57edo: Difference between revisions
m →Theory: (''See regular temperament for more about what all this means and how to use it.'') Tag: Reverted |
m Text replacement - "Ups and Downs Notation" to "Ups and downs notation" |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 5: | Line 5: | ||
57edo is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]]. One way to describe 57edo is that it has a [[5-limit]] part consisting of three [[ring number|ring]]s of 19edo, plus a no-threes no-fives part which is much more accurate. | 57edo is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]]. One way to describe 57edo is that it has a [[5-limit]] part consisting of three [[ring number|ring]]s of 19edo, plus a no-threes no-fives part which is much more accurate. | ||
Using the full prime-limit [[patent val]], the equal temperament tempers out [[81/80]], [[1029/1024]], and [[3125/3072]] in the 7-limit; and [[99/98]], [[385/384]], [[441/440]], and [[625/616]] in the [[11-limit]]. | Using the full prime-limit [[patent val]], the equal temperament tempers out [[81/80]], [[1029/1024]], and [[3125/3072]] in the 7-limit; and [[99/98]], [[385/384]], [[441/440]], and [[625/616]] in the [[11-limit]]. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate [[11/8]], which is 26\57. This gives the [[19-limit]] 46 & 57 temperament [[heinz]]. It can also be used to tune [[mothra]] as well as [[trismegistus]]. | ||
A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate [[11/8]], which is 26\57. This gives the [[19-limit]] 46 & 57 temperament [[heinz]]. It can also be used to tune [[mothra]] as well as [[trismegistus]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 13: | Line 11: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
57edo contains [[3edo]] and [[19edo]] as subsets. | 57edo contains [[3edo]] and [[19edo]] as subsets. | ||
== Intervals == | == Intervals == | ||
| Line 20: | Line 18: | ||
! # | ! # | ||
! [[Cent]]s | ! [[Cent]]s | ||
! [[Ups and downs notation|Ups and | ! [[Ups and downs notation|Ups and downs notation]]<br>(Flat Fifth 11\19) | ||
! [[Ups and downs notation|Ups and | ! [[Ups and downs notation|Ups and downs notation]]<br>(Sharp Fifth 34\57) | ||
|- | |- | ||
| 0 | | 0 | ||
| Line 353: | Line 351: | ||
[[Category:Heinz]] | [[Category:Heinz]] | ||
[[Category:Mothra]] | [[Category:Mothra]] | ||
{{todo|add rank 2 temperaments table | {{todo|add rank 2 temperaments table}} | ||
== Instruments == | |||
Since 57edo contains [[19edo]] as a non-trivial subset, it would be possible to use three 19edo instruments tuned 1\57 apart from each other to play the full gamut of 57edo. | |||
A [[Lumatone mapping for 57edo]] is available. | |||
== Music == | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/watch?v=4NZvSgS3ryY ''57edo improv''] (2025) | |||