27edo: Difference between revisions
m →Intervals: style |
updated ups/down notation, added color names to the comma list, general cleanup |
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= | ==Theory== | ||
If octaves are kept pure, 27edo divides the [[Octave|octave]] in 27 equal parts each exactly 44.444... [[cent|cent]]s in size. However, 27 is a prime candidate for [[octave_shrinking|octave shrinking]], and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the [[5/4|third]], [[3/2|fifth]] and [[7/4|7/4]] sharply. | If octaves are kept pure, 27edo divides the [[Octave|octave]] in 27 equal parts each exactly 44.444... [[cent|cent]]s in size. However, 27 is a prime candidate for [[octave_shrinking|octave shrinking]], and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the [[5/4|third]], [[3/2|fifth]] and [[7/4|7/4]] sharply. | ||
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| style="text-align:center;" | di | | style="text-align:center;" | di | ||
| style="text-align:center;" | ^1, m2 | | style="text-align:center;" | ^1, m2 | ||
| style="text-align:center;" | minor 2nd | | style="text-align:center;" | up-unison, minor 2nd | ||
| style="text-align:center;" | Eb | | style="text-align:center;" | ^D, Eb | ||
|- | |- | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
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| style="text-align:center;" | 16/15, 21/20, 25/24 | | style="text-align:center;" | 16/15, 21/20, 25/24 | ||
| style="text-align:center;" | ra | | style="text-align:center;" | ra | ||
| style="text-align:center;" | | | style="text-align:center;" | ^m2 | ||
| style="text-align:center;" | upminor 2nd | | style="text-align:center;" | upminor 2nd | ||
| style="text-align:center;" | Eb | | style="text-align:center;" | ^Eb | ||
|- | |- | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
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| style="text-align:center;" | ~2 | | style="text-align:center;" | ~2 | ||
| style="text-align:center;" | mid 2nd | | style="text-align:center;" | mid 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | vvE | ||
|- | |- | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
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| style="text-align:center;" | vM2 | | style="text-align:center;" | vM2 | ||
| style="text-align:center;" | downmajor 2nd | | style="text-align:center;" | downmajor 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | vE | ||
|- | |- | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
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| style="text-align:center;" | ^m3 | | style="text-align:center;" | ^m3 | ||
| style="text-align:center;" | upminor 3rd | | style="text-align:center;" | upminor 3rd | ||
| style="text-align:center;" | F | | style="text-align:center;" | ^F | ||
|- | |- | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
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| style="text-align:center;" | ~3 | | style="text-align:center;" | ~3 | ||
| style="text-align:center;" | mid 3rd | | style="text-align:center;" | mid 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^F | ||
|- | |- | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
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| style="text-align:center;" | vM3 | | style="text-align:center;" | vM3 | ||
| style="text-align:center;" | downmajor 3rd | | style="text-align:center;" | downmajor 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | vF# | ||
|- | |- | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
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| style="text-align:center;" | ^4 | | style="text-align:center;" | ^4 | ||
| style="text-align:center;" | up 4th | | style="text-align:center;" | up 4th | ||
| style="text-align:center;" | G | | style="text-align:center;" | ^G | ||
|- | |- | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
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| style="text-align:center;" | 7/5, 18/13 | | style="text-align:center;" | 7/5, 18/13 | ||
| style="text-align:center;" | fi | | style="text-align:center;" | fi | ||
| style="text-align:center;" | | | style="text-align:center;" | ~4 | ||
| style="text-align:center;" | | | style="text-align:center;" | mid 4th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^G | ||
