Aberrismic theory: Difference between revisions
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At times, a scale pattern has varying temperaments according to the tuning. For example, 5L2m3s may be given the temperament structure of either untempered 2.3.5 or Flutterpyth temperament. | At times, a scale pattern has varying temperaments according to the tuning. For example, 5L2m3s may be given the temperament structure of either untempered 2.3.5 or Flutterpyth temperament. | ||
=== Example: blackdye === | === Example: blackdye === | ||
The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye ('''sLmLsLmLsL'''), untempered 2.3.5 and [[Flutterpyth]]. | |||
* ''Untempered 2.3.5'' does not mean that the final tuning must be the JI tuning, but simply that there exists a tuning with no error, or equivalently that no comma needs to be tempered out. | |||
* Flutterpyth, 2.3.7.11.13[32 & 37], is a rank-2 diatonic temperament that tempers out 64/63 like Superpyth but tunes the 3/2 even sharper, as a result tempering C-D# to a 14/11 and C-Fb to a 13/11. [[37edo]] provides a nearly optimal tuning. | |||
{| class="wikitable right-2 right-3 right-4 right-5" | |||
|+ Interval sizes in blackdye | |||
|- | |||
! | Interval class | |||
! Sizes | |||
! Untempered 2.3.5 | |||
! Flutterpyth | |||
|- | |||
!|[[TAMNAMS|1-step]] | |||
| s<br/>m<br/>L | |||
| 81/80<br/>16/15<br/>10/9 | |||
| 78/77, 99/98<br/>22/21, 91/88<br/>44/39 | |||
|- | |||
!|[[TAMNAMS|2-step]] | |||
| L + s<br/>L + m | |||
| 9/8<br/>32/27 | |||
| 8/7, 9/8<br/>7/6 | |||
|- | |||
!|[[TAMNAMS|3-step]] | |||
| L + 2s<br/>L + m + s<br/>2L + s<br/>2L + m | |||
| 729/640<br/>6/5<br/>5/4<br/>320/243 | |||
| 7/6<br/>13/11<br/>14/11<br/>13/10 | |||
|- | |||
!|[[TAMNAMS|4-step]] | |||
| 2L + 2s<br/>2L + m + s | |||
| 81/64<br/>4/3 | |||
| 13/10<br/>4/3 | |||
|- | |||
!|[[TAMNAMS|5-step]] | |||
| 2L + m + 2s<br/>2L + 2m + s<br/>3L + 2s<br/>3L + m + s | |||
| 27/20<br/>64/45<br/>45/32<br/>40/27 | |||
| 66/49<br/>11/8<br/>16/11<br/>49/33 | |||
|- | |||
!|[[TAMNAMS|6-step]] | |||
| 3L + m + 2s<br/>3L + 2m + s | |||
| 3/2<br/>128/81 | |||
| 3/2<br/>20/13 | |||
|- | |||
!|[[TAMNAMS|7-step]] | |||
| 3L + m + 3s<br/>3L + 2m + 2s<br/>4L + m + 2s<br/>4L + 2m + s | |||
| 243/160<br/>8/5<br/>5/3<br/>1280/729 | |||
| 20/13<br/>11/7<br/>22/13<br/>12/7 | |||
|- | |||
!|[[TAMNAMS|8-step]] | |||
| 4L + m + 3s<br/>4L + 2m + 2s | |||
| 27/16<br/>16/9 | |||
| 12/7<br/>7/4 | |||
|- | |||
!|[[TAMNAMS|9-step]] | |||
| 5L + 2m + s<br/>5L + m + 2s<br/>4L + 2m + 2s | |||
| 9/5<br/>15/8<br/>160/81 | |||
| 39/22<br/>21/11<br/>77/39 | |||
|} | |||
==== Untempered 2.3.5 blackdye ==== | ==== Untempered 2.3.5 blackdye ==== | ||
==== Flutterpyth blackdye ==== | ==== Flutterpyth blackdye ==== | ||
[[Category:Terms]] | [[Category:Terms]] | ||
[[Category:Aberrismic theory|*]] | [[Category:Aberrismic theory|*]] | ||