==== Properties of 13-EDO ==== - step size: +92.3c - fret constant: 19.259 ---- Val (13-limit) ---- - notation: <13, 21, 30, 36, 45, 48| - errors (absolute): [-0.0c, +36.5c, -17.1c, -45.7c, +2.5c, -9.8c] - errors (relative): [-0.0%, +39.5%, -18.5%, -49.6%, +2.7%, -10.6%] - TE simple badness: 100.661‰ - subgroup: 2.5.11.13 - tempers out 3-limit 2097152/1594323 (Pythagorean double diminished fifth) - tempers out 5-limit 25/24 (classic chromatic semitone, minor chroma) - tempers out 5-limit 2560/2187 (grave minor third) - tempers out 5-limit 4096/3645 (narrow diminished third) - tempers out 5-limit 262144/253125 (Passion comma) - tempers out 5-limit 2109375/2097152 (semicomma, Fokker's comma) - tempers out 7-limit 49/45 (BP minor semitone) - tempers out 7-limit 64/63 (septimal comma, Archytas' comma) - tempers out 7-limit 525/512 (Avicenna enharmonic diesis) - tempers out 7-limit 625/567 (BP great semitone, major BP chroma) - tempers out 7-limit 1029/1000 (keega) - tempers out 7-limit 3125/3087 (major BP diesis) - tempers out 7-limit 3136/3125 (middle second comma) - tempers out 7-limit 33075/32768 (mirwomo comma) - tempers out 7-limit 64827/64000 (Squalentine) - tempers out 11-limit 56/55 (undecimal diesis, konbini comma) - tempers out 11-limit 77/72 (undecimal secor) - tempers out 11-limit 88/81 (2nd undecimal neutral second) - tempers out 11-limit 121/120 (undecimal seconds comma, biyatisma) - 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 13-limit 40/39 (tridecimal minor diesis) - tempers out 13-limit 65/64 (13th-partial chroma) - tempers out 13-limit 105/104 (small tridecimal comma) - tempers out 13-limit 169/168 (Schulter's comma) - tempers out 13-limit 275/273 (Garibert comma) - tempers out 13-limit 512/507 (tridecimal neutral third comma) - 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 4096/4095 (tridecimal schisma, Sagittal schismina) - tempers out 13-limit 6656/6655 (jacobin comma) - tempers out 13-limit 10648/10647 (harmonisma) - tempered vs. patent location of 7/6: 2 vs. 3 - tempered vs. patent location of 6/5: 4 vs. 3 - tempered vs. patent location of 5/4: 4 vs. 4 - tempered vs. patent location of 4/3: 5 vs. 5 - tempered vs. patent location of 3/2: 8 vs. 8 - tempered vs. patent location of 7/4: 10 vs. 10 - tempered vs. patent location of 2/1: 13 vs. 13 ==== Meantone[5] notation ==== - number of cycles: 1 - 1 primary step = 3 EDO steps - 1 secondary step = 2 EDO steps - 1 sharp (# or -) = 1 EDO steps (antipentic) ---- Note names ---- 0. D 1. D# 2. Eb 3. E 4. E#/Gb 5. G 6. G# 7. Ab 8. A 9. A#/Cb 10. C 11. C# 12. Db ---- Keyboard layout ---- 3 6 9 12 2 5 8 11 1 4 5 8 11 1 4 7 10 0 3 6 7 10 0 3 6 9 12 2 5 8 9 12 2 5 8 11 1 4 7 10 11 1 4 7 10 0 3 6 9 12 0 3 6 9 12 2 5 8 11 1 2 5 8 11 1 4 7 10 0 3 4 7 10 0 3 6 9 12 2 5 6 9 12 2 5 8 11 1 4 7 8 11 1 4 7 10 0 3 6 9 10 0 3 6 9 12 2 5 8 11 ==== Tetracot[7] notation ==== - number of cycles: 1 - 1 primary step = 2 EDO steps - 1 secondary step = 1 EDO steps - 1 sharp (# or -) = 1 EDO steps (archeotonic) ---- Note names ---- 0. D 1. D#/Eb 2. E 3. E#/Fb 4. F 5. F#/Gb 6. G 7. A 8. A#/Bb 9. B 10. B#/Cb 11. C 12. C#/Db ---- Keyboard layout ---- 8 10 12 1 3 5 7 9 11 0 9 11 0 2 4 6 8 10 12 1 10 12 1 3 5 7 9 11 0 2 11 0 2 4 6 8 10 12 1 3 12 1 3 5 7 9 11 0 2 4 0 2 4 6 8 10 12 1 3 5 1 3 5 7 9 11 0 2 4 6 2 4 6 8 10 