5th-octave temperaments - Revision history

Overthink: /* Quint */ move to very low accuracy temperaments

2026-02-27T05:26:49Z

Quint: move to very low accuracy temperaments

← Older revision		Revision as of 05:26, 27 February 2026
Line 212:		Line 212:

	Supporting ETs: {{Optimal ET sequence\|10, 50, 80, 120, 125, 270, 2000, 2460, 3125, 3395, 5585}}		Supporting ETs: {{Optimal ET sequence\|10, 50, 80, 120, 125, 270, 2000, 2460, 3125, 3395, 5585}}

	~~== Quint ==~~
	Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is way more accurately approximated than 5 by 5edo, this temperament provides little improvement to 5edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does.

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 16/15, 27/25~~

	~~{{Mapping\|legend=1\| 5 8 12 0 \| 0 0 0 1 }}~~

	~~: Mapping generators: ~9/8, ~7~~

	~~[[Optimal tuning]]s:~~
	* [[POTE]]: ~9/8 = 1\5, ~7/4 = 1017.903 (~21/20 = 57.903)
	* [[CTE]]: ~9/8 = 1\5, ~7/4 = 968.8259 (~63/64 = 8.8259)

	~~{{Optimal ET sequence\|legend=1\| 5, 15ccd }}~~

	~~[[Badness]]: 0.048312~~

	== Obscenity ==		== Obscenity ==

2026-02-21T01:35:13Z

2025-12-28T00:50:09Z

2025-12-28T00:44:56Z

Obscenity: link to orphan page

2025-11-13T05:00:06Z

← Older revision		Revision as of 05:00, 13 November 2025
Line 225:		Line 225:

	== Obscenity ==		== Obscenity ==
	Obscenity maps [[32/21]] to 3\5 and was named in subtle reference to [[Syntonic–chromatic equivalence continuum#Absurdity (5-limit)\|absurdity]] as a kind of septal (2.3.7) analog to it.		Obscenity maps [[32/21]] to 3\5 and was named in subtle reference to [[Syntonic–chromatic equivalence continuum#Absurdity (5-limit)\|absurdity]] as a kind of septal (2.3.7) analog to it. It tempers out the obsceniton, 4194304/4084101.

	[[Subgroup]]: 2.3.7		[[Subgroup]]: 2.3.7

2025-10-05T23:50:16Z

Obscenity: fixed link

← Older revision		Revision as of 23:50, 5 October 2025
Line 225:		Line 225:

	== Obscenity ==		== Obscenity ==
	Obscenity maps [[32/21]] to 3\5 and was named in subtle reference to [[Syntonic–chromatic equivalence continuum #Absurdity\|absurdity]] as a kind of septal (2.3.7) analog to it.		Obscenity maps [[32/21]] to 3\5 and was named in subtle reference to [[Syntonic–chromatic equivalence continuum#Absurdity (5-limit)\|absurdity]] as a kind of septal (2.3.7) analog to it.

	[[Subgroup]]: 2.3.7		[[Subgroup]]: 2.3.7

2025-09-11T15:16:46Z

Septimal blackwood is now canon

← Older revision		Revision as of 15:16, 11 September 2025
Line 206:		Line 206:

	== Quint ==		== Quint ==
	Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is way more accurately approximated than 5 by 5edo, this temperament provides little improvement to 5edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[~~blacksmith~~]] does.		Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is way more accurately approximated than 5 by 5edo, this temperament provides little improvement to 5edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

2025-07-10T09:09:05Z

Quint: Added obscenity temperament

← Older revision		Revision as of 09:09, 10 July 2025
Line 223:		Line 223:

	[[Badness]]: 0.048312		[[Badness]]: 0.048312

			== Obscenity ==
			Obscenity maps [[32/21]] to 3\5 and was named in subtle reference to [[Syntonic–chromatic equivalence continuum #Absurdity\|absurdity]] as a kind of septal (2.3.7) analog to it.

			[[Subgroup]]: 2.3.7

			[[Comma list]]: 4194304/4084101

			{{Mapping\|legend=1\| 5 0 22 \| 0 1 -1 }}

			: Mapping generators: ~512/441, ~3

			[[Support]]ing [[ET]]s: {{EDOs\|5, 65d, 70, 75, 80, 85, 90, 95}}

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

2025-06-12T05:06:13Z

2025-06-11T12:42:19Z

Slendroschismic: related temperament has been addressed

← Older revision		Revision as of 12:42, 11 June 2025
Line 32:		Line 32:

	[[Tp tuning #T2 tuning\|RMS error]]: 0.0212 cents		[[Tp tuning #T2 tuning\|RMS error]]: 0.0212 cents

	~~Related temperaments: [[Pental family\|hemipental]]~~

	== Thunderclysmic ==		== Thunderclysmic ==