Glacier: Difference between revisions
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'''Glacier''' is a [[rank-2 temperament]] in the 2.3.13 subgroup that tempers out the comma [[373248/371293]], the amount by which 5 [[13/12]]'s exceed [[3/2]]. In this temperament, 5 generators make ~3/2 and 6 generators make ~13/8. It possesses [[MOS scale]]s of the families [[1L 4s]], [[1L 5s]], [[1L 6s]], [[1L 7s]], [[8L 1s]], and [[9L 8s]], although the 1L 4s and 1L 5s scales usually end up as extremely lopsided. [[17edo]] and [[26edo]] are good tunings for this temperament, but [[94edo]] achieves a much better effect with practically perfect fifths and ~13/8 2 cents off. Glacier has a generator nearly identical to [[Bleu]] despite it tempering out different commas, of which [[17edo]] also offers a good generator. | '''Glacier''' is a [[rank-2 temperament]] in the 2.3.13 subgroup that tempers out the comma [[373248/371293]], the amount by which 5 [[13/12]]'s exceed [[3/2]]. In this temperament, 5 generators make ~3/2 and 6 generators make ~13/8. It possesses [[MOS scale]]s of the families [[1L 4s]], [[1L 5s]], [[1L 6s]], [[1L 7s]], [[8L 1s]], and [[9L 8s]], although the 1L 4s and 1L 5s scales usually end up as extremely lopsided. [[17edo]] and [[26edo]] are good tunings for this temperament, but [[94edo]] achieves a much better effect with practically perfect fifths and ~13/8 2 cents off. The optimal patent val in the 2.3.13 subgroup is [[171edo]]. Glacier has a generator nearly identical to [[Bleu]] despite it tempering out different commas, of which [[17edo]] also offers a good generator. | ||
It has extensions to the full [[13-limit]], but they are contrived. | |||
The best 2.3.5.13 extension is arguably [[meantone]], adding [[65/64]] and [[81/80]] to the list of tempered commas, of which good edos are [[43edo|43]] and 26. 43 is best in the 2.3.5.13 meantone subgroup. | |||
Extensions with 7 and 11 are possible. The generator can be close to a pure 13/12, in which case 7/4 will be extremely accurately tuned +7 gens up, tempering out [[62748517/62705664]]. However, the fifths become quite flat as a result. Thusly, [[26edo]] is an optimal tuning for this extension, which also includes [[flattone]] in the 13-limit. | |||
By tempering the [[144/143]], a sharp ~[[11/8]] can be found +4 gens up. | |||
The CTE generator of 140.3 reaches a very accurate 39/32 +11 gens up, which can be equated with 11/9 by tempering [[352/351]], becoming a [[majorminth temperament]]. This means that 11/8 is found here +21 gens up, which is quite complex. | |||
== Interval chain (CTE tuning) == | == Interval chain (CTE tuning) == | ||
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! Generators up | ! Generators up | ||
! Cents | ! Cents | ||
!2.3.7.13 mapping | |||
!Majorminthic | |||
!Grossmic | |||
|- | |- | ||
| 0 | | 0 | ||
| 0.0 | | 0.0 | ||
| | |||
| | |||
| | |||
|- | |- | ||
| 1 | | 1 | ||
| 140.3 | | 140.3 | ||
|13/12 | |||
|88/81 | |||
| | |||
|- | |- | ||
| 2 | | 2 | ||
| 280.6 | | 280.6 | ||
|7/6 | |||
| | |||
| | |||
|- | |- | ||
| 3 | | 3 | ||
| 420.9 | | 420.9 | ||
|9/7 | |||
| | |||
| | |||
|- | |- | ||
| 4 | | 4 | ||
| 561.2 | | 561.2 | ||
|18/13 | |||
| | |||
|11/8 | |||
|- | |- | ||
| 5 | | 5 | ||
| 701.5 | | 701.5 | ||
|3/2 | |||
| | |||
| | |||
|- | |- | ||
| 6 | | 6 | ||
| 841.8 | | 841.8 | ||
|13/8 | |||
|44/27 | |||
| | |||
|- | |- | ||
| 7 | | 7 | ||
| 982.1 | | 982.1 | ||
|12/7 | |||
| | |||
| | |||
|- | |- | ||
| 8 | | 8 | ||
| 1122.4 | | 1122.4 | ||
|7/4 | |||
| | |||
| | |||
|- | |- | ||
| 9 | | 9 | ||
| 62.7 | | 62.7 | ||
|27/26 | |||
| | |||
|33/32 | |||
|- | |- | ||
| 10 | | 10 | ||
| 203.0 | | 203.0 | ||
|9/8 | |||
| | |||
| | |||
|- | |- | ||
| 11 | | 11 | ||
| 343.3 | | 343.3 | ||
|39/32 | |||
|11/9 | |||
| | |||
|} | |} | ||