|- | |- | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
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| style="text-align:center;" | 10/7, 13/9 | | style="text-align:center;" | 10/7, 13/9 | ||
| style="text-align:center;" | se | | style="text-align:center;" | se | ||
| style="text-align:center;" | | | style="text-align:center;" | ~5 | ||
| style="text-align:center;" | | | style="text-align:center;" | mid 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvA | ||
|- | |- | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
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| style="text-align:center;" | v5 | | style="text-align:center;" | v5 | ||
| style="text-align:center;" | down fifth | | style="text-align:center;" | down fifth | ||
| style="text-align:center;" | | | style="text-align:center;" | vA | ||
|- | |- | ||
| style="text-align:center;" | 16 | | style="text-align:center;" | 16 | ||
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| style="text-align:center;" | ^m6 | | style="text-align:center;" | ^m6 | ||
| style="text-align:center;" | upminor 6th | | style="text-align:center;" | upminor 6th | ||
| style="text-align:center;" | Bb | | style="text-align:center;" | ^Bb | ||
|- | |- | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
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| style="text-align:center;" | ~6 | | style="text-align:center;" | ~6 | ||
| style="text-align:center;" | mid 6th | | style="text-align:center;" | mid 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvB | ||
|- | |- | ||
| style="text-align:center;" | 20 | | style="text-align:center;" | 20 | ||
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| style="text-align:center;" | vM6 | | style="text-align:center;" | vM6 | ||
| style="text-align:center;" | downmajor 6th | | style="text-align:center;" | downmajor 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | vB | ||
|- | |- | ||
| style="text-align:center;" | 21 | | style="text-align:center;" | 21 | ||
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| style="text-align:center;" | ^m7 | | style="text-align:center;" | ^m7 | ||
| style="text-align:center;" | upminor 7th | | style="text-align:center;" | upminor 7th | ||
| style="text-align:center;" | C | | style="text-align:center;" | ^C | ||
|- | |- | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
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| style="text-align:center;" | ~7 | | style="text-align:center;" | ~7 | ||
| style="text-align:center;" | mid 7th | | style="text-align:center;" | mid 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^C | ||
|- | |- | ||
| style="text-align:center;" | 25 | | style="text-align:center;" | 25 | ||
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| style="text-align:center;" | vM7 | | style="text-align:center;" | vM7 | ||
| style="text-align:center;" | downmajor 7th | | style="text-align:center;" | downmajor 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | vC# | ||
|- | |- | ||
| style="text-align:center;" | 26 | | style="text-align:center;" | 26 | ||
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| style="text-align:center;" | 10:12:15 | | style="text-align:center;" | 10:12:15 | ||
| style="text-align:center;" | 0-7-16 | | style="text-align:center;" | 0-7-16 | ||
| style="text-align:center;" | C Eb | | style="text-align:center;" | C ^Eb G | ||
| style="text-align:center;" | C | | style="text-align:center;" | C^m | ||
| style="text-align:center;" | C upminor | | style="text-align:center;" | C upminor | ||
|- | |- | ||
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| style="text-align:center;" | 18:22:27 | | style="text-align:center;" | 18:22:27 | ||
| style="text-align:center;" | 0-8-16 | | style="text-align:center;" | 0-8-16 | ||
| style="text-align:center;" | C | | style="text-align:center;" | C vvE G | ||
| style="text-align:center;" | C~ | | style="text-align:center;" | C~ | ||
| style="text-align:center;" | C mid | | style="text-align:center;" | C mid | ||
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| style="text-align:center;" | 4:5:6 | | style="text-align:center;" | 4:5:6 | ||
| style="text-align:center;" | 0-9-16 | | style="text-align:center;" | 0-9-16 | ||
