==== Properties of 15-EDO stretched by -7.9c ==== - step size: +79.5c - fret constant: 22.289 ---- Val (13-limit) ---- - notation: <15, 24, 35, 42, 52, 56| - errors (absolute): [-7.9c, +5.3c, -4.9c, -31.1c, -18.9c, +9.8c] - errors (relative): [-10.0%, +6.7%, -6.1%, -39.1%, -23.7%, +12.3%] - TE simple badness: 37.708‰ - subgroup: 2.3.5.11.13 - tempers out 3-limit 256/243 (limma, Pythagorean minor second) - tempers out 3-limit 65536/59049 (Pythagorean diminished third) - tempers out 3-limit 16777216/14348907 (Pythagorean double diminished fourth) - tempers out 5-limit 128/125 (minor diesis, diesis) - tempers out 5-limit 250/243 (maximal diesis, Porcupine comma) - tempers out 5-limit 15625/15552 (kleisma, semicomma majeur) - tempers out 5-limit 1953125/1889568 (Shibboleth comma) - tempers out 7-limit 28/27 (Archytas' 1/3-tone) - tempers out 7-limit 49/48 (slendro diesis, septimal 1/6-tone) - tempers out 7-limit 64/63 (septimal comma, Archytas' comma) - tempers out 7-limit 126/125 (septimal semicomma, Starling comma) - tempers out 7-limit 875/864 (keema) - tempers out 7-limit 1029/1000 (keega) - tempers out 7-limit 1029/1024 (gamelan residue) - tempers out 7-limit 4000/3969 (small septimal comma) - tempers out 7-limit 6144/6125 (porwell comma) - tempers out 7-limit 15625/15309 (great BP diesis) - tempers out 7-limit 16807/16384 (cloudy) - tempers out 7-limit 64827/64000 (Squalentine) - tempers out 7-limit 250047/250000 (Landscape comma) - tempers out 11-limit 55/54 (telepathma) - tempers out 11-limit 56/55 (undecimal diesis, konbini comma) - tempers out 11-limit 100/99 (Ptolemy's comma) - tempers out 11-limit 121/120 (undecimal seconds comma, biyatisma) - tempers out 11-limit 176/175 (valinorsma) - tempers out 11-limit 245/242 (Nautilus comma) - tempers out 11-limit 385/384 (undecimal kleisma, Keemun comma) - tempers out 11-limit 441/440 (Werckmeister's undecimal septenarian schisma) - tempers out 11-limit 1331/1323 (aphrowe) - tempers out 11-limit 1344/1331 (hemimin) - tempers out 11-limit 3025/3024 (Lehmerisma) - tempers out 11-limit 4000/3993 (undecimal schisma) - tempers out 11-limit 65536/65219 (orgonisma) - tempers out 13-limit 40/39 (tridecimal minor diesis) - tempers out 13-limit 66/65 (Winmeanma) - 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 275/273 (Garibert comma) - tempers out 13-limit 325/324 (marveltwin) - tempers out 13-limit 364/363 (gentle comma) - tempers out 13-limit 640/637 (huntma) - tempers out 13-limit 676/675 (island comma) - tempers out 13-limit 1001/1000 (fairytale comma) - tempers out 13-limit 1188/1183 (kestrel comma) - tempers out 13-limit 1575/1573 (Nicola) - tempers out 13-limit 2080/2079 (ibnsinma) - tempers out 13-limit 6656/6655 (jacobin comma) - tempered vs. patent location of 7/6: 3 vs. 3 - tempered vs. patent location of 6/5: 4 vs. 4 - tempered vs. patent location of 5/4: 5 vs. 5 - tempered vs. patent location of 4/3: 6 vs. 6 - tempered vs. patent location of 3/2: 9 vs. 9 - tempered vs. patent location of 7/4: 12 vs. 12 - tempered vs. patent location of 2/1: 15 vs. 15 ==== Meantone[5] notation ==== - number of cycles: 3 - 1 primary step = 3 EDO steps - 1 secondary step = 3 EDO steps - 1 sharp (# or -) = 0 EDO steps (equalized) ---- Note names ---- 0. D[0] 1. D[1] 2. D[2] 3. E[0] 4. E[1] 5. E[2] 6. G[0] 7. G[1] 8. G[2] 9. A[0] 10. A[1] 11. A[2] 12. C[0] 13. C[1] 14. C[2] ---- Keyboard layout ---- 5 8 11 14 2 5 8 11 14 2 7 10 13 1 4 7 10 13 1 4 9 12 0 3 6 9 12 0 3 6 11 14 2 5 8 11 14 2 5 8 13 1 4 7 10 13 1 4 7 10 0 3 6 9 12 0 3 6 9 12 2 5 8 11 14 2 5 8 11 14 4 7 10 13 1 4 7 10 13 1 6 9 12 0 3 6 9 12 0 3 8 11 14 2 5 8 11 14 2 5 10 13 1 4 7 10 13 1 4 7 ==== Porcupine[8] notation ==== - number of cycles: 1 - 1 primary step = 2 EDO steps - 1 secondary step = 1 EDO steps - 1 sharp (# or -) = 1 EDO steps (pine) ---- Note names ---- 0. D 1. D#/Eb 2. E 3. E#/Fb 4. F 5. F#/Gb 6. G 7. G#/Hb 8. H 9. A 10. A#/Bb 11. B 12. B#/Cb 13. C 14. C#/Db ---- Keyboard layout ---- 10 12 14 1 3 5 7 9 11 13 11 13 0 2 4 6 8 10 12 14 12 14 1 3 5 7 9 11 13 0 13 0 2 4 6 8 10 12 14 1 14 1 3 5 7 9 11 13 0 2 0 2 4 6 8 10 12 14 1 3 1 3 5 7 9 11 13 0 2 4 2 4 6 8 10 12 14 1 3 5 3 5 7 9 11 13 0 2 4 6 4 6 8 10 12 14 1 3 5 7 5 7 9 11 13 0 2 4 6 8 ==== Hanson[7] notation ==== - number of cycles: 1 - 1 primary step = 3 EDO steps - 1 secondary step = 1 EDO steps - 1 sharp (# or -) = 2 EDO steps (smitonic) ---- Note names ---- 0. D 1. Eb 2. D#/Fb 3. E 4. F 5. E#/Gb 6. F#/Ab 7. G 8. A 9. G#/Bb 10. A#/Cb 11. B 12. C 13. B#/Db 14. C# ---- Keyboard layout ---- 10 13 1 4 7 10 13 1 4 7 11 14 2 5 8 11 14 2 5 8 12 0 3 6 9 12 0 3 6 9 13 1 4 7 10 13 1 4 7 10 14 2 5 8 11 14 2 5 8 11 0 3 6 9 12 0 3 6 9 12 1 4 7 10 13 1 4 7 10 13 2 5 8 11 14 2 5 8 11 14 3 6 9 12 0 3 6 9 12 0 4 7 10 13 1 4 7 10 13 1 5 8 11 14 2 5 8 11 14 2