45edo: Difference between revisions
Jump to navigation
Jump to search
Finally finished intervals. |
Still filling in table. |
||
| Line 25: | Line 25: | ||
| 0 | | 0 | ||
|0 | |0 | ||
| | | Unison | ||
| 1 | | 1 | ||
| D | | D | ||
| Line 34: | Line 34: | ||
|26.841 | |26.841 | ||
| -0.174 | | -0.174 | ||
| | |Up unison | ||
| | | | ||
| D^ | | D^ | ||
| Line 43: | Line 43: | ||
|53.273 | |53.273 | ||
|0.060 | |0.060 | ||
| | |Downminor 2nd | ||
| | | | ||
|D# | |D# | ||
| Line 52: | Line 52: | ||
|80.537 | |80.537 | ||
| -0.537 | | -0.537 | ||
| | |Minor 2nd | ||
| | | | ||
|D#^ | |D#^ | ||
| Line 61: | Line 61: | ||
|104.955 | |104.955 | ||
|1.7112 | |1.7112 | ||
| | |Upminor 2nd | ||
| | | | ||
|Ebv | |Ebv | ||
| Line 70: | Line 70: | ||
|133.238 | |133.238 | ||
|0.095 | |0.095 | ||
| | |Downmid 2nd | ||
| | | | ||
|Eb | |Eb | ||
| Line 79: | Line 79: | ||
|165.004 | |165.004 | ||
|<nowiki>-5.004</nowiki> | |<nowiki>-5.004</nowiki> | ||
| | |Downmajor 2nd | ||
| | | | ||
|Ev | |Ev | ||
| Line 88: | Line 88: | ||
|182.404 | |182.404 | ||
|4.262 | |4.262 | ||
| | |Major 2nd | ||
| | | | ||
|E | |E | ||
| Line 97: | Line 97: | ||
|203.910 | |203.910 | ||
|9.423 | |9.423 | ||
| | |Upmajor 2nd | ||
| | | | ||
|E^ | |E^ | ||
| Line 106: | Line 106: | ||
|231.174 | |231.174 | ||
|8.826 | |8.826 | ||
| | |2nd/3rd | ||
| | | | ||
|E# | |E# | ||
| Line 115: | Line 115: | ||
|266.871 | |266.871 | ||
|<nowiki>-0.205</nowiki> | |<nowiki>-0.205</nowiki> | ||
| | |Flat Third | ||
| | | | ||
|Fb | |Fb | ||
| Line 124: | Line 124: | ||
|294.135 | |294.135 | ||
| -0.802 | | -0.802 | ||
| | |Downminor Third | ||
| | | | ||
|Fv | |Fv | ||
| Line 133: | Line 133: | ||
|315.641 | |315.641 | ||
|4.359 | |4.359 | ||
| | |Minor Third | ||
| | | | ||
|F | |F | ||
| Line 142: | Line 142: | ||
|347.408 | |347.408 | ||
| -0.741 | | -0.741 | ||
| | |Mid Third | ||
| | | | ||
|F^ | |F^ | ||
| Line 151: | Line 151: | ||
|386.314 | |386.314 | ||
|<nowiki>-12.980</nowiki> | |<nowiki>-12.980</nowiki> | ||
| | |Downmajor Third | ||
| | | | ||
|F# | |F# | ||
| Line 160: | Line 160: | ||
|386.314 | |386.314 | ||
|13.686 | |13.686 | ||
| | |Upmajor Third | ||
| | | | ||
|F#^ | |F#^ | ||
| Line 169: | Line 169: | ||
|435.084 | |435.084 | ||
| -8.418 | | -8.418 | ||
| | |Sharp Third | ||
| | | | ||
|Gbv | |Gbv | ||
