Glacier - Revision history

Eufalesio: Added some things and revamped the interval table

2026-01-23T01:33:43Z

Added some things and revamped the interval table

Overthink: no here links

2026-01-13T21:13:40Z

no here links

← Older revision		Revision as of 21:13, 13 January 2026
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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]]. 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. [[No-fives subgroup temperaments#~~Glaceir\|See here for technical information.~~]]		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.

Eufalesio at 00:50, 13 January 2026

2026-01-13T00:50:07Z

← Older revision		Revision as of 00:50, 13 January 2026
Line 1:		Line 1:
	'''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]]. 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.		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. [[No-fives subgroup temperaments#Glaceir\|See here for technical information.]]

	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.

Overthink: /* Interval chain (CTE tuning) */ fix errors

2026-01-13T00:32:00Z

Interval chain (CTE tuning): fix errors

← Older revision		Revision as of 00:32, 13 January 2026
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	\| 7		\| 7
	\| 982.1		\| 982.1
	\|12/7		\| 7/4
	\|		\|
	\|		\|
Line 70:		Line 70:
	\| 8		\| 8
	\| 1122.4		\| 1122.4
	\|7/4		\| 27/14
	\|		\|
	\|		\|

Eufalesio: I will link with non 5-subgroup temps

2026-01-12T23:46:04Z

I will link with non 5-subgroup temps

← Older revision		Revision as of 23:46, 12 January 2026
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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]]. 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.		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.

	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.

Eufalesio: Added many things, expanded tables, need to format correctly (Is this a unique temperament (family)?)

2025-11-03T01:36:35Z

Added many things, expanded tables, need to format correctly (Is this a unique temperament (family)?)

← Older revision		Revision as of 01:36, 3 November 2025
Line 1:		Line 1:
	'''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) ==
Line 6:		Line 16:
	! 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
			\|
	\|}		\|}

Eufalesio: added some extra info

2025-08-24T06:30:48Z

added some extra info

← Older revision		Revision as of 06:30, 24 August 2025
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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]]. 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. Glacier has a generator nearly identical to [[Bleu]] despite it tempering out different commas.		'''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.

	== Interval chain (CTE tuning) ==		== Interval chain (CTE tuning) ==

FloraC: - parent category

2025-04-28T14:10:09Z

- parent category

← Older revision		Revision as of 14:10, 28 April 2025
Line 4:		Line 4:
	{\|class="wikitable"		{\|class="wikitable"
	\|-		\|-
	!Generators up		! Generators up
	!Cents		! Cents
	\|-		\|-
	\|0		\| 0
	\|0.0		\| 0.0
	\|-		\|-
	\|1		\| 1
	\|140.3		\| 140.3
	\|-		\|-
	\|2		\| 2
	\|280.6		\| 280.6
	\|-		\|-
	\|3		\| 3
	\|420.9		\| 420.9
	\|-		\|-
	\|4		\| 4
	\|561.2		\| 561.2
	\|-		\|-
	\|5		\| 5
	\|701.5		\| 701.5
	\|-		\|-
	\|6		\| 6
	\|841.8		\| 841.8
	\|-		\|-
	\|7		\| 7
	\|982.1		\| 982.1
	\|-		\|-
	\|8		\| 8
	\|1122.4		\| 1122.4
	\|-		\|-
	\|9		\| 9
	\|62.7		\| 62.7
	\|-		\|-
	\|10		\| 10
	\|203.0		\| 203.0
	\|-		\|-
	\|11		\| 11
	\|343.3		\| 343.3
	\|}		\|}

	[[Category:~~Temperaments~~]]		[[Category:Glacier\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~13-limit~~]]		[[Category:Subgroup temperaments]]

Lériendil at 23:07, 19 April 2025

2025-04-19T23:07:23Z

← Older revision		Revision as of 23:07, 19 April 2025
Line 45:		Line 45:

	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Rank 2]]		[[Category:Rank-2 temperaments]]
	[[Category:13-limit]]		[[Category:13-limit]]

Fredg999: Categories

2023-04-23T21:19:49Z

← Older revision		Revision as of 21:19, 23 April 2023
Line 45:		Line 45:

	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Rank-2]]		[[Category:Rank 2]]
	[[Category:13-limit]]		[[Category:13-limit]]