60edo: Difference between revisions
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The 60 equal division divides the octave into 60 parts of exactly 20 cents each | The '''60 equal division''' divides the octave into 60 parts of exactly 20 cents each. | ||
= | == Theory == | ||
Since 60 = 5×12, 60edo belongs to the family of edos which contain [[12edo]], and like the other small edos of this kind, it tempers out the [[Pythagorean comma]], 531441/524288 = {{monzo|-19 12}}. In the [[5-limit]], it tempers out both the [[magic comma]], 3125/3072, and the [[amity comma]], 1600000/1594323, and supplies the optimal patent val for 5-limit [[magic]], tempering out 3125/3072. In the [[7-limit]] it tempers out [[875/864]], [[245/243]], [[225/224]] and [[10976/10935]], and supports [[magic]], [[compton]] and [[tritonic]] temperaments. In the [[11-limit]], the 60e [[val]] scores lower in [[badness]] than the [[patent val]], and makes for an excellent tritonic tuning. It tempers out [[121/120]] and [[441/440]], whereas the patent val tempers out [[100/99]], [[385/384]] and [[540/539]]. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for [[13-limit]] tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 [[Chromatic_pairs#Bleu|bleu temperament]]. | |||
{| class="wikitable" | == Intervals == | ||
{| class="wikitable center-all right-2 left-3 left-4" | |||
|- | |- | ||
! Degrees | |||
! Cents | |||
! Approximate Ratios<br>in the 2.3.5.13 subgroup | |||
! Additional Ratios<br>of 7 and 11 (tending flat, i.e. 60e val) | |||
|- | |- | ||
| 0 | | 0 | ||
|0 | | 0 | ||
| | |||
| | |||
|- | |- | ||
| | 1 | | | 1 | ||
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|} | |} | ||
=Compositions= | == Compositions == | ||
[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/rojqoq.html Rojqoq (So-Called Peace)] [http://micro.soonlabel.com/gene_ward_smith/Others/Sethares/Rojqoq.mp3 play] by William Sethares | [http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/rojqoq.html Rojqoq (So-Called Peace)] [http://micro.soonlabel.com/gene_ward_smith/Others/Sethares/Rojqoq.mp3 play] by William Sethares | ||
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by Graham Breed | by Graham Breed | ||
=Images= | == Images == | ||
[[File:60edo_wheel_with_cents_values.png|alt=60edo wheel with cents values.png|560x560px|60edo wheel with cents values.png]] | [[File:60edo_wheel_with_cents_values.png|alt=60edo wheel with cents values.png|560x560px|60edo wheel with cents values.png]] | ||
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Robin Perry guitar | Robin Perry guitar | ||
[[Category:60edo]] | [[Category:60edo]] | ||
[[Category:edo]] | [[Category:edo]] | ||
[[Category:listen]] | [[Category:listen]] | ||
Revision as of 07:06, 15 August 2020
The 60 equal division divides the octave into 60 parts of exactly 20 cents each.
Theory
Since 60 = 5×12, 60edo belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the Pythagorean comma, 531441/524288 = [-19 12⟩. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports magic, compton and tritonic temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 bleu temperament.
Intervals
| Degrees | Cents | Approximate Ratios in the 2.3.5.13 subgroup |
Additional Ratios of 7 and 11 (tending flat, i.e. 60e val) |
|---|---|---|---|
| 0 | 0 | ||
| 1 | 20 | ||
| 2 | 40 | ||
| 3 | 60 | ||
| 4 | 80 | ||
| 5 | 100 | ||
| 6 | 120 | 16/15 | 15/14 |
| 7 | 140 | 13/12 | |
| 8 | 160 | 12/11, 11/10 | |
| 9 | 180 | 10/9 | |
| 10 | 200 | 9/8 | |
| 11 | 220 | ||
| 12 | 240 | 15/13 | 8/7 |
| 13 | 260 | 7/6 | |
| 14 | 280 | 13/11, 33/28 | |
| 15 | 300 | ||
| 16 | 320 | 6/5 | |
| 17 | 340 | 11/9 | |
| 18 | 360 | 16/13 | 27/22 |
| 19 | 380 | 5/4 | |
| 20 | 400 | ||
| 21 | 420 | 33/26, 14/11 | |
| 22 | 440 | 9/7 | |
| 23 | 460 | 13/10 | |
| 24 | 480 | ||
| 25 | 500 | 4/3 | |
| 26 | 520 | ||
| 27 | 540 | 11/8, 15/11 | |
| 28 | 560 | 18/13 | |
| 29 | 580 | 7/5 | |
| 30 | 600 | ||
| 31 | 620 | 10/7 | |
| 32 | 640 | 13/9 | |
| 33 | 660 | 16/11, 22/15 | |
| 34 | 680 | ||
| 35 | 700 | 3/2 | |
| 36 | 720 | ||
| 37 | 740 | 20/13 | |
| 38 | 760 | 14/9 | |
| 39 | 780 | 52/33, 11/7 | |
| 40 | 800 | ||
| 41 | 820 | 8/5 | |
| 42 | 840 | 13/8 | |
| 43 | 860 | 18/11, 44/27 | |
| 44 | 880 | 5/3 | |
| 45 | 900 | ||
| 46 | 920 | 22/13, 56/33 | |
| 47 | 940 | 12/7 | |
| 48 | 960 | 26/15 | 7/4 |
| 49 | 980 | ||
| 50 | 1000 | 16/9 | |
| 51 | 1020 | 9/5 | |
| 52 | 1040 | 11/6, 20/11 | |
| 53 | 1060 | ||
| 54 | 1080 | 15/8 | 28/15 |
| 55 | 1100 | ||
| 56 | 1120 | ||
| 57 | 1140 | ||
| 58 | 1160 | ||
| 59 | 1180 | ||
| 60 | 1200 |
Compositions
Rojqoq (So-Called Peace) play by William Sethares
Black Salt - White Pepper play
all by Robin Perry
Dingshi and
Gene's Jitterbug (ogg) Gene's Jitterbug (mp3) Score
by Graham Breed
Images
Robin Perry guitar