ED5 - Revision history

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 ==

FloraC: Cleanup

2025-05-28T13:44:52Z

Cleanup

← Older revision		Revision as of 13:44, 28 May 2025
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	~~The~~ '''equal division of the 5th harmonic''' ('''ed5''') is a [[tuning]] obtained by dividing the [[5/1\|5th harmonic]] in a certain number of [[equal]] steps.		An '''equal division of the 5th harmonic''' ('''ed5''') is a [[tuning]] obtained by dividing the [[5/1\|5th harmonic]] in a certain number of [[equal]] steps.

	~~== Theory ==~~		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 is particularly wide as far as [[equivalence]]s go~~. There~~ are (at absolute most~~) ~~~4.8 ~~pentaves~~ within the human hearing range~~; imagine if that were the case with octaves~~. If one does indeed deal with ~~pentave~~ equivalence, this range restriction is a crucial consideration~~. Pentave equivalence itself may have a basis in Western music seeing as minor chords have an octave of 5 in their root (i.e. 10:12:15)~~.

	One way to treat 5/1 as an equivalence is by eliminating the primes 2 and 3. The most fundamental chord in this paradigm is 5:7:11. This chord can be approximated in a 5.7.11 ~~(or "no~~-~~twos-or-threes [[11-limit]]")~~ subgroup [[regular temperament]] by eliminating the comma 859375/823543, equating a stack of 7 [[7/5]] generators with [[11/5]]. Other equivalences that could be used for such "no-~~two~~-~~or-threes"~~ 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]]. 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]].

	The quintessential example of a ~~pentave~~ based tuning is hyperpyth (see [[17ed5]]). However, perhaps the more common reason to use these ~~scales~~ 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-~~fives~~", full on zeta)~~. Other reasons for taking the ''n''-th root of 5 include finding temperaments like [[orwell]], [[meantone]], and [[thuja]]. This approach can of course be used indiscriminately~~.		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).

	~~Some equal divisions~~ of ~~the pentave are known by alternate names or have special interest:~~		== As generator chains for temperaments ==
			One reason for taking the ''n''-th root of 5 include finding temperaments like [[orwell]], [[meantone]], and [[thuja]]. This approach can of course be used indiscriminately. The ed5's serve as generator chains for

	* [[3ed5]] [[orwell]] generator		* [[3ed5]] – [[orwell]] generator
	* [[4ed5]] [[meantone]] generator		* [[4ed5]] – [[meantone]] generator
	* [[5ed5]] [[~~2L_7s\|~~thuja]] generator		* [[5ed5]] – [[thuja]] generator
	* [[6ed5]] [[~~Trienstonic clan #Uncle\|~~uncle]] generator		* [[6ed5]] – [[uncle]] generator
	* [[8ed5]] [[mohajira]] generator		* [[8ed5]] – [[mohajira]] generator
	* [[Hyperpyth]] tuning (e.g. [[17ed5]])		* [[Hyperpyth]] tuning (e.g. [[17ed5]])
	* [[20ed5]] Hieronymus Tuning		* [[20ed5]] – Hieronymus Tuning
	* [[25ed5]] (Stockhausen, McLaren)		* [[25ed5]] – Stockhausen, McLaren

	== Individual pages for ed5's ==		== Individual pages for ed5's ==

Lériendil: Lériendil moved page Ed5 to ED5: consistency w/ EDT, etc.

2024-08-26T22:33:14Z

Lériendil moved page Ed5 to ED5: consistency w/ EDT, etc.

← Older revision	Revision as of 22:33, 26 August 2024
(No difference)

FloraC: Recategorize

2024-05-19T09:22:01Z

Recategorize

← Older revision		Revision as of 09:22, 19 May 2024
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	* [[Pentave Reduced Subharmonics]]		* [[Pentave Reduced Subharmonics]]
	* [[Relative errors of small ED5s]]		* [[Relative errors of small ED5s]]
	* http://www.nonoctave.com/tuning/fifth_harmonic.html

	[~~[Category~~:~~Equal-step~~ tuning]]		== External links ==
			* [http://www.nonoctave.com/tuning/fifth_harmonic.html\| Nonoctave.com: tuning: equal division of the fifth harmonic]

	[[Category:Ed5\| ]] <!-- main article -->		[[Category:Ed5\| ]] <!-- main article -->
	[[category:~~Nonoctave~~]]		[[category:Edonoi]]
			[[Category:Lists of scales]]
	[[Category:Pentave]]		[[Category:Pentave]]

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

FloraC: Rework the trivial statement into something more informative; improve linking and style; misc. cleanup

2024-05-19T08:43:17Z

Rework the trivial statement into something more informative; improve linking and style; misc. cleanup

Show changes

BudjarnLambeth: /* Individual pages for ED5s */ Copied table structure from EDO page

2024-01-15T09:57:27Z

Individual pages for ED5s: Copied table structure from EDO page

Show changes