Breuddwyd inverse

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The breuddwyd inverse scale⁠ ⁠^{[idiosyncratic term ]} is a polymicrotonal scale.

It is a just intonation scale, created by including all the intervals from the scales 5ifdo, 11ifdo, 13ifdo and 31ifdo. (See Ifdo for more information.) This process pretends that the ifdos have a tonic - not everyone treats ifdos as having one but pretending they do is the only way this process makes sense.

The breuddwyd inverse scale belongs to a collection of scales called the breuddwyd scales.⁠ ⁠^{[idiosyncratic term ]} It is octave-repeating, featuring 57 notes per octave.

It approximates the 2.5.7 subgroup very well. Its approximation of 3/1, on the other hand, is only barely useable, with about 15 cents of error.

Scala file

! BreuddwydInverse.scl
! Created using Scale Workshop 3.1.0
!
! https://scaleworkshop.plainsound.org/scale/CtmIRzPZ7
!
BreuddwydInverse
 57
!
 62/61
 31/30
 26/25
 22/21
 62/59
 31/29
 13/12
 62/57
 11/10
 31/28
 10/9
 62/55
 26/23
 31/27
 22/19
 62/53
 13/11
 31/26
 62/51
 11/9
 26/21
 31/25
 5/4
 62/49
 31/24
 22/17
 13/10
 62/47
 31/23
 26/19
 11/8
 62/45
 31/22
 10/7
 62/43
 13/9
 22/15
 31/21
 62/41
 26/17
 31/20
 11/7
 62/39
 13/8
 31/19
 5/3
 62/37
 22/13
 31/18
 26/15
 62/35
 31/17
 11/6
 13/7
 62/33
 31/16
 2/1

Subsets

Vinyl braid scale

The vinyl braid scale⁠ ⁠^{[idiosyncratic term ]} is a 30-tone subset of the breuddwyd inverse scale.

Its name derives from the fact that the uneven grooves in its linear horogram look like grooves on a vinyl record.

It has all the same benefits and drawbacks of its parent scale, breuddwyd inverse. The main advantage compared to breuddwyd inverse is that most of the intervals with high harmonic entropy have been trimmed away, giving the consonances more spotlight.

Its equave is 2/1, and it has 30 notes per octave. It is too unevenly spaced to be approached as a well temperament. Edos with exceptional approximations of vinyl braid for their size include: 58edo (8.7¢ err), 63edo (8.1¢), 90edo (6.3¢), 99edo (5.8¢), 103edo (5.3¢) and 121edo (4.0¢).

(Scala file)

! BreuddwydInverse.scl
! Created using Scale Workshop 3.1.0
!
! https://scaleworkshop.plainsound.org
!
BreuddwydInverse
 30
!
 22/21
 31/29
 13/12
 11/10
 10/9
 62/55
 31/27
 62/53
 22/19
 62/51
 5/4
 62/49
 31/24
 62/47
 31/23
 62/45
 31/22
 10/7
 62/41
 11/7
 62/39
 13/8
 5/3
 22/13
 26/15
 62/35
 11/6
 13/7
 62/33
 2/1