353edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:31:42Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:31, 13 March 2026
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	\| [[Marvo]] (353c) / [[zarvo]] (353cd)		\| [[Marvo]] (353c) / [[zarvo]] (353cd)
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

Lériendil at 05:06, 2 March 2025

2025-03-02T05:06:18Z

← Older revision		Revision as of 05:06, 2 March 2025
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	== Theory ==		== Theory ==
	353edo is in[[consistent]] in the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. It is suitable for use with the 2.9.15.7.11.13.17.23.29.31.37 [[subgroup]]. This makes 353edo an "upside-down" edo—poor approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the [[optimal patent val]] for [[didacus]], the 2.5.7 subgroup temperament tempering out [[3136/3125]].		353edo is in[[consistent]] in the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. It is suitable for use with the 2.9.15.7.11.13.17.23.29.31.37 [[subgroup]]. This makes 353edo an "upside-down" edo—poor approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the [[optimal patent val]] for [[didacus]], the 2.5.7 subgroup temperament tempering out [[3136/3125]], and serves as a very close approximation of its just-[[7/4]] tuning.

	Using the [[patent val]] nonetheless, 353edo supports [[apparatus]], [[marvo]] and [[zarvo]].		Using the [[patent val]] nonetheless, 353edo supports [[apparatus]], [[marvo]] and [[zarvo]].

ArrowHead294 at 22:53, 20 February 2025

2025-02-20T22:53:18Z

← Older revision		Revision as of 22:53, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|353~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 15:24, 16 January 2025

2025-01-16T15:24:34Z

← Older revision		Revision as of 15:24, 16 January 2025
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	\| [[Marvo]] (353c) / [[zarvo]] (353cd)		\| [[Marvo]] (353c) / [[zarvo]] (353cd)
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

ArrowHead294 at 15:19, 16 January 2025

2025-01-16T15:19:56Z

← Older revision		Revision as of 15:19, 16 January 2025
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	== Theory ==		== Theory ==
	353edo is in[[consistent]] in the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. It is suitable for use with the 2.9.15.7.11.13.17.23.29.31.37 [[subgroup]]. This makes 353edo an "upside-down" ~~edo – poor~~ approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the [[optimal patent val]] for [[didacus]], the 2.5.7 subgroup temperament tempering out [[3136/3125]].		353edo is in[[consistent]] in the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. It is suitable for use with the 2.9.15.7.11.13.17.23.29.31.37 [[subgroup]]. This makes 353edo an "upside-down" edo—poor approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the [[optimal patent val]] for [[didacus]], the 2.5.7 subgroup temperament tempering out [[3136/3125]].

	Using the [[patent val]] nonetheless, 353edo supports [[apparatus]], [[marvo]] and [[zarvo]].		Using the [[patent val]] nonetheless, 353edo supports [[apparatus]], [[marvo]] and [[zarvo]].
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	The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה), the deficient year.		The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה), the deficient year.

	It is possible to use a superpyth-ish fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, 76 & 353 temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo\|-103 0 -38 51 0 13}}.		It is possible to use a superpyth-ish fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, {{nowrap\|76 & 353}} temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo\|-103 0 -38 51 0 13}}.

