16ed5/3 - Revision history

Overthink: /* Temperaments */ avoid first person in mainspace

2026-03-20T00:45:56Z

Temperaments: avoid first person in mainspace

← Older revision		Revision as of 00:45, 20 March 2026
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	16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 183 225 241 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the mapping of prime 7 (val 65d).		16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 183 225 241 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the mapping of prime 7 (val 65d).

	As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] ~~propose~~ the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:		As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|Ayceman]] proposes the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:

	=== Tristone ===		=== Tristone ===

Contribution: /* Temperaments */

2026-03-06T09:16:20Z

Temperaments

← Older revision		Revision as of 09:16, 6 March 2026
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	This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.		This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.

	16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 183 225 241 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the mapping of prime 7.		16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 183 225 241 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the mapping of prime 7 (val 65d).

	As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:		As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:

Contribution: /* Temperaments */

2026-03-06T09:15:24Z

Temperaments

← Older revision		Revision as of 09:15, 6 March 2026
Line 528:		Line 528:
	This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.		This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.

	16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 183 225 241 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the mapping of ~~primes~~ 7.		16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 183 225 241 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the mapping of prime 7.

	As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:		As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:

Contribution: /* Temperaments */

2026-03-06T09:12:40Z

Temperaments

← Older revision		Revision as of 09:12, 6 March 2026
Line 528:		Line 528:
	This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.		This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.

	16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 ~~177~~ 225 ~~235~~ 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the ~~mappings~~ of primes 7 ~~and 13~~.		16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 183 225 241 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the mapping of primes 7.

	As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:		As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:

Contribution: /* Temperaments */

2026-03-05T23:19:39Z

Temperaments

← Older revision		Revision as of 23:19, 5 March 2026
Line 528:		Line 528:
	This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.		This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.

	16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 177 225 235 266 276 294 316 322], using every 3 steps of a shrinked 65edo (-2.431¢ per octave). It differs from the patent val of 65edo in the mappings of primes 7 and 13.		16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 177 225 235 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the mappings of primes 7 and 13.

	As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:		As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:

Contribution: /* Temperaments */

2026-03-05T23:08:05Z

Temperaments

← Older revision		Revision as of 23:08, 5 March 2026
Line 527:		Line 527:

	This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.		This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.

			16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 177 225 235 266 276 294 316 322], using every 3 steps of a shrinked 65edo (-2.431¢ per octave). It differs from the patent val of 65edo in the mappings of primes 7 and 13.

	As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:		As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman\|I]] propose the name '''tristone''' for the basic [[Diaschismic family\|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:

Xenllium at 06:59, 22 February 2026

2026-02-22T06:59:25Z

← Older revision		Revision as of 06:59, 22 February 2026
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	\| Ab		\| Ab
	\| Eb		\| Eb
	\| Db		\| Bb
	\| Fbb		\| Fbb
	\| Cbb		\| Cbb
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	== See also ==		== See also ==
	* [~~https://en.xen.wiki/w/Equal-step_tuning#~~Alpha-beta~~-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions~~]		* [[Alpha, beta, and gamma family of equal divisions]]

	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Contribution at 01:46, 28 October 2025

2025-10-28T01:46:48Z

← Older revision		Revision as of 01:46, 28 October 2025
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	'''16ed5/3''' also supports [[Blackcomb]] temperament which is built on [[5/4]] and [[3/2]] in a very similar way to octave-repeating [[meantone]] but is less accurate. Blackcomb tempers out the comma [[250/243]], the amount by which 3 [[3/2]]'s exceed [[5/4]] sixth-reduced, in the 5/3.2.3 subgroup (equal to the [[5-limit]]).		'''16ed5/3''' also supports [[Blackcomb]] temperament which is built on [[5/4]] and [[3/2]] in a very similar way to octave-repeating [[meantone]] but is less accurate. Blackcomb tempers out the comma [[250/243]], the amount by which 3 [[3/2]]'s exceed [[5/4]] sixth-reduced, in the 5/3.2.3 subgroup (equal to the [[5-limit]]).

			== See also ==
			* [https://en.xen.wiki/w/Equal-step_tuning#Alpha-beta-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions]

	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:20:39Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:20, 1 August 2025
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	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	~~[[Category:Edonoi]]~~

Sintel: /* MOS scales */ -pathological

2025-04-16T09:22:54Z

MOS scales: -pathological

← Older revision		Revision as of 09:22, 16 April 2025
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	\| 1		\| 1
	\| 1\16		\| 1\16
	\| 1L ~~ns (pathological)~~		\| 1L Ns
	\|-		\|-
	\| 1		\| 1