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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. 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.
'''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]].


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]].
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 [[43edo|43]] and 26. 43 is best in the 2.3.5.13 meantone subgroup.
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. 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.
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]].


By tempering the [[144/143]], a sharp ~[[11/8]] can be found +4 gens up.
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 [https://mysingingmonsters.fandom.com/wiki/Glaishur Glaishur.]


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 (CWE tuning) ==
 
== Interval chain (CTE tuning) ==
{|class="wikitable"
{|class="wikitable"
|-
|-
! Generators up
! Generators up
! Cents
! Cents
!2.3.7.13 mapping
!Mapping
!Majorminthic
!Grossmic
|-
|-
| 0
| 0
| 0.0
| 0.0
|
|1
|
|
|-
|-
| 1
| 1
| 140.3
| 140.384
|13/12
|13/12
|88/81
|
|-
|-
| 2
| 2
| 280.6
| 280.768
|7/6
|27/23
|
|
|-
|-
| 3
| 3
| 420.9
| 421.152
|9/7
|14/11
|
|
|-
|-
| 4
| 4
| 561.2
| 561.536
|18/13
|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
|
|
|11/8
|-
|-
| 5
|15
| 701.5
|905.76
|3/2
|'''27/16'''
|-
|16
|1046.144
|
|
|-
|17
|1186.528
|
|
|-
|-
| 6
|18
| 841.8
|126.912
|13/8
|14/13
|44/27
|-
|19
|267.296
|
|
|-
|-
| 7
|20
| 982.1
|407.68
| 7/4
|81/64
|-
|21
|548.064
|'''11/8'''
|-
|22
|688.448
|
|
|-
|23
|828.832
|
|
|-
|-
| 8
|24
| 1122.4
|969.216
| 27/14
|'''7/4'''
|-
|25
|1109.6
|243/128
|-
|26
|49.984
|
|
|-
|27
|190.368
|
|
|-
|-
| 9
|28
| 62.7
|330.752
|27/26
|
|
|33/32
|-
|-
| 10
|29
| 203.0
|471.136
|9/8
|
|
|-
|30
|611.52
|729/512
|-
|31
|751.904
|
|
|-
|-
| 11
|32
| 343.3
|892.288
|39/32
|11/9
|
|
|-
|33
|1032.672
|'''29/16'''
|}
|}


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