Hyperpyth - Revision history

Sintel: -TempClean

2026-05-28T14:42:03Z

-TempClean

← Older revision		Revision as of 14:42, 28 May 2026
Line 1:		Line 1:
	~~{{URWTC}}~~

	'''Hyperpyth temperament''' is a pentave-based 5.9.13 subgroup temperament which tempers out 28561/28125 (quadtho-aquingu comma).		'''Hyperpyth temperament''' is a pentave-based 5.9.13 subgroup temperament which tempers out 28561/28125 (quadtho-aquingu comma).

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:24:15Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:24, 29 April 2025
Line 27:		Line 27:
	[[Category:Hyperpyth\| ]] <!-- main article -->		[[Category:Hyperpyth\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Subgroup~~ temperaments]]		[[Category:Non-octave temperaments]]
	~~[[Category:Nonoctave~~]]

FloraC: - parent category

2025-04-28T14:15:39Z

- parent category

← Older revision		Revision as of 14:15, 28 April 2025
Line 25:		Line 25:
	Looking at the primes, 7 and 11 (and 19) are "conspicuously absent" which begs comparison to the Meantone/Orgone dichotomy. The search being on, in the context of simple scales, 11/5 is close enough to the square root of 5, that one might as well just use it (1393 v the real 11/5 at 1365 cents); eventually as step sizes get closer to 60 cents or so, better approximations will abound. This would make a good period for a scale. The pure 7/5 then is around 582 cents, and among the simpler temperaments 557-cent (from 5ED5, 10ED5, 15ED5) and 596-cent (from [[14ed5\|14ED5]], which is a slightly compressed [[6edo\|6EDO]]) intervals are the closest approximations. That is, until [[19ed5\|19ED5]] (14+5) which is a very slightly stretched [[13edt\|13EDT]] (Bohlen-Pierce) scale, and [[24ed5\|24ED5]] which is something completely different.		Looking at the primes, 7 and 11 (and 19) are "conspicuously absent" which begs comparison to the Meantone/Orgone dichotomy. The search being on, in the context of simple scales, 11/5 is close enough to the square root of 5, that one might as well just use it (1393 v the real 11/5 at 1365 cents); eventually as step sizes get closer to 60 cents or so, better approximations will abound. This would make a good period for a scale. The pure 7/5 then is around 582 cents, and among the simpler temperaments 557-cent (from 5ED5, 10ED5, 15ED5) and 596-cent (from [[14ed5\|14ED5]], which is a slightly compressed [[6edo\|6EDO]]) intervals are the closest approximations. That is, until [[19ed5\|19ED5]] (14+5) which is a very slightly stretched [[13edt\|13EDT]] (Bohlen-Pierce) scale, and [[24ed5\|24ED5]] which is something completely different.

	[[Category:Hyperpyth\| ]]		[[Category:Hyperpyth\| ]] <!-- main article -->
	~~[[Category:Fifth harmonic]]~~
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Temperaments~~]]		[[Category:Subgroup temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Lériendil at 23:09, 19 April 2025

2025-04-19T23:09:57Z

← Older revision		Revision as of 23:09, 19 April 2025
Line 27:		Line 27:
	[[Category:Hyperpyth\| ]]		[[Category:Hyperpyth\| ]]
	[[Category:Fifth harmonic]]		[[Category:Fifth harmonic]]
			[[Category:Rank-2 temperaments]]
	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Lériendil at 05:17, 11 October 2024

2024-10-11T05:17:28Z

← Older revision		Revision as of 05:17, 11 October 2024
Line 21:		Line 21:

	== Hyperreich? ==		== Hyperreich? ==
	{{~~see~~\|Juggernaut}}		{{main\|Juggernaut}}

	Looking at the primes, 7 and 11 (and 19) are "conspicuously absent" which begs comparison to the Meantone/Orgone dichotomy. The search being on, in the context of simple scales, 11/5 is close enough to the square root of 5, that one might as well just use it (1393 v the real 11/5 at 1365 cents); eventually as step sizes get closer to 60 cents or so, better approximations will abound. This would make a good period for a scale. The pure 7/5 then is around 582 cents, and among the simpler temperaments 557-cent (from 5ED5, 10ED5, 15ED5) and 596-cent (from [[14ed5\|14ED5]], which is a slightly compressed [[6edo\|6EDO]]) intervals are the closest approximations. That is, until [[19ed5\|19ED5]] (14+5) which is a very slightly stretched [[13edt\|13EDT]] (Bohlen-Pierce) scale, and [[24ed5\|24ED5]] which is something completely different.		Looking at the primes, 7 and 11 (and 19) are "conspicuously absent" which begs comparison to the Meantone/Orgone dichotomy. The search being on, in the context of simple scales, 11/5 is close enough to the square root of 5, that one might as well just use it (1393 v the real 11/5 at 1365 cents); eventually as step sizes get closer to 60 cents or so, better approximations will abound. This would make a good period for a scale. The pure 7/5 then is around 582 cents, and among the simpler temperaments 557-cent (from 5ED5, 10ED5, 15ED5) and 596-cent (from [[14ed5\|14ED5]], which is a slightly compressed [[6edo\|6EDO]]) intervals are the closest approximations. That is, until [[19ed5\|19ED5]] (14+5) which is a very slightly stretched [[13edt\|13EDT]] (Bohlen-Pierce) scale, and [[24ed5\|24ED5]] which is something completely different.

