==== Properties of 19-EDO ==== - step size: +63.2c - fret constant: 27.914 ---- Val (13-limit) ---- - notation: <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 - 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[7] notation ==== - number of cycles: 1 - 1 primary step = 3 EDO steps - 1 secondary step = 2 EDO steps - 1 sharp (# or -) = 1 EDO steps (diatonic) ---- Note names ---- 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 ---- 9 12 15 18 2 5 8 11 14 17 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 ==== Meantone[5] notation ==== - number of cycles: 1 - 1 primary step = 3 EDO steps - 1 secondary step = 5 EDO steps - 1 sharp (# or -) = -2 EDO steps (pentic) ---- Note names ---- 0. D 1. E- 2. D+ 3. E 4. D++/G-- 5. E+ 6. G- 7. E++/A-- 8. G 9. A- 10. G+ 11. A 12. G++/C-- 13. A+ 14. C- 15. A++/D-- 16. C 17. D- 18. C+ ---- Keyboard layout ---- 13 16 0 3 6 9 12 15 18 2 18 2 5 8 11 14 17 1 4 7 4 7 10 13 16 0 3 6 9 12 9 12 15 18 2 5 8 11 14 17 14 17 1 4 7 10 13 16 0 3 0 3 6 9 12 15 18 2 5 8 5 8 11 14 17 1 4 7 10 13 10 13 16 0 3 6 9 12 15 18 15 18 2 5 8 11 14 17 1 4 1 4 7 10 13 16 0 3 6 9 6 9 12 15 18 2 5 8 11 14 ==== Hanson[7] notation ==== - number of cycles: 1 - 1 primary step = 4 EDO steps - 1 secondary step = 1 EDO steps - 1 sharp (# or -) = 3 EDO steps (smitonic) ---- Note names ---- 0. D 1. Eb 2. Fb 3. D# 4. E 5. F 6. Gb 7. E#/Ab 8. F# 9. G 10. A 11. Bb 12. G#/Cb 13. A# 14. B 15. C 16. Db 17. B# 18. C# ---- Keyboard layout ---- 14 18 3 7 11 15 0 4 8 12 15 0 4 8 12 16 1 5 9 13 16 1 5 9 13 17 2 6 10 14 17 2 6 10 14 18 3 7 11 15 18 3 7 11 15 0 4 8 12 16 0 4 8 12 16 1 5 9 13 17 1 5 9 13 17 2 6 10 14 18 2 6 10 14 18 3 7 11 15 0 3 7 11 15 0 4 8 12 16 1 4 8 12 16 1 5 9 13 17 2 5 9 13 17 2 6 10 14 18 3