Breuddwyd6

The breuddwyd-6 scale⁠ ⁠^{[idiosyncratic term ]} is a polymicrotonal scale. Breuddwyd-6 is created by including all the intervals from the scales 5ed6, 11ed6, 13ed6 and 31ed6.

It belongs to a collection of scales called the breuddwyd scales.⁠ ⁠^{[idiosyncratic term ]} Its equave is 6/1, and it has 57 notes per equave - so about 19 per octave on average.

It approximates the full 11-limit quite well.

Scala file

! Breuddwyd6.scl
! Created using Scale Workshop 3.1.0
!
! https://scaleworkshop.plainsound.org/scale/AtmRTbIv-
!
Polymicrotonal scale of 5ed6, 11ed6, 13ed6 and 31ed6
 57
!
 100.063 ! 1\31<6>
 200.126 ! 2\31<6>
 238.612 ! 1\13<6>
 281.996 ! 1\11<6>
 300.189 ! 3\31<6>
 400.252 ! 4\31<6>
 477.224 ! 2\13<6>
 500.315 ! 5\31<6>
 563.992 ! 2\11<6>
 600.378 ! 6\31<6>
 620.391 ! 1\5<6>
 700.441 ! 7\31<6>
 715.836 ! 3\13<6>
 800.505 ! 8\31<6>
 845.988 ! 3\11<6>
 900.568 ! 9\31<6>
 954.448 ! 4\13<6>
 1000.631 ! 10\31<6>
 1100.694 ! 11\31<6>
 1127.984 ! 4\11<6>
 1193.060 ! 5\13<6>
 1200.757 ! 12\31<6>
 1240.782 ! 2\5<6>
 1300.820 ! 13\31<6>
 1400.883 ! 14\31<6>
 1409.980 ! 5\11<6>
 1431.672 ! 6\13<6>
 1500.946 ! 15\31<6>
 1601.009 ! 16\31<6>
 1670.283 ! 7\13<6>
 1691.975 ! 6\11<6>
 1701.072 ! 17\31<6>
 1801.135 ! 18\31<6>
 1861.173 ! 3\5<6>
 1901.198 ! 19\31<6>
 1908.895 ! 8\13<6>
 1973.971 ! 7\11<6>
 2001.261 ! 20\31<6>
 2101.324 ! 21\31<6>
 2147.507 ! 9\13<6>
 2201.387 ! 22\31<6>
 2255.967 ! 8\11<6>
 2301.450 ! 23\31<6>
 2386.119 ! 10\13<6>
 2401.514 ! 24\31<6>
 2481.564 ! 4\5<6>
 2501.577 ! 25\31<6>
 2537.963 ! 9\11<6>
 2601.640 ! 26\31<6>
 2624.731 ! 11\13<6>
 2701.703 ! 27\31<6>
 2801.766 ! 28\31<6>
 2819.959 ! 10\11<6>
 2863.343 ! 12\13<6>
 2901.829 ! 29\31<6>
 3001.892 ! 30\31<6>
 6/1 ! 5\5<6>

Subsets

Snow braid scale

The snow braid scale⁠ ⁠^{[idiosyncratic term ]} is a 37-tone subset of the breuddwyd-6 scale.

Its name derives from the iceface tuning because that also contains an even mix of 12edo-like intervals with xenharmonic intervals.

The snow braid scale approximates the full 11-limit quite well.

Its equave is 6/1, and it has 37 notes per equave - so about 12 per octave on average. It can be viewed as a well temperament of 37ed6. Ed6s with exceptional approximations of snow braid for their size include: 168ed6 (8.4¢ err), 195ed6 (7.2¢), 196ed6 (7.2¢), 235ed6 (6.0¢), 288ed6 (4.9¢), 289ed6 (4.9¢) and 341ed6 (2.1¢).

(Scala file)

! SnowBraid.scl
! Created using Scale Workshop 3.1.0
!
! https://scaleworkshop.plainsound.org/
!
Subset of Breuddwyd6
 37
!
 100.063 ! 1\31<6>
 200.126 ! 2\31<6>
 238.612 ! 1\13<6>
 281.996 ! 1\11<6>
 400.252 ! 4\31<6>
 500.315 ! 5\31<6>
 563.992 ! 2\11<6>
 620.391 ! 1\5<6>
 700.441 ! 7\31<6>
 800.505 ! 8\31<6>
 900.568 ! 9\31<6>
 954.448 ! 4\13<6>
 1000.631 ! 10\31<6>
 1127.984 ! 4\11<6>
 1193.060 ! 5\13<6>
 1300.820 ! 13\31<6>
 1409.980 ! 5\11<6>
 1500.946 ! 15\31<6>
 1601.009 ! 16\31<6>
 1691.975 ! 6\11<6>
 1801.135 ! 18\31<6>
 1908.895 ! 8\13<6>
 2001.261 ! 20\31<6>
 2101.324 ! 21\31<6>
 2147.507 ! 9\13<6>
 2255.967 ! 8\11<6>
 2301.450 ! 23\31<6>
 2401.514 ! 24\31<6>
 2481.564 ! 4\5<6>
 2537.963 ! 9\11<6>
 2601.640 ! 26\31<6>
 2701.703 ! 27\31<6>
 2801.766 ! 28\31<6>
 2863.343 ! 12\13<6>
 2901.829 ! 29\31<6>
 3001.892 ! 30\31<6>
 6/1 ! 5\5<6>