Lériendil at 05:17, 11 October 2024

2024-10-11T05:17:12Z

← Older revision		Revision as of 05:17, 11 October 2024
Line 1:		Line 1:
			{{URWTC}}

	'''Hyperpyth temperament''' is a pentave-based 5.9.13 subgroup temperament which tempers out 28561/28125 (quadtho-aquingu comma).		'''Hyperpyth temperament''' is a pentave-based 5.9.13 subgroup temperament which tempers out 28561/28125 (quadtho-aquingu comma).

Line 19:		Line 21:

	== Hyperreich? ==		== Hyperreich? ==
			{{see\|Juggernaut}}

	Looking at the primes, 7 and 11 (and 19) are "conspicuously absent" which begs comparison to the Meantone/Orgone dichotomy. The search being on, in the context of simple scales, 11/5 is close enough to the square root of 5, that one might as well just use it (1393 v the real 11/5 at 1365 cents); eventually as step sizes get closer to 60 cents or so, better approximations will abound. This would make a good period for a scale. The pure 7/5 then is around 582 cents, and among the simpler temperaments 557-cent (from 5ED5, 10ED5, 15ED5) and 596-cent (from [[14ed5\|14ED5]], which is a slightly compressed [[6edo\|6EDO]]) intervals are the closest approximations. That is, until [[19ed5\|19ED5]] (14+5) which is a very slightly stretched [[13edt\|13EDT]] (Bohlen-Pierce) scale, and [[24ed5\|24ED5]] which is something completely different.		Looking at the primes, 7 and 11 (and 19) are "conspicuously absent" which begs comparison to the Meantone/Orgone dichotomy. The search being on, in the context of simple scales, 11/5 is close enough to the square root of 5, that one might as well just use it (1393 v the real 11/5 at 1365 cents); eventually as step sizes get closer to 60 cents or so, better approximations will abound. This would make a good period for a scale. The pure 7/5 then is around 582 cents, and among the simpler temperaments 557-cent (from 5ED5, 10ED5, 15ED5) and 596-cent (from [[14ed5\|14ED5]], which is a slightly compressed [[6edo\|6EDO]]) intervals are the closest approximations. That is, until [[19ed5\|19ED5]] (14+5) which is a very slightly stretched [[13edt\|13EDT]] (Bohlen-Pierce) scale, and [[24ed5\|24ED5]] which is something completely different.

Lériendil at 07:13, 22 August 2024

2024-08-22T07:13:41Z

← Older revision		Revision as of 07:13, 22 August 2024
Line 2:		Line 2:

	== Hyperpyth ==		== Hyperpyth ==
	Using the fifth harmonic ([[5/1]], pentave) as an interval of equivalence, instead of the more common octave or even [[tritave]], the first place to look for xenharmonies is isoharmonic chords, of which there are two. 1:2:3:4:5, and 5:9:13:17:21:25. The latter is more xenharmonic, though 16ed5 suits the former and can be strange. It turns out that the key to making a scale of this chord is to use as the generator ~13/5, which, in the fifth harmonic, results in a scale of the same shape as meantone and similar placement of consonances. Thus it is a [[~~MacrodiatonicAndMicrodiatonic~~\|macrodiatonic]] tuning. In this case, the most suitable scales are such as would have a sharp fifth, in octaves known as "superpythagorean", so I dub this "hyperpyth".		Using the fifth harmonic ([[5/1]], pentave) as an interval of equivalence, instead of the more common octave or even [[tritave]], the first place to look for xenharmonies is isoharmonic chords, of which there are two. 1:2:3:4:5, and 5:9:13:17:21:25. The latter is more xenharmonic, though 16ed5 suits the former and can be strange. It turns out that the key to making a scale of this chord is to use as the generator ~13/5, which, in the fifth harmonic, results in a scale of the same shape as meantone and similar placement of consonances. Thus it is a [[Macrodiatonic and microdiatonic scales\|macrodiatonic]] tuning. In this case, the most suitable scales are such as would have a sharp fifth, in octaves known as "superpythagorean", so I dub this "hyperpyth".

