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Constant structure: Difference between revisions

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note the practical significance of CS for isomorphic instruments
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diatonic example: removed table of note names
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The corresponding note names:
The highlighted intervals, from F to B and from B to F, are the same size in 12edo: 6\12, or 600 cents. From F to B, this interval spans four steps of our diatonic scale (an “augmented fourth”); but from B to F it spans five (a “diminished fifth”). Since the same interval spans different numbers of scale steps at different points in the scale, this scale is not a constant structure.
 
{| 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 6\12 interval spans different numbers of scale steps at different points in the scale, this scale is not a constant structure.


However, in other tunings of the diatonic scale, the F–B and B–F intervals may have distinct sizes. For example, [[31edo]] (meantone) tunes F–B and B–F to 15\31 (581¢) and 16\31 (619¢) respectively:
However, in other tunings of the diatonic scale, the F–B and B–F intervals may have distinct sizes. For example, [[31edo]] (meantone) tunes F–B and B–F to 15\31 (581¢) and 16\31 (619¢) respectively:
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