| Line 178: | Line 178: | ||
|454.294 | |454.294 | ||
| -0.961 | | -0.961 | ||
| | |Diminished 4th | ||
| | | | ||
|Gb | |Gb | ||
| Line 187: | Line 187: | ||
|470.781 | |470.781 | ||
|9.219 | |9.219 | ||
| | |Blackwood 4th | ||
| | | | ||
|Gv | |Gv | ||
| Line 196: | Line 196: | ||
|498.045 | |498.045 | ||
|8.622 | |8.622 | ||
| | |perfect 4th | ||
| | | | ||
|G | |G | ||
| Line 205: | Line 205: | ||
|533.742 | |533.742 | ||
| -0.409 | | -0.409 | ||
| | |Up 4th | ||
| | | | ||
|G^ | |G^ | ||
| Line 214: | Line 214: | ||
|563.382 | |563.382 | ||
|<nowiki>-3.382</nowiki> | |<nowiki>-3.382</nowiki> | ||
| | |Downmid 4th | ||
| | | | ||
|G# | |G# | ||
| Line 223: | Line 223: | ||
|582.512 | |582.512 | ||
|4.155 | |4.155 | ||
| | |Mid 4th | ||
| | | | ||
|G#^ | |G#^ | ||
| Line 232: | Line 232: | ||
|617.488 | |617.488 | ||
|<nowiki>-4.155</nowiki> | |<nowiki>-4.155</nowiki> | ||
| | |Mid 5th | ||
| | | | ||
|Abv | |Abv | ||
| Line 241: | Line 241: | ||
|636.618 | |636.618 | ||
|3.382 | |3.382 | ||
| | |Upmid 5th | ||
| | | | ||
|Ab | |Ab | ||
| Line 250: | Line 250: | ||
|66.258 | |66.258 | ||
|0.409 | |0.409 | ||
| | |Down 5th | ||
| | | | ||
|Av | |Av | ||
| Line 259: | Line 259: | ||
|701.955 | |701.955 | ||
| -8.622 | | -8.622 | ||
| | |Perfect 5th | ||
| | | | ||
|A | |A | ||
| Line 268: | Line 268: | ||
|729.219 | |729.219 | ||
|<nowiki>-9.219</nowiki> | |<nowiki>-9.219</nowiki> | ||
| | |Blackwood 5th | ||
| | | | ||
|A^ | |A^ | ||
| Line 277: | Line 277: | ||
|745.786 | |745.786 | ||
| 0.961 | | 0.961 | ||
| | |Augmented 5th | ||
| | | | ||
| A# | | A# | ||
| Line 286: | Line 286: | ||
|764.916 | |764.916 | ||
|8.418 | |8.418 | ||
| | |Flat 6th | ||
| | | | ||
|A#^ | |A#^ | ||
| Line 295: | Line 295: | ||
|813.686 | |813.686 | ||
|<nowiki>-13.686</nowiki> | |<nowiki>-13.686</nowiki> | ||
| | |Downminor 6th | ||
| | | | ||
|Bbv | |Bbv | ||
| Line 304: | Line 304: | ||
|813.686 | |813.686 | ||
|12.980 | |12.980 | ||
| | |Upminor 6th | ||
| | | | ||
|Bb | |Bb | ||
| Line 313: | Line 313: | ||
|852.592 | |852.592 | ||
|0.741 | |0.741 | ||
| | |Mid 6th | ||
| | | | ||
|Bv | |Bv | ||
| Line 322: | Line 322: | ||
|884.359 | |884.359 | ||
|<nowiki>-4.359</nowiki> | |<nowiki>-4.359</nowiki> | ||
| | |Major 6th | ||
| | | | ||
|B | |B | ||
| Line 331: | Line 331: | ||
|905.865 | |905.865 | ||
|0.802 | |0.802 | ||