	The quintessential comma of which is 28561/28125, wherein (13 the "perfect fifth")^4 = 9 (the "major third") and 5's are fungible. 13^3 (ie. a "major sixth") can also constitute the 17/5 interval, and 21/5 is liable to be an augmented sixth, (and a bonus, 19/5 can be found as a dominant seventh). This is eerily similar to the case in meantone (especially if you call the sixth a 13/8). [http://x31eq.com/cgi-bin/rt.cgi?ets=c22_c5&limit=5_9_13]		The quintessential comma of which is 28561/28125, wherein (13 the "perfect fifth")^4 = 9 (the "major third") and 5's are fungible. 13^3 (ie. a "major sixth") can also constitute the 17/5 interval, and 21/5 is liable to be an augmented sixth, (and a bonus, 19/5 can be found as a dominant seventh). This is eerily similar to the case in meantone (especially if you call the sixth a 13/8). [http://x31eq.com/cgi-bin/rt.cgi?ets=c22_c5&limit=5_9_13]

Fredg999 category edits: Moving from Category:Temperament to Category:Temperaments using Cat-a-lot

2022-02-28T22:34:44Z

Moving from Category:Temperament to Category:Temperaments using Cat-a-lot

← Older revision		Revision as of 22:34, 28 February 2022
Line 23:		Line 23:
	[[Category:Hyperpyth\| ]]		[[Category:Hyperpyth\| ]]
	[[Category:Fifth harmonic]]		[[Category:Fifth harmonic]]
	[[Category:~~Temperament~~]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Xenllium at 07:40, 28 August 2021

2021-08-28T07:40:24Z

← Older revision		Revision as of 07:40, 28 August 2021
Line 13:		Line 13:
	* [[22ed5\|22ED5]]		* [[22ed5\|22ED5]]
	* [[27ed5\|27ED5]]		* [[27ed5\|27ED5]]
			* [[29ed5\|29ED5]]
	* [[39ed5\|39ED5]]		* [[39ed5\|39ED5]]

Line 20:		Line 21:
	Looking at the primes, 7 and 11 (and 19) are "conspicuously absent" which begs comparison to the Meantone/Orgone dichotomy. The search being on, in the context of simple scales, 11/5 is close enough to the square root of 5, that one might as well just use it (1393 v the real 11/5 at 1365 cents); eventually as step sizes get closer to 60 cents or so, better approximations will abound. This would make a good period for a scale. The pure 7/5 then is around 582 cents, and among the simpler temperaments 557-cent (from 5ED5, 10ED5, 15ED5) and 596-cent (from [[14ed5\|14ED5]], which is a slightly compressed [[6edo\|6EDO]]) intervals are the closest approximations. That is, until [[19ed5\|19ED5]] (14+5) which is a very slightly stretched [[13edt\|13EDT]] (Bohlen-Pierce) scale, and [[24ed5\|24ED5]] which is something completely different.		Looking at the primes, 7 and 11 (and 19) are "conspicuously absent" which begs comparison to the Meantone/Orgone dichotomy. The search being on, in the context of simple scales, 11/5 is close enough to the square root of 5, that one might as well just use it (1393 v the real 11/5 at 1365 cents); eventually as step sizes get closer to 60 cents or so, better approximations will abound. This would make a good period for a scale. The pure 7/5 then is around 582 cents, and among the simpler temperaments 557-cent (from 5ED5, 10ED5, 15ED5) and 596-cent (from [[14ed5\|14ED5]], which is a slightly compressed [[6edo\|6EDO]]) intervals are the closest approximations. That is, until [[19ed5\|19ED5]] (14+5) which is a very slightly stretched [[13edt\|13EDT]] (Bohlen-Pierce) scale, and [[24ed5\|24ED5]] which is something completely different.

			[[Category:Hyperpyth\| ]]
	[[Category:Fifth harmonic]]		[[Category:Fifth harmonic]]
	[[Category:Temperament]]		[[Category:Temperament]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Xenllium at 00:27, 28 August 2021

2021-08-28T00:27:29Z

← Older revision		Revision as of 00:27, 28 August 2021
Line 12:		Line 12:
	* [[17ed5\|17ED5]]		* [[17ed5\|17ED5]]
	* [[22ed5\|22ED5]]		* [[22ed5\|22ED5]]
	* [[~~29ed5~~\|~~29ED5~~]]		* [[27ed5\|27ED5]]
	* [[39ed5\|39ED5]]		* [[39ed5\|39ED5]]

Line 22:		Line 22:
	[[Category:Fifth harmonic]]		[[Category:Fifth harmonic]]
	[[Category:Temperament]]		[[Category:Temperament]]
			[[Category:Nonoctave]]