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User:TallKite/Solfeges: Difference between revisions

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autopatrolled, Sysops
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autopatrolled, Sysops
4,223 edits
Line 19,742: Line 19,742:
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
2L7s MOS scales (L = , s = ^1 = v<sup>4</sup>M2)
2L7s MOS scales (L = v4 = ^<sup>4</sup>m3, s = ^1 = v<sup>4</sup>M2)
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
Line 19,875: Line 19,875:


== Multi-edo pergens of the form (P8/m, ^1) ==
== Multi-edo pergens of the form (P8/m, ^1) ==
These pergens map the 5th to an edo, and other primes to other rings (offset copies of the edo). They only make sense musically if the edo's approximation of the 5th has a relative error < 25%. Otherwise there will be a better Sa on another ring. For example, 4-edo with 34% error has 3/2 = 600¢, but additional rings will add a note between 600¢ and 850¢ that will be a much better approximation. With 3-edo, error 24.5%, for 2\3 to be the best approximation, the generator must be more than twice the absolute error of 102¢, but less than half an edostep, leaving only the small range of 196-200¢.
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
 
rank-2 edos with Sa mapped to a good spot
!pergen
!edo
!period
!rel. error
!EI
!generator range
!perchain
!mapping
!notes
|-
!2-edo
|17%
|204-300¢
|(2 3...) (0 0...)
|maximum of 4 notes
|-
|-
|(P8/2, ^1)
!3-edo
|A4 / d5
|24.5%
|d2
|196-200¢
|Da - Pa/Sha - Da
|(3 5...) (0 0...)
|maximum of 6 notes, within 4¢ of 6-edo
|-
|-
|(P8/3, ^1)
!4-edo
|M3 / d4
|34%
|d2
|none
|Da - Ma - Fla - Da
|
|
|-
|-
|(P8/4, ^1)
!5-edo
|m3 / A2
|7.5%
|d2
|36-120¢
|Da - Na - Pa/Sha - La - Da
|(5 8...) (0 0...)
|Sawa aka Blackwood
|-
|-
|(P8/5, ^1)
!6-edo
|M2 / m3
|49%
|d2
|none
|Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da
|
|
|-
|-
|(P8/6, ^1)
!7-edo
|M2 / d3
|9.5%
|d2
|32-85¢
|Da - Ra - Ma - Pa/Sha - Fla - Tha - Da
|(7 11...) (0 0...)
|Lawa aka Whitewood
|-
|-
|(P8/7, ^1)
!8-edo
|M2 / m2
|32%
|A1
|none
|Da - Ra - Ma - Fa - Sa - La - Ta - Da
|
|
|-
|-
|(P8/8, ^1)
!9-edo
|26.5%
|none
|
|
|
|
|???
|-
|-
|(P8/9, ^1)
!10-edo
|15%
|36-60¢
|(10 16...) (0 0...)
|needs 2 more primes to be a valid mapping
|-
!11-edo
|47.5%
|none
|
|
|
|
|???
|-
|-
|(P8/10, ^1)
!12-edo
|???
|2%
|???
|4-50¢
|Da - Fra - Ra/Na - Ma - Fa - Pa/Sha - Sa - Fla - La/Tha - Ta - Da
|(12 19...) (0 0...)
|Lalawa aka Compton
|-
|-
|(P8/11, ^1)
!13-edo
|40%
|none
|
|
|
|
|???
|-
|-
|(P8/12, ^1)
!14-edo
|A1 / m2
|19%
|d2
|32-43¢
|Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
|(14 22...) (0 0...)
|needs 2 more primes to be a valid mapping
|-
!15-edo
|
|
|
|
|}
|}
===(P8/5, ^1)===
===(P8/5, ^1)===
*P = M2/m3 = 200¢
*P = M2/m3 = 200¢
Line 20,395: Line 20,427:
===(P8/7, ^1) ===
===(P8/7, ^1) ===
*P = M2/m2 = 171¢
*P = M2/m2 = 171¢
*G = ^1 = c
*G = ^1 = c (stands for 135/128 in Whitewood)
*EI = A1 = 0¢
*EI = A1 = 0¢
*^ = c
*^ = c
Line 20,906: Line 20,938:
Da - Du - Di/Re - Ro - Ra
Da - Du - Di/Re - Ro - Ra
|(2 3...) (0 2...)
|(2 3...) (0 2...)
|
|(1/2 0)
 
(-3/4 1/2)
|-
|-
!33
!33
Line 20,915: Line 20,949:
|Da - Ri - Fo - Su - The - Da
|Da - Ri - Fo - Su - The - Da
|(5 5...) (0 1...)
|(5 5...) (0 1...)
|
|(1/5 0) (-1 1)
|-
|-
!34
!34
Line 20,964: Line 20,998:
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
Multi-edo pergens
Multi-edo pergens -- genchain is De Do Da Du Di
!pergen
!pergen
!period
!period
!5-limit generator
!EI
!EI
!perchain
!perchain
|-
!mapping
|(P8/2, ^1)
!notes
|A4 / d5
|d2
| Da - Pa/Sha - Da
|-
|(P8/3, ^1)
|M3 / d4
|d2
|Da - Ma - Fla - Da
|-
|(P8/4, ^1)
|m3 / A2
|d2
|Da - Na - Pa/Sha - La - Da
|-
|-
| (P8/5, ^1)
| (P8/5, ^1)
|M2 / m3
|M2 / m3
|d2
|16/15 or 81/80
|m2
|Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da
|Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da
|-
|(5 8...)
|(P8/6, ^1)
 
|M2 / d3
(0 0...)
|d2
|Sawa/Blackwood
|Da - Ra - Ma - Pa/Sha - Fla - Tha - Da
|-
|-
|(P8/7, ^1)
|(P8/7, ^1)
|M2 / m2
|M2 / m2
|135/128 or 80/81
|A1
|A1
|Da - Ra - Ma - Fa - Sa - La - Ta - Da
|Da - Ra - Ma - Fa - Sa - La - Ta - Da
|(7 11...)
(0 0...)
|Lawa/Whitewood
|-
|-
|(P8/10, ^1)
|(P8/10, ^1)
|???
|???
|
|???
|???
|Da - Fra - Ra/Na - Ma - Fa - Pa/Sha - Sa - Fla - La/Tha - Ta - Da
|Da - Fra - Ra/Na - Ma - Fa - Pa/Sha - Sa - Fla - La/Tha - Ta - Da
|(10 16...)
(0 0...)
|
|-
|-
|(P8/12, ^1)
|(P8/12, ^1)
|A1 / m2
|A1 / m2
|
|d2
|d2
|Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
|Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
|(12 19...) (0 0...)
|Lalawa/Compton
|}
|}
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