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.
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. However, adding the schisma is a possibility as 77, 94 and 171edo support schismic, albeit 5/4 will be found at -40 generators.
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. This is Bleu.
The best extension is found by tempering out 352/351 and 729/728, which is much more complex than Bleu, but much more accurate, called Glaishur.
Interval chain (CWE tuning)
| Generators up | Cents | Mapping |
|---|---|---|
| 0 | 0.0 | 1 |
| 1 | 140.384 | 13/12 |
| 2 | 280.768 | 27/23 |
| 3 | 421.152 | 14/11 |
| 4 | 561.536 | 18/13 |
| 5 | 701.92 | 3/2 |
| 6 | 842.304 | 13/8 |
| 7 | 982.688 | 81/46 |
| 8 | 1123.072 | 44/23 |
| 9 | 63.456 | 27/26 |
| 10 | 203.84 | 9/8 |
| 11 | 344.224 | 11/9 |
| 12 | 484.608 | 81/46 |
| 13 | 624.992 | 23/16 |
| 14 | 765.376 | |
| 15 | 905.76 | 27/16 |
| 16 | 1046.144 | |
| 17 | 1186.528 | |
| 18 | 126.912 | 14/13 |
| 19 | 267.296 | |
| 20 | 407.68 | 81/64 |
| 21 | 548.064 | 11/8 |
| 22 | 688.448 | |
| 23 | 828.832 | |
| 24 | 969.216 | 7/4 |
| 25 | 1109.6 | 243/128 |
| 26 | 49.984 | |
| 27 | 190.368 | |
| 28 | 330.752 | |
| 29 | 471.136 | |
| 30 | 611.52 | 729/512 |
| 31 | 751.904 | |
| 32 | 892.288 | |
| 33 | 1032.672 | 29/16 |