3/2: Difference between revisions
m Cleanup; +links |
Added table with 3/2 approximations in different EDOs (5-EDO to 31-EDO). Also added a overview of the fifths classes (and their resulting EDOs). |
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{| class="wikitable" | |||
|+Comparison of 3/2 approximations and "fifth classes", with 3/2 = 701.955 cents. | |||
(from 5-EDO to 31-EDO, no subsets of 12-EDO.) | |||
![[EDO]] | |||
!degree | |||
!cents | |||
!fifth category | |||
!error | |||
|- | |||
|5 | |||
|3/5 | |||
|720 | |||
|pentatonic EDO | |||
| +18.045¢ | |||
|- | |||
|7 | |||
|4/7 | |||
|685.714 | |||
|perfect EDO | |||
| -16.241¢ | |||
|- | |||
|8 | |||
|5/8 | |||
|750 | |||
|supersharp EDO | |||
| +48.045¢ | |||
|- | |||
|9 | |||
|5/9 | |||
|666.667 | |||
|superflat EDO | |||
| -35.288¢ | |||
|- | |||
|10 | |||
|6/10 | |||
|720 | |||
|pentatonic EDO | |||
| +18.045¢ | |||
|- | |||
|11 | |||
|6/11 | |||
|654.545 | |||
|superflat EDO | |||
| -47.41¢ | |||
|- | |||
|12 | |||
|7/12 | |||
|700 | |||
|diatonic EDO | |||
| -1.955¢ | |||
|- | |||
|13 | |||
|8/13 | |||
|738.462 | |||
|supersharp EDO | |||
| +36.507¢ | |||
|- | |||
|14 | |||
|8/14 | |||
|685.714 | |||
|perfect EDO | |||
| -16.241¢ | |||
|- | |||
|15 | |||
|9/15 | |||
|720 | |||
|pentatonic EDO | |||
| +18.045¢ | |||
|- | |||
|16 | |||
|9/16 | |||
|675 | |||
|superflat EDO | |||
| -26.955¢ | |||
|- | |||
|17 | |||
|10/17 | |||
|705.882 | |||
|diatonic EDO | |||
| +3.927¢ | |||
|- | |||
|18 | |||
|11/18 | |||
|733.333 | |||
|supersharp EDO | |||
| +31.378¢ | |||
|- | |||
|19 | |||
|11/19 | |||
|694.737 | |||
|diatonic EDO | |||
| -7.218¢ | |||
|- | |||
|20 | |||
|12/20 | |||
|720 | |||
|pentatonic EDO | |||
| +18.045¢ | |||
|- | |||
|21 | |||
|12/21 | |||
|685.714 | |||
|perfect EDO | |||
| -16.241¢ | |||
|- | |||
|22 | |||
|13/22 | |||
|709.091 | |||
|diatonic EDO | |||
| +7.136¢ | |||
|- | |||
|23 | |||
|13/23 | |||
|678.261 | |||
|superflat EDO | |||
| -23.694¢ | |||
|- | |||
|24 | |||
|14/24 | |||
|700 | |||
|diatonic EDO | |||
| -1.955¢ | |||
|- | |||
|25 | |||
|15/25 | |||
|720 | |||
|pentatonic EDO | |||
| +18.045¢ | |||
|- | |||
|26 | |||
|15/26 | |||
|692.308 | |||
|diatonic EDO | |||
| -9.647¢ | |||
|- | |||
|27 | |||
|16/27 | |||
|711.111 | |||
|diatonic EDO | |||
| +9.156¢ | |||
|- | |||
|28 | |||
|16/28 | |||
|685.714 | |||
|perfect EDO | |||
| -16.241¢ | |||
|- | |||
|29 | |||
|17/29 | |||
|703.448 | |||
|diatonic EDO | |||
| +1.493¢ | |||
|- | |||
|30 | |||
|17/30 | |||
|720 | |||
|pentatonic EDO | |||
| +18.045¢ | |||
|- | |||
|31 | |||
|18/31 | |||
|696.774 | |||
|diatonic EDO | |||
| -5.181¢ | |||
|} | |||
* The many and various 3/2 approximations in different EDOs can be classified as (after [[Kite Giedraitis]]): | |||
** '''superflat''' EDO - fifth is narrower than 686 cents. | |||
** '''perfect''' EDO - fifth is 686 cents wide (and 4/7 steps). | |||
** '''diatonic''' EDO - fifth is between 686.1 - 719.9 cents wide. | |||
** '''pentatonic''' EDO - fifth is exactly 720 cents wide. | |||
** '''supersharp''' EDO - fifth is wider than 720 cents. | |||
== See also == | == See also == | ||