Talk:Constant structure

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Note names in the diatonic scale

The Examples section currently contains the following table:

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Interval matrix as note names:

	1	2	3	4	5	6	7	(8)
C	C	D	E	F	G	A	B	C
D	C	D	Eb	F	G	A	Bb	C
E	C	Db	Eb	F	G	Ab	Bb	C
F	C	D	E	F#	G	A	B	C
G	C	D	E	F	G	A	Bb	C
A	C	D	Eb	F	G	Ab	Bb	C
B	C	Db	Eb	F	Gb	Ab	Bb	C

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This usage seems incoherent to me: if the scale in the example is the diatonic scale containing C, D, E, F, G, A, and B, then _the scale in question doesn't contain any notes with sharps or flats_, and it's nonsensical to talk about those notes. Instead, the table should describe the notes from a single scale, and the paragraph that follows it should also refer to the notes within that same scale.

I suggest something like the following instead:

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Interval matrix as steps of 12edo:

	1	2	3	4	5	6	7	(8)
0\12	0\12	2\12	4\12	5\12	7\12	9\12	11\12	12\12
2\12	0\12	2\12	3\12	5\12	7\12	9\12	10\12	12\12
4\12	0\12	1\12	3\12	5\12	7\12	8\12	10\12	12\12
5\12	0\12	2\12	4\12	6\12	7\12	9\12	11\12	12\12
7\12	0\12	2\12	4\12	5\12	7\12	9\12	10\12	12\12
9\12	0\12	2\12	3\12	5\12	7\12	8\12	10\12	12\12
11\12	0\12	1\12	3\12	5\12	6\12	8\12	10\12	12\12

Interval matrix as note names:

	1	2	3	4	5	6	7	(8)
C	C	D	E	F	G	A	B	C
D	D	E	F	G	A	B	C	D
E	E	F	G	A	B	C	D	E
F	F	G	A	B	C	D	E	F
G	G	A	B	C	D	E	F	G
A	A	B	C	D	E	F	G	A
B	B	C	D	E	F	G	A	B

In 12edo, the intervals from F to B and from B to F are the same size: 6\12, or 600 cents. From F to B, this interval spans four steps of our diatonic scale; but from B to F it spans five. Since the same (600¢) interval spans different numbers of scale steps at different points in the scale, this scale is not a constant structure.

However, in tunings that assign different interval sizes for F–B and B–F — such as meantone and superpyth — the diatonic scale is a constant structure. For example, 31edo (meantone) tunes F–B and B–F to 15\31 (581¢) and 16\31 (619¢) respectively, so the four-scale-step interval is distinct from the five-scale-step one:

	1	2	3	4	5	6	7	(8)
0\31	0\31	5\31	10\31	13\31	18\31	23\31	28\31	31\31
5\31	0\31	5\31	8\31	13\31	18\31	23\31	26\31	31\31
10\31	0\31	3\31	8\31	13\31	18\31	21\31	26\31	31\31
13\31	0\31	5\31	10\31	15\31	18\31	23\31	28\31	31\31
18\31	0\31	5\31	10\31	13\31	18\31	23\31	26\31	31\31
23\31	0\31	5\31	8\31	13\31	18\31	21\31	26\31	31\31
28\31	0\31	3\31	8\31	13\31	16\31	21\31	26\31	31\31

--Bcmills (talk) 12:18, 2 May 2024 (UTC)