12 1 3 5 7 3 5 7 9 11 0 2 4 6 8 4 6 8 10 12 1 3 5 7 9 5 7 9 11 0 2 4 6 8 10 ==== Properties of 13b-EDO ==== - step size: +92.3c - fret constant: 19.259 ---- Val (13-limit) ---- - notation: <13, 20, 30, 36, 45, 48| - errors (absolute): [-0.0c, -55.8c, -17.1c, -45.7c, +2.5c, -9.8c] - errors (relative): [-0.0%, -60.5%, -18.5%, -49.6%, +2.7%, -10.6%] - TE simple badness: 183.868‰ - subgroup: 2.5.11.13 - tempers out 3-limit 1594323/1048576 (Pythagorean double augmented fourth) - tempers out 5-limit 27/25 (large limma, BP small semitone, Zarlino semitone) - tempers out 5-limit 1125/1024 (double augmented prime) - tempers out 5-limit 1215/1024 (wide augmented second) - tempers out 5-limit 3125/3072 (small diesis, magic comma) - tempers out 5-limit 6561/5120 (acute major third) - tempers out 7-limit 21/20 (minor semitone) - tempers out 7-limit 36/35 (septimal diesis, 1/4-tone) - tempers out 7-limit 49/48 (slendro diesis, septimal 1/6-tone) - tempers out 7-limit 1728/1715 (Orwell comma) - tempers out 7-limit 3136/3125 (middle second comma) - tempers out 7-limit 16875/16807 (small BP diesis, mirkwai comma) - tempers out 7-limit 18225/16807 (minimal BP chroma) - tempers out 11-limit 33/32 (undecimal comma, al-Farabi's 1/4-tone) - tempers out 11-limit 56/55 (undecimal diesis, konbini comma) - tempers out 11-limit 99/98 (small undecimal comma) - tempers out 11-limit 385/384 (undecimal kleisma, Keemun comma) - tempers out 11-limit 4000/3993 (undecimal schisma) - 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 196/195 (mynucuma) - tempers out 13-limit 273/256 (Ibn Sina's minor second) - tempers out 13-limit 364/363 (gentle comma) - tempers out 13-limit 847/845 (Cuthbert comma) - tempers out 13-limit 1001/1000 (fairytale comma) - tempers out 13-limit 2200/2197 (Parizek comma, petrma) - tempers out 13-limit 4225/4224 (leprechaun comma) - 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: 3 vs. 3 - tempered vs. patent location of 5/4: 4 vs. 4 - tempered vs. patent location of 4/3: 6 vs. 5 - tempered vs. patent location of 3/2: 7 vs. 8 - tempered vs. patent location of 7/4: 10 vs. 10 - tempered vs. patent location of 2/1: 13 vs. 13 ==== Mavila[9] notation ==== - number of cycles: 1 - 1 primary step = 1 EDO steps - 1 secondary step = 3 EDO steps - 1 sharp (# or -) = -2 EDO steps (balzano) ---- Note names ---- 0. D 1. E 2. F 3. E+/G- 4. F+/H- 5. G 6. H 7. Z 8. A 9. Z+/B- 10. A+/C- 11. B 12. C ---- Keyboard layout ---- 11 12 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 4 5 6 7 8 9 10 11 12 0 7 8 9 10 11 12 0 1 2 3 10 11 12 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 9 3 4 5 6 7 8 9 10 11 12 6 7 8 9 10 11 12 0 1 2 9 10 11 12 0 1 2 3 4 5 12 0 1 2 3 4 5 6 7 8 2 3 4 5 6 7 8 9 10 11 ==== Meantone[7] notation ==== - number of cycles: 1 - 1 primary step = 1 EDO steps - 1 secondary step = 4 EDO steps - 1 sharp (# or -) = -3 EDO steps (antidiatonic) ---- Note names ---- 0. D 1. E 2. C+/F- 3. D+/G- 4. E+/A- 5. F 6. G 7. A 8. B 9. G+/C- 10. A+/D- 11. B+/E- 12. C ---- Keyboard layout ---- 6 7 8 9 10 11 12 0 1 2 10 11 12 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 5 6 7 8 9 10 11 12 0 1 9 10 11 12 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 4 5 6 7 8 9 10 11 12 0 8 9 10 11 12 0 1 2 3 4 12 0 1 2 3 4 5 6 7 8 3 4 5 6 7 8 9 10 11 12 7 8 9 10 11 12 0 1 2 3