15edo: Difference between revisions
m cat sorting |
added M2, m2 and A1 to the template, moved the primes-error table up to the top |
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| Prime factorization = 3 * 5 | | Prime factorization = 3 * 5 | ||
| Subgroup = 2.3.5.7.11 | | Subgroup = 2.3.5.7.11 | ||
| Step size = | | Step size = 80¢ | ||
| Fifth type = [[5edo]] | | Fifth type = 9\15 = 720¢ = [[5edo]] | ||
| Major 2nd = 3\15 = 240¢ | |||
| Minor 2nd = 0\15 = 0¢ | |||
| Augmented 1sn = 3\15 = 240¢ | |||
| Common uses = blackwood, porcupine | | Common uses = blackwood, porcupine | ||
| Important MOS = [[blackwood]] 5L5s 2121212121 (2\15, 1\5)<br/>[[porcupine]] 7L1s 12222222 (2\15, 1\1)<br/>[[orgone]]/[[hanson]] 4L3s 3313131 (4\15, 1\2)<br/>[[augmented]] ([[augene]]) 3L6s 311311311 (1\15, 1\3)<br/>[[triforce]] 6L3s 221221221 (2\15, 1\3) | | Important MOS = [[blackwood]] 5L5s 2121212121 (2\15, 1\5)<br/>[[porcupine]] 7L1s 12222222 (2\15, 1\1)<br/>[[orgone]]/[[hanson]] 4L3s 3313131 (4\15, 1\2)<br/>[[augmented]] ([[augene]]) 3L6s 311311311 (1\15, 1\3)<br/>[[triforce]] 6L3s 221221221 (2\15, 1\3) | ||
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'''15 equal temperament''' or 15-EDO is a tuning which divides the octave into 15 equally spaced pitches. | '''15 equal temperament''' or 15-EDO is a tuning which divides the octave into 15 equally spaced pitches. | ||
== Theory == | |||
{| class="wikitable" | |||
! | |||
!prime 2 | |||
!prime 3 | |||
!prime 5 | |||
!prime 7 | |||
!prime 11 | |||
!prime 13 | |||
!prime 17 | |||
!prime 19 | |||
|- | |||
!Error (¢) | |||
|0 | |||
|18.04 | |||
|13.7 | |||
| -8.8 | |||
|8.7 | |||
|39.5 | |||
| -25.0 | |||
|22.5 | |||
|- | |||
!Error (%) | |||
|0 | |||
|23 | |||
|17 | |||
| -11 | |||
|11 | |||
|49 | |||
| -31 | |||
|28 | |||
|- | |||
![[Patent val|Nearest edomapping]] | |||
|15 | |||
|9 | |||
|5 | |||
|12 | |||
|7 | |||
|11 | |||
|1 | |||
|4 | |||
|} | |||
15-edo can be thought of as three sets of 5-EDO which do not connect by fifths. The fifth at 720 cents is quite wide yet still useable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15 EDO returns to the octave if stacked five times which is radically different than a meantone system. | 15-edo can be thought of as three sets of 5-EDO which do not connect by fifths. The fifth at 720 cents is quite wide yet still useable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15 EDO returns to the octave if stacked five times which is radically different than a meantone system. | ||
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A recommended method to the notation of 15-edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the "quill" is the name given to the two step interval (160¢) of 15-edo while the "small quill" (80¢) is the chroma of 15-edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15-edo into a seven nominal based framework. | A recommended method to the notation of 15-edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the "quill" is the name given to the two step interval (160¢) of 15-edo while the "small quill" (80¢) is the chroma of 15-edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15-edo into a seven nominal based framework. | ||
[[File:15_tone_keyboard.png|left|thumb|400x400px|Porcupine layout for 15edo]] | |||
[[File:Screen Shot 2020-04-23 at 11.59.17 PM.png|left|thumb|Hanson layout for 15edo]] | |||
<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br> | |||
== Intervals == | == Intervals == | ||