	== Table of intervals ==		== Table of intervals ==
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	\| {{monzo\| 820 -353 }}		\| {{monzo\| 820 -353 }}
	\| {{mapping\| 353 820 }}		\| {{mapping\| 353 820 }}
	\| ~~−0~~.263		\| −0.263
	\| 0.263		\| 0.263
	\| 7.74		\| 7.74
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	\| 3136/3125, {{monzo\| 209 -9 -67 }}		\| 3136/3125, {{monzo\| 209 -9 -67 }}
	\| {{mapping\| 353 820 991 }}		\| {{mapping\| 353 820 991 }}
	\| ~~−0~~.177		\| −0.177
	\| 0.247		\| 0.247
	\| 7.26		\| 7.26
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	\| 3136/3125, 5767168/5764801, {{monzo\| -20 -6 1 9 }}		\| 3136/3125, 5767168/5764801, {{monzo\| -20 -6 1 9 }}
	\| {{mapping\| 353 820 991 1221 }}		\| {{mapping\| 353 820 991 1221 }}
	\| ~~−0~~.089		\| −0.089
	\| 0.263		\| 0.263
	\| 7.73		\| 7.73
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	\| 3136/3125, 4394/4375, 6656/6655, 5767168/5764801		\| 3136/3125, 4394/4375, 6656/6655, 5767168/5764801
	\| {{mapping\| 353 820 991 1221 1306 }}		\| {{mapping\| 353 820 991 1221 1306 }}
	\| ~~−0~~.024		\| −0.024
	\| 0.268		\| 0.268
	\| 7.89		\| 7.89
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	\| 3136/3125, 4394/4375, 7744/7735, 60112/60025, 64141/64000		\| 3136/3125, 4394/4375, 7744/7735, 60112/60025, 64141/64000
	\| {{mapping\| 353 820 991 1221 1306 1443 }}		\| {{mapping\| 353 820 991 1221 1306 1443 }}
	\| ~~−0~~.037		\| −0.037
	\| 0.247		\| 0.247
	\| 7.26		\| 7.26
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	== Scales ==		== Scales ==
	* RectifiedHebrew[19] ~~–~~ 18L 1s		* RectifiedHebrew[19] – 18L 1s
	* RectifiedHebrew[130] ~~–~~ 93L 37s		* RectifiedHebrew[130] – 93L 37s
	* Austro-Hungarian Minor[9] ~~–~~ 57 38 38 38 38 38 38 38 30		* Austro-Hungarian Minor[9] – 57 38 38 38 38 38 38 38 30

	== See also ==		== See also ==
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	== Music ==		== Music ==
	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=JrSEGE6_oys ''Snow On My City''] (2022) ~~–~~ cover of [[wikipedia:Naomi Shemer\|Naomi Shemer]] in Rectified Hebrew and apparatus		* [https://www.youtube.com/watch?v=JrSEGE6_oys ''Snow On My City''] (2022) – cover of [[wikipedia:Naomi Shemer\|Naomi Shemer]] in Rectified Hebrew and apparatus
	; [[Mercury Amalgam]]		; [[Mercury Amalgam]]
	* [https://www.youtube.com/watch?v=z-SxvrnkTzU ''Bottom Text''] (2022) in Rectified Hebrew		* [https://www.youtube.com/watch?v=z-SxvrnkTzU ''Bottom Text''] (2022) in Rectified Hebrew

ArrowHead294: Partial undo

2024-11-16T11:44:34Z

Partial undo

← Older revision		Revision as of 11:44, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	Assuming 353edo is treated as the 2.5.7.11.13.17 subgroup temperament.		Assuming 353edo is treated as the 2.5.7.11.13.17 subgroup temperament.
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.5		\| 2.5
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	\| 0.247		\| 0.247
	\| 7.26		\| 7.26
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperament
	\|-		\|-
	\| 1		\| 1
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	\| 27/20		\| 27/20
	\| [[Marvo]] (353c) / [[zarvo]] (353cd)		\| [[Marvo]] (353c) / [[zarvo]] (353cd)
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==

ArrowHead294: /* Table of intervals */

2024-11-16T06:01:43Z

Table of intervals

← Older revision		Revision as of 06:01, 16 November 2024
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	\|-		\|-
	! Step		! Step
	! Note name~~<br /><span style="font-size: 0.75em;">(diatonic Hebrew[19] version)</span>~~		! Note name*
	! Associated ratio~~<br /><span style="font-size: 0.75em;">(2.5.7.13 subgroup)</span>~~		! Associated ratio**
	\|-		\|-
	\| 0		\| 0
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	\| 2/1		\| 2/1
	\|}		\|}
			<nowiki />* Diatonic Hebrew[19] version

			<nowiki />** 2.5.7.13 subgroup

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294 at 06:00, 16 November 2024