| | |Upmajor 6th | ||
| | | | ||
|B^ | |B^ | ||
| Line 340: | Line 340: | ||
|933.129 | |933.129 | ||
|0.205 | |0.205 | ||
| | |Sharp 6th | ||
| | | | ||
|B# | |B# | ||
| Line 349: | Line 349: | ||
|968.826 | |968.826 | ||
|<nowiki>-8.826</nowiki> | |<nowiki>-8.826</nowiki> | ||
| | |6th/7th | ||
| | | | ||
|Cb | |Cb | ||
| Line 358: | Line 358: | ||
|996.089 | |996.089 | ||
|<nowiki>-9.423</nowiki> | |<nowiki>-9.423</nowiki> | ||
| | |Downminor 7th | ||
| | | | ||
|Cv | |Cv | ||
| Line 367: | Line 367: | ||
| 1017.596 | | 1017.596 | ||
|<nowiki>-4.262</nowiki> | |<nowiki>-4.262</nowiki> | ||
| | |Minor 7th | ||
| | | | ||
|C | |C | ||
| Line 376: | Line 376: | ||
|1034.996 | |1034.996 | ||
|5.004 | |5.004 | ||
| | |Upminor 7th | ||
| | | | ||
|C^ | |C^ | ||
| Line 385: | Line 385: | ||
|1066.762 | |1066.762 | ||
|<nowiki>-0.095</nowiki> | |<nowiki>-0.095</nowiki> | ||
| | |Mid 7th | ||
| | | | ||
|C# | |C# | ||
| Line 394: | Line 394: | ||
|1095.044 | |1095.044 | ||
| -1.7112 | | -1.7112 | ||
| | |Downmajor 7th | ||
| | | | ||
|C#^ | |C#^ | ||
| Line 403: | Line 403: | ||
|1119.463 | |1119.463 | ||
|0.537 | |0.537 | ||
| | |Major 7th | ||
| | | | ||
|Dbv | |Dbv | ||
| Line 412: | Line 412: | ||
|1146.727 | |1146.727 | ||
|<nowiki>-0.060</nowiki> | |<nowiki>-0.060</nowiki> | ||
| | |Upmajor 7th | ||
| | | | ||
|Db | |Db | ||
| Line 421: | Line 421: | ||
|1173.158 | |1173.158 | ||
|0.174 | |0.174 | ||
| | |Down 8ve | ||
| | | | ||
|Dv | |Dv | ||
Revision as of 10:32, 9 July 2020
45edo divides the octave into 45 equal parts of 26.667 cents. It has two major thirds, each almost equally far from Just, but as the flat one is slightly closer, it qualifies as a meantone temperament, forming a good approximation to 2/5 comma meantone. It is the optimal patent val for flattone temperament, the 7-limit 525/512 planar avicennmic temperament, the 11-limit calliope temperament tempering out 45/44 and 81/80, and the rank four temperament tempering out 45/44. It tempers out 81/80, 3125/3087, 525/512, 875/864 and 45/44. It is a flat-tending system in the 7-limit, with 3, 5 and 7 all flat, but the 11 is sharp. Also supports messed-up ennealimmal, if you want. Since 45 is a multiple of 5 and 9, it can be used to model Indonesian music in both Slendro (~ 5edo) and Pelog (~ modes of 9edo) tunings.
