136/135: Difference between revisions
add temperaments and explanation of the importance and function of this comma & shorten name to avoid conflict with "diatonic" |
m →Diatismic: mention potential desirable EDO tunings of diatismic |
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=== Diatismic === | === Diatismic === | ||
The only EDO tuning that has less than 25% [[relative error]] for all primes in the [[17-limit]] tempering [[136/135]] is [[46edo]], which also tunes 20/17 with less than 25% relative error and 51/40 even more accurately. | The only EDO tuning that has less than 25% [[relative error]] for all primes in the [[17-limit]] tempering [[136/135]] is [[46edo]], which also tunes 20/17 with less than 25% relative error and 51/40 even more accurately. If you allow 7/4 to be sharper than 25% then [[80edo]] makes a good and more accurate tuning that extends to the [[23-limit]]. Alternatively, if you don't care (as much) about prime 11, [[68edo]] makes a great tuning in the no-11's [[19-limit]] and no-11's no-29's [[31-limit]]. | ||
Subgroup: [[17-limit]] | Subgroup: [[17-limit]] | ||
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[[CTE]] generators: [same as diatic with purely tuned 7, 11 and 13 added] | [[CTE]] generators: [same as diatic with purely tuned 7, 11 and 13 added] | ||
EDO tunings with less than 33% [[relative error]] for all primes in the [[17-limit]]: 46, 56 | EDO tunings with less than 33% [[relative error]] for all primes in the no-7's no-11's [[17-limit]]: 10, 24, 34, 44, 46, 56, 80, 114 | ||
== Etymology == | == Etymology == | ||