| style="text-align:center;" | C | | style="text-align:center;" | C vE G | ||
| style="text-align:center;" | | | style="text-align:center;" | Cv | ||
| style="text-align:center;" | C downmajor or C | | style="text-align:center;" | C downmajor or C down | ||
|- | |- | ||
| style="text-align:center;" | ru | | style="text-align:center;" | ru | ||
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==Commas== | ==Commas== | ||
27 EDO tempers out the following commas. (Note: This assumes the val < 27 43 63 76 93 100 |.) | 27 EDO tempers out the following [[commas]]. (Note: This assumes the val < 27 43 63 76 93 100 |.) | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | | ! | [[Ratio]] | ||
! | Monzo | ! | [[Monzo]] | ||
! | | ! | Cents | ||
![[Color notation/Temperament Names|Color Name]] | |||
! | Name 1 | ! | Name 1 | ||
! | Name 2 | ! | Name 2 | ||
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| |<nowiki> | 7 0 -3 </nowiki>> | | |<nowiki> | 7 0 -3 </nowiki>> | ||
| style="text-align:right;" | 41.06 | | style="text-align:right;" | 41.06 | ||
| style="text-align:center;" |Trigu | |||
| style="text-align:center;" | Diesis | | style="text-align:center;" | Diesis | ||
| style="text-align:center;" | Augmented Comma | | style="text-align:center;" | Augmented Comma | ||
| Line 438: | Line 440: | ||
| |<nowiki> | 5 -9 4 </nowiki>> | | |<nowiki> | 5 -9 4 </nowiki>> | ||
| style="text-align:right;" | 27.66 | | style="text-align:right;" | 27.66 | ||
| style="text-align:center;" |Saquadyo | |||
| style="text-align:center;" | Minimal Diesis | | style="text-align:center;" | Minimal Diesis | ||
| style="text-align:center;" | Tetracot Comma | | style="text-align:center;" | Tetracot Comma | ||
| Line 445: | Line 448: | ||
| |<nowiki> | 2 9 -7 </nowiki>> | | |<nowiki> | 2 9 -7 </nowiki>> | ||
| style="text-align:right;" | 13.40 | | style="text-align:right;" | 13.40 | ||
| style="text-align:center;" |Sepgu | |||
| style="text-align:center;" | Medium Semicomma | | style="text-align:center;" | Medium Semicomma | ||
| style="text-align:center;" | Sensipent Comma | | style="text-align:center;" | Sensipent Comma | ||
| Line 452: | Line 456: | ||
| |<nowiki> | 1 -27 18 </nowiki>> | | |<nowiki> | 1 -27 18 </nowiki>> | ||
| style="text-align:right;" | 0.86 | | style="text-align:right;" | 0.86 | ||
| style="text-align:center;" |Satritribiyo | |||
| style="text-align:center;" | Ennealimma | | style="text-align:center;" | Ennealimma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 459: | Line 464: | ||
| |<nowiki> | 1 -3 -2 3 </nowiki>> | | |<nowiki> | 1 -3 -2 3 </nowiki>> | ||
| style="text-align:right;" | 27.99 | | style="text-align:right;" | 27.99 | ||
| style="text-align:center;" |Trizo-agugu | |||
| style="text-align:center;" | Senga | | style="text-align:center;" | Senga | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 466: | Line 472: | ||
| |<nowiki> | 6 -2 0 -1 </nowiki>> | | |<nowiki> | 6 -2 0 -1 </nowiki>> | ||
| style="text-align:right;" | 27.26 | | style="text-align:right;" | 27.26 | ||
| style="text-align:center;" |Ru | |||
| style="text-align:center;" | Septimal Comma | | style="text-align:center;" | Septimal Comma | ||
| style="text-align:center;" | Archytas' Comma | | style="text-align:center;" | Archytas' Comma | ||
| Line 473: | Line 480: | ||
| |<nowiki> | -4 1 -5 5 </nowiki>> | | |<nowiki> | -4 1 -5 5 </nowiki>> | ||
| style="text-align:right;" | 14.52 | | style="text-align:right;" | 14.52 | ||
| style="text-align:center;" |Quinzogu | |||
| style="text-align:center;" | Trimyna | | style="text-align:center;" | Trimyna | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 480: | Line 488: | ||
| |<nowiki> | 0 -5 1 2 </nowiki>> | | |<nowiki> | 0 -5 1 2 </nowiki>> | ||
| style="text-align:right;" | 14.19 | | style="text-align:right;" | 14.19 | ||
| style="text-align:center;" |Zozoyo | |||
| style="text-align:center;" | Sensamagic | | style="text-align:center;" | Sensamagic | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 487: | Line 496: | ||
| |<nowiki> | 1 2 -3 1 </nowiki>> | | |<nowiki> | 1 2 -3 1 </nowiki>> | ||
| style="text-align:right;" | 13.79 | | style="text-align:right;" | 13.79 | ||
| style="text-align:center;" |Zotrigu | |||
| style="text-align:center;" | Septimal Semicomma | | style="text-align:center;" | Septimal Semicomma | ||
