Glacier
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 scales 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. Glacier works much better as a no-5s temperament, whose best subgroup is 2.3.7.11.13.23.29, finding each prime only in positive generators. For technical data on this extension, see No-fives subgroup temperaments#Glaishur.
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 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)
| Generators up | Cents | 2.3.7.13 mapping | Majorminthic | Grossmic |
|---|---|---|---|---|
| 0 | 0.0 | |||
| 1 | 140.3 | 13/12 | 88/81 | |
| 2 | 280.6 | 7/6 | ||
| 3 | 420.9 | 9/7 | ||
| 4 | 561.2 | 18/13 | 11/8 | |
| 5 | 701.5 | 3/2 | ||
| 6 | 841.8 | 13/8 | 44/27 | |
| 7 | 982.1 | 7/4 | ||
| 8 | 1122.4 | 27/14 | ||
| 9 | 62.7 | 27/26 | 33/32 | |
| 10 | 203.0 | 9/8 | ||
| 11 | 343.3 | 39/32 | 11/9 |