| Step # | ET | Just | Difference (ET minus Just) |
Ups and Downs Notation | |||
| Cents | Interval | Cents | |||||
| 0 | 0¢ | 1:1 | 0 | 0 | Unison | 1 | D |
| 1 | 26.666 | 65:64 | 26.841 | -0.174 | Up unison | D^ | |
| 2 | 53.333 | 33:32 | 53.273 | 0.060 | Downminor 2nd | D# | |
| 3 | 80.0 | 22:21 | 80.537 | -0.537 | Minor 2nd | D#^ | |
| 4 | 106.666 | 17:16 | 104.955 | 1.7112 | Upminor 2nd | Ebv | |
| 5 | 133.333 | 27:25 | 133.238 | 0.095 | Downmid 2nd | Eb | |
| 6 | 160 | 11:10 | 165.004 | -5.004 | Downmajor 2nd | Ev | |
| 7 | 186.666 | 10:9 | 182.404 | 4.262 | Major 2nd | E | |
| 8 | 213.333 | 9:8 | 203.910 | 9.423 | Upmajor 2nd | E^ | |
| 9 | 240 | 8:7 | 231.174 | 8.826 | 2nd/3rd | E# | |
| 10 | 266.666 | 7:6 | 266.871 | -0.205 | Flat Third | Fb | |
| 11 | 293.333 | 32:27 | 294.135 | -0.802 | Downminor Third | Fv | |
| 12 | 320 | 6:5 | 315.641 | 4.359 | Minor Third | F | |
| 13 | 346.666 | 11:9 | 347.408 | -0.741 | Mid Third | F^ | |
| 14 | 373.333 | 5:4- | 386.314 | -12.980 | Downmajor Third | F# | |
| 15 | 400 | 5:4+ | 386.314 | 13.686 | Upmajor Third | F#^ | |
| 16 | 426.666 | 9:7 | 435.084 | -8.418 | Sharp Third | Gbv | |
| 17 | 453.333 | 13:10 | 454.294 | -0.961 | Diminished 4th | Gb | |
| 18 | 480 | 21:16 | 470.781 | 9.219 | Blackwood 4th | Gv | |
| 19 | 506.666 | 4:3 | 498.045 | 8.622 | perfect 4th | G | |
| 20 | 533.333 | 49:36 | 533.742 | -0.409 | Up 4th | G^ | |
| 21 | 560 | 18:13 | 563.382 | -3.382 | Downmid 4th | G# | |
| 22 | 586.666 | 7:5 | 582.512 | 4.155 | Mid 4th | G#^ | |
| 23 | 613.333 | 10:7 | 617.488 | -4.155 | Mid 5th | Abv | |
| 24 | 640 | 13:9 | 636.618 | 3.382 | Upmid 5th | Ab | |
| 25 | 666.666 | 72:49 | 66.258 | 0.409 | Down 5th | Av | |
| 26 | 693.333 | 3:2 | 701.955 | -8.622 | Perfect 5th | A | |
| 27 | 720 | 32:21 | 729.219 | -9.219 | Blackwood 5th | A^ | |
| 28 | 746.666 | 20:13 | 745.786 | 0.961 | Augmented 5th | A# | |
| 29 | 773.333 | 14:9 | 764.916 | 8.418 | Flat 6th | A#^ | |
| 30 | 800 | 8:5- | 813.686 | -13.686 | Downminor 6th | Bbv | |
| 31 | 826.666 | 8:5+ | 813.686 | 12.980 | Upminor 6th | Bb | |
| 32 | 853.333 | 18:11 | 852.592 | 0.741 | Mid 6th | Bv | |
| 33 | 880 | 5:3 | 884.359 | -4.359 | Major 6th | B | |
| 34 | 906.666 | 27:16 | 905.865 | 0.802 | Upmajor 6th | B^ | |
| 35 | 933.333 | 12:7 | 933.129 | 0.205 | Sharp 6th | B# | |
| 36 | 960 | 7:4 | 968.826 | -8.826 | 6th/7th | Cb | |
| 37 | 986.666 | 16:9 | 996.089 | -9.423 | Downminor 7th | Cv | |
| 38 | 1013.333 | 9:5 | 1017.596 | -4.262 | Minor 7th | C | |
| 39 | 1040 | 20:11 | 1034.996 | 5.004 | Upminor 7th | C^ | |
| 40 | 1066.666 | 50:27 | 1066.762 | -0.095 | Mid 7th | C# | |
| 41 | 1093.333 | 32:17 | 1095.044 | -1.7112 | Downmajor 7th | C#^ | |
| 42 | 1120 | 21:11 | 1119.463 | 0.537 | Major 7th | Dbv | |
| 43 | 1146.666 | 64:33 | 1146.727 | -0.060 | Upmajor 7th | Db | |
| 44 | 1173.333 | 128:65 | 1173.158 | 0.174 | Down 8ve | Dv | |
| 45 | 1200 | 2:1 | 1200 | 0 | Octave | D | |