72edo: Difference between revisions
No edit summary |
added the template, moved the primes-error table up to the top |
||
| Line 5: | Line 5: | ||
| es = | | es = | ||
| ja = | | ja = | ||
}} | |||
{{Infobox ET | |||
| Prime factorization = 2<sup>3</sup> × 3<sup>2</sup> | |||
| Step size = 16.667¢ | |||
| Fifth = 42\72 = 700¢ (→[[12edo|7\12]]) | |||
| Major 2nd = 12\72 = 200¢ | |||
| Minor 2nd = 6\72 = 100¢ | |||
| Augmented 1sn = 6\72 = 100¢ | |||
}} | }} | ||
== Theory == | == Theory == | ||
'''72-tone equal temperament''', or '''72-edo''', divides the octave into 72 steps or ''moria''. This produces a twelfth-tone tuning, with the whole tone measuring 200 cents, the same as in 12-tone equal temperament. 72-tone is also a superset of [[24edo|24-tone equal temperament]], a common and standard tuning of [[Arabic,_Turkish,_Persian|Arabic]] music, and has itself been used to tune Turkish music. | {| class="wikitable center-all" | ||
! colspan="2" | | |||
! prime 2 | |||
! prime 3 | |||
! prime 5 | |||
! prime 7 | |||
! prime 11 | |||
! prime 13 | |||
! prime 17 | |||
! prime 19 | |||
! prime 23 | |||
! prime 29 | |||
! prime 31 | |||
|- | |||
! rowspan="2" |Error | |||
! absolute (¢) | |||
| 0.000 | |||
| -1.955 | |||
| -2.980 | |||
| -2.159 | |||
| -1.318 | |||
| -7.194 | |||
| -4.955 | |||
| +2.487 | |||
| +5.059 | |||
| +3.756 | |||
| +4.964 | |||
|- | |||
![[Relative error|relative]] (%) | |||
| 0.0 | |||
| -11.7 | |||
| -17.9 | |||
| -13.0 | |||
| -7.9 | |||
| -43.2 | |||
| -29.7 | |||
| +14.9 | |||
| +30.4 | |||
| +22.5 | |||
| +29.8 | |||
|}'''72-tone equal temperament''', or '''72-edo''', divides the octave into 72 steps or ''moria''. This produces a twelfth-tone tuning, with the whole tone measuring 200 cents, the same as in 12-tone equal temperament. 72-tone is also a superset of [[24edo|24-tone equal temperament]], a common and standard tuning of [[Arabic,_Turkish,_Persian|Arabic]] music, and has itself been used to tune Turkish music. | |||
Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with [[96edo]]), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri. | Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with [[96edo]]), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri. | ||
| Line 633: | Line 681: | ||
== Just approximation == | == Just approximation == | ||
=== Temperament measures === | === Temperament measures === | ||