==== Properties of 19-EDO ====

-- Patent val (13-limit) --
val: <19, 30, 44, 53, 66, 70|
errors (absolute): [-0.0c, -7.2c, -7.4c, -21.5c, +17.1c, -19.5c]
errors (relative): [-0.0%, -11.4%, -11.7%, -34.0%, +27.1%, -30.8%]
TE simple badness: 35.440‰
subgroup: 2.3.5.7.11.13

- supports meantone temperament
- tempers out 3-limit 1162261467/1073741824 (Pythagorean-19 comma)
- tempers out 5-limit 81/80 (syntonic comma, Didymus comma)
- tempers out 5-limit 3125/3072 (small diesis, magic comma)
- tempers out 5-limit 6561/6400 (Mathieu superdiesis)
- tempers out 5-limit 15625/15552 (kleisma, semicomma majeur)
- tempers out 5-limit 16875/16384 (double augmentation diesis, Negri comma)
- tempers out 5-limit 78732/78125 (medium semicomma, Sensi comma)
- tempers out 5-limit 1594323/1562500 (Unicorn comma)
- tempers out 5-limit 48828125/47775744 (Sycamore comma)
- tempers out 5-limit 1224440064/1220703125 (parakleisma)
- tempers out 5-limit 19073486328125/19042491875328 ('19-tone' comma)
- tempers out 7-limit 49/48 (slendro diesis, septimal 1/6-tone)
- tempers out 7-limit 126/125 (septimal semicomma, Starling comma)
- tempers out 7-limit 225/224 (septimal kleisma)
- tempers out 7-limit 245/243 (minor BP diesis, Sensamagic comma)
- tempers out 7-limit 525/512 (Avicenna enharmonic diesis)
- tempers out 7-limit 686/675 (senga)
- tempers out 7-limit 875/864 (keema)
- tempers out 7-limit 1029/1000 (keega)
- tempers out 7-limit 3136/3125 (middle second comma)
- tempers out 7-limit 4375/4374 (ragisma)
- tempers out 7-limit 10976/10935 (hemimage)
- tempers out 7-limit 19683/19600 (cataharry comma)
- tempers out 7-limit 59049/57344 (Harrison's comma)
- tempers out 11-limit 45/44 (1/5-tone)
- tempers out 11-limit 56/55 (undecimal diesis, konbini comma)
- tempers out 11-limit 100/99 (Ptolemy's comma)
- tempers out 11-limit 385/384 (undecimal kleisma, Keemun comma)
- tempers out 11-limit 540/539 (Swets' comma)
- tempers out 11-limit 729/704 (undecimal major diesis)
- tempers out 11-limit 896/891 (undecimal semicomma, pentacircle)
- tempers out 11-limit 26411/26244 (mechanism comma)
- tempers out 11-limit 65536/65219 (orgonisma)
- tempers out 13-limit 65/64 (13th-partial chroma)
- tempers out 13-limit 78/77 (tridecimal minor third comma)
- tempers out 13-limit 91/90 (medium tridecimal comma, superleap)
- tempers out 13-limit 105/104 (small tridecimal comma)
- tempers out 13-limit 144/143 (Grossma)
- tempers out 13-limit 169/168 (Schulter's comma)
- tempers out 13-limit 196/195 (mynucuma)
- tempers out 13-limit 325/324 (marveltwin)
- tempers out 13-limit 351/350 (ratwolf comma)
- tempers out 13-limit 676/675 (island comma)
- tempers out 13-limit 729/728 (squbema)
- tempers out 13-limit 1001/1000 (fairytale comma)
- tempers out 13-limit 1053/1024 (tridecimal major diesis)
- tempers out 13-limit 2080/2079 (ibnsinma)
- tempers out 13-limit 10985/10976 (cantonisma)

Tempered vs. patent location of 7/6: 4 vs. 4
Tempered vs. patent location of 6/5: 5 vs. 5
Tempered vs. patent location of 5/4: 6 vs. 6
Tempered vs. patent location of 4/3: 8 vs. 8
Tempered vs. patent location of 3/2: 11 vs. 11
Tempered vs. patent location of 7/4: 15 vs. 15
Tempered vs. patent location of 2/1: 19 vs. 19

== Meantone notation ==

-- Step sizes --
Number of cycles: 1
1 primary step = 3 EDO steps
1 secondary step = 2 EDO steps
1 sharp (# or -) = 1 EDO steps (diatonic)

-- Scale steps --
  0. D
  1. D#
  2. Eb
  3. E
  4. E#/Fb
  5. F
  6. F#
  7. Gb
  8. G
  9. G#
 10. Ab
 11. A
 12. A#
 13. Bb
 14. B
 15. B#/Cb
 16. C
 17. C#
 18. Db

-- Keyboard layout --
 11  14  17  1   4   7   10  13  16  0  
 13  16  0   3   6   9   12  15  18  2  
 15  18  2   5   8   11  14  17  1   4  
 17  1   4   7   10  13  16  0   3   6  
 0   3   6   9   12  15  18  2   5   8  
 2   5   8   11  14  17  1   4   7   10 
 4   7   10  13  16  0   3   6   9   12 
 6   9   12  15  18  2   5   8   11  14 
 8   11  14  17  1   4   7   10  13  16 
 10  13  16  0   3   6   9   12  15  18 