| style="text-align:center;" | Starling Comma | | style="text-align:center;" | Starling Comma | ||
| Line 494: | Line 504: | ||
| |<nowiki> | 5 -4 3 -2 </nowiki>> | | |<nowiki> | 5 -4 3 -2 </nowiki>> | ||
| style="text-align:right;" | 13.47 | | style="text-align:right;" | 13.47 | ||
| style="text-align:center;" |Rurutriyo | |||
| style="text-align:center;" | Octagar | | style="text-align:center;" | Octagar | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 501: | Line 512: | ||
| |<nowiki> | 6 3 -1 -3 </nowiki>> | | |<nowiki> | 6 3 -1 -3 </nowiki>> | ||
| style="text-align:right;" | 13.07 | | style="text-align:right;" | 13.07 | ||
| style="text-align:center;" |Triru-agu | |||
| style="text-align:center;" | Orwellisma | | style="text-align:center;" | Orwellisma | ||
| style="text-align:center;" | Orwell Comma | | style="text-align:center;" | Orwell Comma | ||
| Line 508: | Line 520: | ||
| |<nowiki> | -6 -8 2 5 </nowiki>> | | |<nowiki> | -6 -8 2 5 </nowiki>> | ||
| style="text-align:right;" | 1.12 | | style="text-align:right;" | 1.12 | ||
| style="text-align:center;" |Quinzo-ayoyo | |||
| style="text-align:center;" | Wizma | | style="text-align:center;" | Wizma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 515: | Line 528: | ||
| |<nowiki> | -5 -1 -2 4 </nowiki>> | | |<nowiki> | -5 -1 -2 4 </nowiki>> | ||
| style="text-align:right;" | 0.72 | | style="text-align:right;" | 0.72 | ||
| style="text-align:center;" |Bizozogu | |||
| style="text-align:center;" | Breedsma | | style="text-align:center;" | Breedsma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 522: | Line 536: | ||
| |<nowiki> | -1 -7 4 1 </nowiki>> | | |<nowiki> | -1 -7 4 1 </nowiki>> | ||
| style="text-align:right;" | 0.40 | | style="text-align:right;" | 0.40 | ||
| style="text-align:center;" |Zoquadyo | |||
| style="text-align:center;" | Ragisma | | style="text-align:center;" | Ragisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 529: | Line 544: | ||
| |<nowiki> | -4 6 -6 3 </nowiki>> | | |<nowiki> | -4 6 -6 3 </nowiki>> | ||
| style="text-align:right;" | 0.33 | | style="text-align:right;" | 0.33 | ||
| style="text-align:center;" |Trizogugu | |||
| style="text-align:center;" | Landscape Comma | | style="text-align:center;" | Landscape Comma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 536: | Line 552: | ||
| |<nowiki> | -1 2 0 -2 1 </nowiki>> | | |<nowiki> | -1 2 0 -2 1 </nowiki>> | ||
| style="text-align:right;" | 17.58 | | style="text-align:right;" | 17.58 | ||
| style="text-align:center;" |Loruru | |||
| style="text-align:center;" | Mothwellsma | | style="text-align:center;" | Mothwellsma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 543: | Line 560: | ||
| |<nowiki> | 7 -4 0 1 -1 </nowiki>> | | |<nowiki> | 7 -4 0 1 -1 </nowiki>> | ||
| style="text-align:right;" | 9.69 | | style="text-align:right;" | 9.69 | ||
| style="text-align:center;" |Saluzo | |||
| style="text-align:center;" | Pentacircle | | style="text-align:center;" | Pentacircle | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 550: | Line 568: | ||
| |<nowiki> | -7 -1 1 1 1 </nowiki>> | | |<nowiki> | -7 -1 1 1 1 </nowiki>> | ||
| style="text-align:right;" | 4.50 | | style="text-align:right;" | 4.50 | ||
| style="text-align:center;" |Lozoyo | |||
| style="text-align:center;" | Keenanisma | | style="text-align:center;" | Keenanisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 557: | Line 576: | ||
| |<nowiki> | -1 -2 -1 1 0 1 </nowiki>> | | |<nowiki> | -1 -2 -1 1 0 1 </nowiki>> | ||
| style="text-align:right;" | 19.13 | | style="text-align:right;" | 19.13 | ||
| style="text-align:center;" |Thozogu | |||
| style="text-align:center;" | Superleap | | style="text-align:center;" | Superleap | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 562: | Line 582: | ||
|} | |} | ||
=Music= | ==Music== | ||
* [http://www.archive.org/details/MusicForYourEars Music For Your Ears] ([http://www.archive.org/download/MusicForYourEars/musicfor.mp3 play]) by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]]. | * [http://www.archive.org/details/MusicForYourEars Music For Your Ears] ([http://www.archive.org/download/MusicForYourEars/musicfor.mp3 play]) by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]]. | ||