2024-11-16T06:00:45Z

Show changes

Eliora: /* Music */ add another item of music

2023-11-13T12:45:24Z

Music: add another item of music

← Older revision		Revision as of 12:45, 13 November 2023
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	== Music ==		== Music ==
			; [[Eliora]]
			* [https://www.youtube.com/watch?v=JrSEGE6_oys ''Snow On My City''] (2022) - cover of [[wikipedia:Naomi Shemer\|Naomi Shemer]] in Rectified Hebrew and apparatus
	; [[Mercury Amalgam]]		; [[Mercury Amalgam]]
	* [https://www.youtube.com/watch?v=z-SxvrnkTzU ''Bottom Text''] (2022)		* [https://www.youtube.com/watch?v=z-SxvrnkTzU ''Bottom Text''] (2022) in Rectified Hebrew

	== External links ==		== External links ==

FloraC: /* Theory */ review and rework

2023-11-12T10:45:55Z

Theory: review and rework

← Older revision		Revision as of 10:45, 12 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~From~~ the ~~prime number standpoint, 353edo~~ is suitable for use with 2.7.11.17.23.29.31.37 subgroup. This makes 353edo an "upside-down" ~~EDO~~ – poor approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the [[optimal patent val]] for [[didacus]], the 2.5.7 subgroup temperament tempering out [[3136/3125]].		353edo is in[[consistent]] in the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. It is suitable for use with the 2.9.15.7.11.13.17.23.29.31.37 [[subgroup]]. This makes 353edo an "upside-down" edo – poor approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the [[optimal patent val]] for [[didacus]], the 2.5.7 subgroup temperament tempering out [[3136/3125]].

			Using the [[patent val]] nonetheless, 353edo supports [[apparatus]], [[marvo]] and [[zarvo]].

	=== Odd harmonics ===		=== Odd harmonics ===
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	353edo is the 71st [[prime edo]].		353edo is the 71st [[prime edo]].

	=== ~~Relation to a calendar reform~~ ===		=== Miscellaneous properties ===
	~~''Main article:~~ [[~~Rectified Hebrew~~]]''		[[Eliora]] associates 353edo with a reformed Hebrew calendar. In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern (makhzor (מחזור), plural: makhzorim) are leap. When converted to [[19edo]], this results in [[5L 2s]] mode, and simply the diatonic major scale. Following this logic, a temperament (→ [[rectified hebrew]]) can be constructed for the Rectified Hebrew calendar. The 11-step perfect fifth in this scale becomes 209\353, and it corresponds to 98/65, which is sharp of 3/2 by 196/195.

	In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern (makhzor (מחזור), plural:makhzorim) are leap. When converted to [[19edo]], this results in [[5L 2s]] mode, and simply the diatonic major scale. Following this logic, a temperament can be constructed for the Rectified Hebrew calendar.

	The 11-step perfect fifth in this scale becomes 209\353, and it corresponds to 98/65, which is sharp of 3/2 by 196/195.

	In addition, every sub-pattern in a 19-note generator is actually a Hebrew makhzor, that is a mini-19edo on its own, until it is truncated to an 11-note pattern. Just as the original calendar reform consists of 18 makhzorim with 1 hendecaeteris, Hebrew[130] scale consists of a stack of naively 18 "major scales" finished with one 11-edo tetratonic.		In addition, every sub-pattern in a 19-note generator is actually a Hebrew makhzor, that is a mini-19edo on its own, until it is truncated to an 11-note pattern. Just as the original calendar reform consists of 18 makhzorim with 1 hendecaeteris, Hebrew[130] scale consists of a stack of naively 18 "major scales" finished with one 11-edo tetratonic.

	The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה)'','' the deficient year.		The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה), the deficient year.

	~~=== Other ===~~
	It's possible to use superpyth fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, 76 & 353 temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo\|-103 0 -38 51 0 13}}.

	~~353edo also supports apparatus temperaments~~, and ~~marvo and zarvo~~.		It is possible to use a superpyth-ish fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, 76 & 353 temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo\|-103 0 -38 51 0 13}}.

	== Table of intervals ==		== Table of intervals ==