
35	B#	vC#	vD
36	C#	C#	C#
37	D	D	D

And for anti-diatonic systems, use x and y instead of ^ and v, using harmonic notation.

An example in 13-EDO:

Steps	Pythagorean/old notation	26-EDO Subset	New notation
0	D	D	D
1	E	Dx, Ebb	E, xC
2	Eb	E	Eb, xD
3	Fx	Ex, Fb	xE, yF
4	F#	F#	F#, yG
5	F	Gb	F, yA
6	G	G#	G, yB
7	A	Ab	A, xF
8	B	A#	B, xG
9	Bb	Bb	Bb, xA
10	Cx	B#	xB, yC
11	C#	C	C#, yD
12	C	Cx, Dbb	C, yE
13	D	D	D

Cloudy scales

I don't know about you, but I love the seventh harmonic. These scales are named after the cloudy comma.

Cumulus Alpha is a 5L6s MOS with 7/4 as the generator and 2/1 as the period.

Steps	Ratio	Cents
0	1/1	0.000
1	16807/16384	43.130
2	8/7	231.174
3	2401/2048	275.304
4	64/49	462.348
5	343/256	506.478
6	512/343	693.522
7	49/32	737.652
8	4096/2401	924.696
9	7/4	968.826
10	32768/16807	1155.870
11	2/1	1200.000

Cumulus Beta is an 4L5s MOS with 7/6 as the generator and 2/1 as the period. Amazingly, it approximates all intervals of 9-EDO within a cent!

Steps	Ratio	Cents	9-EDO Difference
0	1/1	0.000	0.000
1	2592/2401	132.516	-0.817
2	7/6	266.871	0.204
3	432/343	399.387	-0.613
4	49/36	533.742	0.409
5	72/49	666.258	-0.409
6	343/216	800.613	0.613
7	12/7	933.129	-0.204
8	2401/1296	1067.484	0.817
9	7/4	1200.000	0.000

Cumulus Gamma is an 3L5s MOS with 9/7 as the generator and 2/1 as the period. It appears to partially approximate 11-EDO.

Steps	Ratio	Cents	Approx. 11-EDO Degree
0	1/1	0.000	0
1	729/686	105.252	1
2	98/81	329.832	3
3	9/7	435.084	4
4	6561/4802	540.336	5
5	14/9	764.916	7
6	81/49	870.168	8
7	1372/729	1094.748	10
8	2/1	1200.000	11