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

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