15edo/Unque's compositional approach: Difference between revisions
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Removed subtle joke poking fun at porcupine inaccuracy ("10/9" link leads to the 11/10 page). Obviously, not fit for main space material, and is so obscure anyways that it just looks like a mistake. |
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{| class="wikitable" | {| class="wikitable" | ||
|+Intervals of 15edo | |+Intervals of 15edo | ||
!Interval | ! Interval | ||
!Cents | ! Cents | ||
!JI intervals | ! JI intervals | ||
!As a generator | ! As a generator | ||
!Notes | ! Notes | ||
|- | |- | ||
|1\15 | | 1\15 | ||
|80 | | 80 | ||
|[[23/22]], [[21/20]] | | [[23/22]], [[21/20]] | ||
|[[Valentine]] | | [[Valentine]] | ||
|Melodic semitone | | Melodic semitone | ||
|- | |- | ||
|2\15 | | 2\15 | ||
|160 | | 160 | ||
|[[12/11]], [[ | | [[12/11]], [[10/9]] | ||
|[[Porcupine]] | | [[Porcupine]] | ||
|One possible choice of whole tone (see below) | | One possible choice of whole tone (see below) | ||
|- | |- | ||
|3\15 | | 3\15 | ||
|240 | | 240 | ||
|[[8/7]], [[38/33]] | | [[8/7]], [[38/33]] | ||
|[[5edo]], [[Slendric]] | | [[5edo]], [[Slendric]] | ||
|One possible choice of whole tone (see below) | | One possible choice of whole tone (see below) | ||
|- | |- | ||
|4\15 | | 4\15 | ||
|320 | | 320 | ||
|[[6/5]] | | [[6/5]] | ||
|[[Kleismic]] | | [[Kleismic]] | ||
|Relatively accurate, though noticeably sharper than optimal kleismic | | Relatively accurate, though noticeably sharper than optimal kleismic | ||
|- | |- | ||
|5\15 | | 5\15 | ||
|400 | | 400 | ||
|[[5/4]], [[14/11]] | | [[5/4]], [[14/11]] | ||
|[[3edo]]; [[triforce]] period | | [[3edo]]; [[triforce]] period | ||
|Same mapping as [[12edo]] | | Same mapping as [[12edo]] | ||
|- | |- | ||
|6\15 | | 6\15 | ||
|480 | | 480 | ||
|[[29/22]], [[4/3]] | | [[29/22]], [[4/3]] | ||
|5edo; [[ | | 5edo; [[blackwood]] period | ||
|Highly contentious interpretation; see below | | Highly contentious interpretation; see below | ||
|- | |- | ||
|7\15 | | 7\15 | ||
|560 | | 560 | ||
|[[15/11]], [[11/8]] | | [[15/11]], [[11/8]] | ||
|[[Thuja]] | | [[Thuja]] | ||
| | | | ||
|- | |- | ||
|8\15 | | 8\15 | ||
|640 | | 640 | ||
|[[16/11]] | | [[16/11]] | ||
|Thuja | | Thuja | ||
| | | | ||
|- | |- | ||
|9\15 | | 9\15 | ||
|720 | | 720 | ||
|[[3/2]], [[50/33]] | | [[3/2]], [[50/33]] | ||
|5edo; blackwood period | | 5edo; blackwood period | ||
|Highly contentious interpretation; see below | | Highly contentious interpretation; see below | ||
|- | |- | ||
|10\15 | | 10\15 | ||
|800 | | 800 | ||
|[[8/5]], [[35/22]] | | [[8/5]], [[35/22]] | ||
|3edo; triforce period | | 3edo; triforce period | ||
|Same mapping as 12edo | | Same mapping as 12edo | ||
|- | |- | ||
|11\15 | | 11\15 | ||
|880 | | 880 | ||
|[[5/3]] | | [[5/3]] | ||
|Kleismic | | Kleismic | ||
|Relatively accurate, though noticeably flatter than optimal kleismic | | Relatively accurate, though noticeably flatter than optimal kleismic | ||
|- | |- | ||
|12\15 | | 12\15 | ||
|960 | | 960 | ||
|[[7/4]], [[19/11]] | | [[7/4]], [[19/11]] | ||
|5edo, Slendric | | 5edo, Slendric | ||
| | | | ||
|- | |- | ||
|13\15 | | 13\15 | ||
|1040 | | 1040 | ||
|[[ | | [[9/5]], [[11/6]] | ||
|Porcupine | | Porcupine | ||
| | | | ||
|- | |- | ||
|14\15 | | 14\15 | ||
|1120 | | 1120 | ||
|[[21/11]] | | [[21/11]] | ||
|Valentine | | Valentine | ||
| | | | ||
|- | |- | ||
|15\15 | | 15\15 | ||
|1200 | | 1200 | ||
|[[2/1]] | | [[2/1]] | ||
| | | | ||
|Tuned justly | | Tuned justly | ||
|} | |} | ||
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This interpretation may also be criticized once again due to a lack of accuracy, but it is notably more consistent than the Carlos Alpha interpretations as the difference between the tunings does not accrue per step. | This interpretation may also be criticized once again due to a lack of accuracy, but it is notably more consistent than the Carlos Alpha interpretations as the difference between the tunings does not accrue per step. | ||
=== 15edo and Mode 31 === | |||
[[31afdo|Mode 31]] of the Harmonic Series provides yet another lens through which to interpret 15edo. The intervals [0 2 5 6 7 8 9 10 12 15] can be interpreted as an approximation of the chord 31:34:39:41:43:45:47:49:54:62. Additionally, 11\15 can be interpreted somewhat inaccurately as 52/31; in spite of the error, this interval naturally lends itself to the structure of 15edo. Similarly, 13\15 and 14\15 can be interpreted respectively as 57/31 and 59/31. Finally, 1\15 can be said to represent 32/31 or 33/31, both with very high error but lending well to the harmonic structure of 15edo. | |||
This yields the full chord 31:33:34:39:41:43:45:47:49:52:54:57:59:62. | |||
=== 15edo's fifth === | === 15edo's fifth === | ||
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[[Category:15edo]] | [[Category:15edo]] | ||
[[Category:Approaches to tuning systems]] | [[Category:Approaches to tuning systems]] | ||