ED5 - Revision history

CompactStar at 02:29, 7 August 2026

2026-08-07T02:29:46Z

← Older revision		Revision as of 02:29, 7 August 2026
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	The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.		The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.

	One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]] and using subgroups like 5.7.11.13.17... In this approach, [[5:7:11]] could be seen as analogous to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, ~~Other~~ equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]], although this trades consonance for smaller size.		One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]] and using subgroups like 5.7.11.13.17... In this approach, [[5:7:11]] could be seen as analogous to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, other equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]], although this trades consonance for smaller size.

	The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).		The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).

CompactStar at 02:29, 7 August 2026

2026-08-07T02:29:31Z

← Older revision		Revision as of 02:29, 7 August 2026
Line 3:		Line 3:
	The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.		The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.

	One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]]. In this approach, [[5:7:11]] could be seen as analogous to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, Other equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]], although this trades consonance for smaller size.		One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]] and using subgroups like 5.7.11.13.17... In this approach, [[5:7:11]] could be seen as analogous to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, Other equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]], although this trades consonance for smaller size.

	The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).		The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).

CompactStar at 02:29, 7 August 2026

2026-08-07T02:29:11Z

← Older revision		Revision as of 02:29, 7 August 2026
Line 3:		Line 3:
	The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.		The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.

	One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]]. In this approach, [[5:7:11]] could be ~~compared~~ to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, Other equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]], although this trades consonance for smaller size.		One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]]. In this approach, [[5:7:11]] could be seen as analogous to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, Other equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]], although this trades consonance for smaller size.

	The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).		The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).

CompactStar at 02:28, 7 August 2026

2026-08-07T02:28:59Z

← Older revision		Revision as of 02:28, 7 August 2026
Line 3:		Line 3:
	The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.		The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.

	One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]]. ~~The most fundamental chord in~~ this ~~paradigm is~~ [[5:7:11]]. Other equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]].		One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]]. In this approach, [[5:7:11]] could be compared to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, Other equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]], although this trades consonance for smaller size.

	The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).		The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).

CompactStar: Removing that part because that temperament is pretty bad

2026-08-07T02:27:40Z

Removing that part because that temperament is pretty bad

← Older revision		Revision as of 02:27, 7 August 2026
Line 3:		Line 3:
	The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.		The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.

	One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]]. The most fundamental chord in this paradigm is [[5:7:11]]. ~~This chord can be approximated in a 5.7.11-subgroup [[regular temperament]] by eliminating the comma 859375/823543, equating a stack of seven [[7/5]] generators with [[11/5]].~~ Other equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]].		One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics\|primes]] [[2/1\|2]] and [[3/1\|3]]. The most fundamental chord in this paradigm is [[5:7:11]]. Other equivalences that could be used for such no-2's no-3's music include [[ed11/5\|equal divisions of 11/5]] and [[ed11/7\|equal divisions of 11/7]].

	The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).		The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).

BudjarnLambeth: /* Individual pages for ed5's */ add 175

2025-08-01T23:59:06Z

Individual pages for ed5's: add 175

← Older revision		Revision as of 23:59, 1 August 2025
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	; 100 and beyond		; 100 and beyond
	* [[116ed5\|116]], [[139ed5\|139]], [[256ed5\|256]]		* [[116ed5\|116]], [[139ed5\|139]], [[175ed5\|175]], [[256ed5\|256]]

	<!-- Uncomment this when there are more pages		<!-- Uncomment this when there are more pages

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

2025-08-01T19:39:42Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:39, 1 August 2025
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	[[Category:Ed5's\| ]]		[[Category:Ed5's\| ]]
	<!-- main article -->		<!-- main article -->
	~~[[category:Edonoi]]~~
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:Pentave]]		[[Category:Pentave]]

	{{Todo\|add sound example}}		{{Todo\|add sound example}}

Fredg999 category edits: Moving from Category:Ed5 to Category:Ed5's using Cat-a-lot

2025-08-01T18:39:15Z

Moving from Category:Ed5 to Category:Ed5's using Cat-a-lot

← Older revision		Revision as of 18:39, 1 August 2025
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	* [http://www.nonoctave.com/tuning/fifth_harmonic.html\| Nonoctave.com: tuning: equal division of the fifth harmonic]		* [http://www.nonoctave.com/tuning/fifth_harmonic.html\| Nonoctave.com: tuning: equal division of the fifth harmonic]

	[[Category:Ed5\| ]] <!-- main article -->		[[Category:Ed5's\| ]]
			<!-- main article -->
	[[category:Edonoi]]		[[category:Edonoi]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

FloraC: /* Ed5-edo correspondence */ cleanup

2025-05-28T13:48:17Z

Ed5-edo correspondence: cleanup

← Older revision		Revision as of 13:48, 28 May 2025
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	-->		-->

	== ~~Ed5-edo~~ correspondence ==		== Ed5–edo correspondence ==
	Following ed5's (up to 339) contain good correspondences to edo tunings<ref>Edo with relative error of 5th harmonic below 1/3</ref>.		Following ed5's (up to 339) contain good correspondences to edo tunings<ref>Edo with relative error of 5th harmonic below 1/3</ref>.

	{\| class="wikitable"		{\| class="wikitable center-1 center-2"
	\|-		\|-
	! Ed5		! Ed5
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	\| [[7ed5]]		\| [[7ed5]]
	\| [[3edo]]		\| [[3edo]]
	\| 7ed5 is 3edo with ~5.9 cent compressed octaves. ~~<br>~~Equivalently, 3edo is 7ed5 with pentaves stretched by ~13.7 cents. ~~<br>~~Patent vals match through the 67-limit.		\| 7ed5 is 3edo with ~5.9 cent compressed octaves. Equivalently, 3edo is 7ed5 with pentaves stretched by ~13.7 cents. Patent vals match through the 67-limit.
	\|-		\|-
	\| [[9ed5]]		\| [[9ed5]]

FloraC: /* Individual pages for ed5's */ cleanup

2025-05-28T13:47:11Z

Individual pages for ed5's: cleanup

← Older revision		Revision as of 13:47, 28 May 2025
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	\| [[99ed5\|99]]		\| [[99ed5\|99]]
	\|}		\|}

			; 100 and beyond
			* [[116ed5\|116]], [[139ed5\|139]], [[256ed5\|256]]

			<!-- Uncomment this when there are more pages
	{\| class="wikitable center-all mw-collapsible mw-collapsed"		{\| class="wikitable center-all mw-collapsible mw-collapsed"
	\|+ style=white-space:nowrap \| 100…199		\|+ style=white-space:nowrap \| 100…199
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	\| [[299ed5\|299]]		\| [[299ed5\|299]]
	\|}		\|}
			-->

	== Ed5-edo correspondence ==		== Ed5-edo correspondence ==