Talk:Constant structure: Difference between revisions

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Bcmills (talk | contribs)
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discuss the diatonic scale example
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== Note names in the diatonic scale ==
The Examples section currently contains the following table:
----
Interval matrix as note names:
{| class="wikitable center-all"
!
! 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
| <span style="background-color: #ffcc44;">F#</span>
| 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
| <span style="background-color: #ffcc44;">Gb</span>
| 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:
{| class="wikitable center-all"
!
! 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
| <span style="background-color: #ffcc44;">6\12</span>
| 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
| <span style="background-color: #ffcc44;">6\12</span>
| 8\12
| 10\12
| 12\12
|}
Interval matrix as note names:
{| class="wikitable center-all"
!
! 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
| <span style="background-color: #ffcc44;">B</span>
| 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
| <span style="background-color: #ffcc44;">F</span>
| 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:
{| class="wikitable center-all"
!
! 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
| <span style="background-color: #ffcc44;">15\31</span>
| 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
| <span style="background-color: #ffcc44;">16\31</span>
| 21\31
| 26\31
| 31\31
|}

Revision as of 04:07, 2 May 2024

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
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