Talk:Constant structure
This page also contains archived Wikispaces discussion.
Note names in the diatonic scale
The Examples section currently contains the following table:
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 |
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:
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)
I like this one better:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | (8) | |
|---|---|---|---|---|---|---|---|---|
| C | P1 | M2 | M3 | P4 | P5 | M6 | M7 | P8 |
| D | P1 | M2 | m3 | P4 | P5 | M6 | m7 | P8 |
| E | P1 | m2 | m3 | P4 | P5 | m6 | m7 | P8 |
| F | P1 | M2 | M3 | A4 | P5 | M6 | M7 | P8 |
| G | P1 | M2 | M3 | P4 | P5 | M6 | m7 | P8 |
| A | P1 | M2 | m3 | P4 | P5 | m6 | m7 | P8 |
| B | P1 | m2 | m3 | P4 | d5 | m6 | m7 | P8 |
Because now the CS violation can be called out as A4 = d5 when L = 2s.
--Frostburn (talk) 15:24, 3 May 2024 (UTC)
“has” vs. “is”
The current version of the page uses two variations: “have/has constant structure” and “is a constant structure”. (See the previous discussion from the Wikispaces archive.)
Erv Wilson's original papers tended to mention only “constant structures” (plural noun), and the Yahoo tuning list entries cited in the [entry] on constant structures consistently use “is”, with or without an article (“is/was a constant structure” or “is CS”). As far as I can tell, “has constant structure” is a neologism created in the Wikispaces entry.
The only Google results I see for "has constant structure" and "have constant structure" are a couple of pages on this wiki, the phrase “you can have constant-structure 17 and 19-limit otonal scales” in the Yahoo tuning list message 8271, and a bunch of mathematical and chemical contexts that have nothing to do with the use of the phrase in the context of Xenharmonic music.
So I'm going to resolve this inconsistency by changing this article to consistently use “is”.