==== Properties of 16-EDO ==== - step size: +75.0c - fret constant: 23.587 ---- Val (13-limit) ---- - notation: <16, 25, 37, 45, 55, 59| - errors (absolute): [-0.0c, -27.0c, -11.3c, +6.2c, -26.3c, -15.5c] - errors (relative): [-0.0%, -35.9%, -15.1%, +8.2%, -35.1%, -20.7%] - TE simple badness: 69.918‰ - subgroup: 2.5.7.13 - tempers out 3-limit 43046721/33554432 (Pythagorean double augmented second) - tempers out 5-limit 135/128 (major chroma, major limma) - tempers out 5-limit 648/625 (major diesis) - tempers out 5-limit 2187/2000 (Gorgo limma) - tempers out 5-limit 3125/3072 (small diesis, magic comma) - tempers out 5-limit 6115295232/6103515625 (Vishnu comma) - tempers out 7-limit 36/35 (septimal diesis, 1/4-tone) - tempers out 7-limit 50/49 (Erlich's decatonic comma, tritonic diesis) - tempers out 7-limit 126/125 (septimal semicomma, Starling comma) - tempers out 7-limit 243/224 (Archytas' 2/3-tone) - tempers out 7-limit 525/512 (Avicenna enharmonic diesis) - tempers out 7-limit 1029/1024 (gamelan residue) - tempers out 7-limit 3125/3087 (major BP diesis) - tempers out 7-limit 6144/6125 (porwell comma) - tempers out 7-limit 64827/64000 (Squalentine) - tempers out 7-limit 390625/388962 (dimcomp comma) - tempers out 11-limit 33/32 (undecimal comma, al-Farabi's 1/4-tone) - tempers out 11-limit 45/44 (1/5-tone) - tempers out 11-limit 121/120 (undecimal seconds comma, biyatisma) - tempers out 11-limit 176/175 (valinorsma) - tempers out 11-limit 352/343 (supracomma) - 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 3025/3024 (Lehmerisma) - tempers out 11-limit 234375/234256 (sesdecal) - tempers out 13-limit 27/26 (tridecimal comma) - tempers out 13-limit 65/64 (13th-partial chroma) - tempers out 13-limit 66/65 (Winmeanma) - tempers out 13-limit 78/77 (tridecimal minor third comma) - 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 275/273 (Garibert comma) - tempers out 13-limit 640/637 (huntma) - tempers out 13-limit 847/845 (Cuthbert comma) - tempers out 13-limit 1001/1000 (fairytale comma) - tempers out 13-limit 1575/1573 (Nicola) - tempers out 13-limit 2200/2197 (Parizek comma, petrma) - tempers out 13-limit 4225/4224 (leprechaun comma) - tempers out 13-limit 10648/10647 (harmonisma) - tempered vs. patent location of 7/6: 4 vs. 4 - 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: 7 vs. 7 - tempered vs. patent location of 3/2: 9 vs. 9 - tempered vs. patent location of 7/4: 13 vs. 13 - tempered vs. patent location of 2/1: 16 vs. 16 ==== Mavila[9] notation ==== - number of cycles: 1 - 1 primary step = 2 EDO steps - 1 secondary step = 1 EDO steps - 1 sharp (# or -) = 1 EDO steps (armotonic) ---- Note names ---- 0. D 1. D#/Eb 2. E 3. E#/Fb 4. F 5. G 6. G#/Hb 7. H 8. H#/Zb 9. Z 10. Z#/Ab 11. A 12. B 13. B#/Cb 14. C 15. C#/Db ---- Keyboard layout ---- 11 13 15 1 3 5 7 9 11 13 12 14 0 2 4 6 8 10 12 14 13 15 1 3 5 7 9 11 13 15 14 0 2 4 6 8 10 12 14 0 15 1 3 5 7 9 11 13 15 1 0 2 4 6 8 10 12 14 0 2 1 3 5 7 9 11 13 15 1 3 2 4 6 8 10 12 14 0 2 4 3 5 7 9 11 13 15 1 3 5 4 6 8 10 12 14 0 2 4 6 5 7 9 11 13 15 1 3 5 7 ==== Meantone[7] notation ==== - number of cycles: 1 - 1 primary step = 2 EDO steps - 1 secondary step = 3 EDO steps - 1 sharp (# or -) = -1 EDO steps (antidiatonic) ---- Note names ---- 0. D 1. D+/E- 2. E 3. E+ 4. F- 5. F 6. F+/G- 7. G 8. G+/A- 9. A 10. A+/B- 11. B 12. B+ 13. C- 14. C 15. C+/D- ---- Keyboard layout ---- 1 3 5 7 9 11 13 15 1 3 4 6 8 10 12 14 0 2 4 6 7 9 11 13 15 1 3 5 7 9 10 12 14 0 2 4 6 8 10 12 13 15 1 3 5 7 9 11 13 15 0 2 4 6 8 10 12 14 0 2 3 5 7 9 11 13 15 1 3 5 6 8 10 12 14 0 2 4 6 8 9 11 13 15 1 3 5 7 9 11 12 14 0 2 4 6 8 10 12 14 15 1 3 5 7 9 11 13 15 1 ==== Meantone[5] notation ==== - number of cycles: 1 - 1 primary step = 2 EDO steps - 1 secondary step = 5 EDO steps - 1 sharp (# or -) = -3 EDO steps (pentic) ---- Note names ---- 0. D 1. C+ 2. E 3. D+ 4. G- 5. E+ 6. A- 7. G 8. E++/C-- 9. A 10. G+ 11. C- 12. A+ 13. D- 14. C 15. E- ---- Keyboard layout ---- 7 9 11 13 15 1 3 5 7 9 12 14 0 2 4 6 8 10 12 14 1 3 5 7 9 11 13 15 1 3 6 8 10 12 14 0 2 4 6 8 11 13 15 1 3 5 7 9 11 13 0 2 4 6 8 10 12 14 0 2 5 7 9 11 13 15 1 3 5 7 10 12 14 0 2 4 6 8 10 12 15 1 3 5 7 9 11 13 15 1 4 6 8 10 12 14 0 2 4 6 9 11 13 15 1 3 5 7 9 11 ==== Properties of 16b-EDO ==== - step size: +75.0c - fret constant: 23.587 ---- Val (13-limit) ---- - notation: <16, 26, 37, 45, 55, 59| - errors (absolute): [-0.0c, +48.0c, -11.3c, +6.2c, -26.3c, -15.5c] - errors (relative): [-0.0%, +64.1%, -15.1%, +8.2%, -35.1%, -20.7%] - TE simple badness: 181.856‰ - subgroup: 2.5.7.13 - tempers out 3-limit 8192/6561 (Pythagorean diminished fourth) - tempers out 3-limit 67108864/43046721 (Pythagorean double diminished seventh) - tempers out 5-limit 25/24 (classic chromatic semitone, minor chroma) - tempers out 7-limit 49/48 (slendro diesis, septimal 1/6-tone) - tempers out 7-limit 50/49 (Erlich's decatonic comma, tritonic diesis) - tempers out 7-limit 2401/2400 (Breedsma) - tempers out 7-limit 65625/65536 (horwell comma) - tempers out 7-limit 201768035/201326592 (wadisma) - tempers out 11-limit 22/21 (undecimal minor semitone) - tempers out 11-limit 77/72 (undecimal secor) - tempers out 11-limit 176/175 (valinorsma) - tempers out 11-limit 352/343 (supracomma) - tempers out 11-limit 4000/3993 (undecimal schisma) - tempers out 13-limit 40/39 (tridecimal minor diesis) - tempers out 13-limit 65/64 (13th-partial chroma) - tempers out 13-limit 196/195 (mynucuma) - tempers out 13-limit 364/363 (gentle comma) - tempers out 13-limit 512/507 (tridecimal neutral third comma) - tempers out 13-limit 640/637 (huntma) - tempers out 13-limit 847/845 (Cuthbert comma) - tempers out 13-limit 1001/1000 (fairytale comma) - tempers out 13-limit 1716/1715 (lummic comma) - tempers out 13-limit 2200/2197 (Parizek comma, petrma) - tempered vs. patent location of 7/6: 3 vs. 4 - tempered vs. patent location of 6/5: 5 vs. 4 - tempered vs. patent location of 5/4: 5 vs. 5 - tempered vs. patent location of 4/3: 6 vs. 7 - tempered vs. patent location of 3/2: 10 vs. 9 - tempered vs. patent location of 7/4: 13 vs. 13 - tempered vs. patent location of 2/1: 16 vs. 16 ==== Porcupine[8] notation ==== - number of cycles: 2 - 1 primary step = 2 EDO steps - 1 secondary step = 2 EDO steps - 1 sharp (# or -) = 0 EDO steps (equalized) ---- Note names ---- 0. D[0] 1. D[1] 2. E[0] 3. E[1] 4. F[0] 5. F[1] 6. G[0] 7. G[1] 8. H[0] 9. H[1] 10. A[0] 11. A[1] 12. B[0] 13. B[1] 14. C[0] 15. C[1] ---- Keyboard layout ---- 11 13 15 1 3 5 7 9 11 13 12 14 0 2 4 6 8 10 12 14 13 15 1 3 5 7 9 11 13 15 14 0 2 4 6 8 10 12 14 0 15 1 3 5 7 9 11 13 15 1 0 2 4 6 8 10 12 14 0 2 1 3 5 7 9 11 13 15 1 3 2 4 6 8 10 12 14 0 2 4 3 5 7 9 11 13 15 1 3 5 4 6 8 10 12 14 0 2 4 6 5 7 9 11 13 15 1 3 5 7