730edo - 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"

2026-03-13T13:38:15Z

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 13:38, 13 March 2026
Line 140:		Line 140:
	\| [[Deca]]		\| [[Deca]]
	\|}		\|}
	<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 ==

FloraC: /* Regular temperament properties */ crazy update

2025-03-06T11:38:36Z

Regular temperament properties: crazy update

← Older revision		Revision as of 11:38, 6 March 2025
Line 46:		Line 46:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
Line 53:		Line 53:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| -1157 730 }}		\| {{Monzo\| -1157 730 }}
	\| {{~~mapping~~\| 730 1157 }}		\| {{Mapping\| 730 1157 }}
	\| +0.0117		\| +0.0117
	\| 0.0117		\| 0.0117
Line 60:		Line 60:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| -53 10 16 }}, {{monzo\| -16 35 -17 }}		\| {{Monzo\| -53 10 16 }}, {{monzo\| -16 35 -17 }}
	\| {{~~mapping~~\| 730 1157 1695 }}		\| {{Mapping\| 730 1157 1695 }}
	\| +0.0096		\| +0.0096
	\| 0.0100		\| 0.0100
Line 68:		Line 68:
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 2100875/2097152, {{monzo\| 12 -3 -14 9 }}		\| 4375/4374, 2100875/2097152, {{monzo\| 12 -3 -14 9 }}
	\| {{~~mapping~~\| 730 1157 1695 2049 }}		\| {{Mapping\| 730 1157 1695 2049 }}
	\| +0.0612		\| +0.0612
	\| 0.0899		\| 0.0899
Line 75:		Line 75:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 4375/4374, 391314/390625, 2100875/2097152		\| 3025/3024, 4375/4374, 391314/390625, 2100875/2097152
	\| {{~~mapping~~\| 730 1157 1695 2049 2525 }}		\| {{Mapping\| 730 1157 1695 2049 2525 }}
	\| +0.0856		\| +0.0856
	\| 0.0940		\| 0.0940
Line 82:		Line 82:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 1001/1000, 3025/3024, 4225/4224, 4375/4374, 2100875/2097152		\| 1001/1000, 3025/3024, 4225/4224, 4375/4374, 2100875/2097152
	\| {{~~mapping~~\| 730 1157 1695 2049 2525 2701 }}		\| {{Mapping\| 730 1157 1695 2049 2525 2701 }}
	\| +0.0951		\| +0.0951
	\| 0.0884		\| 0.0884
Line 92:		Line 92:
	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 102:		Line 102:
	\| 162.74		\| 162.74
	\| 1125/1024		\| 1125/1024
	\| [[~~Kwazy~~]]		\| [[Crazy]]
	\|-		\|-
	\| 1		\| 1
Line 113:		Line 113:
	\| 113\730		\| 113\730
	\| 185.75		\| 185.75
	\| {{~~monzo~~\| 24 4 -13 }}		\| {{Monzo\| 24 4 -13 }}
	\| [[Pirate]]		\| [[Pirate]]
	\|-		\|-
Line 135:		Line 135:
	\|-		\|-
	\| 10		\| 10
	\| 192\730<br />(27\730)		\| 192\730<br>(27\730)
	\| 315.62<br />(44.38)		\| 315.62<br>(44.38)
	\| 6/5<br />(40/39)		\| 6/5<br>(40/39)
	\| [[Deca]]		\| [[Deca]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal~~ lists\|minimal form]] in parentheses if 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 16:07, 20 February 2025

2025-02-20T16:07:09Z

← Older revision		Revision as of 16:07, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|730~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	730edo is a very strong 5-limit system, but is also [[consistency\|distinctly consistent]] up to the [[15-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the {{monzo\| -69 45 -1 }} ([[counterschisma]]), {{monzo\| -16 35 -17 }} (minortone comma), {{monzo\| -53 10 16 }} ([[kwazy comma]]), {{monzo\| 37 25 -33 }} (whoosh comma), and {{monzo\| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.		730edo is a very strong 5-limit system, but is also [[consistency\|distinctly consistent]] up to the [[15-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the {{monzo\| -69 45 -1 }} ([[counterschisma]]), {{monzo\| -16 35 -17 }} (minortone comma), {{monzo\| -53 10 16 }} ([[kwazy comma]]), {{monzo\| 37 25 -33 }} (whoosh comma), and {{monzo\| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.

	{{W\|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure\|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.		{{W\|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure\|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146, and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: /* Theory */ cleanup

2025-01-17T16:34:31Z

Theory: cleanup

← Older revision		Revision as of 16:34, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	730edo is a very strong 5-limit system, but is also [[consistency\|distinctly consistent]] up to the [[15-odd-limit]]. It [[tempers out]] the {{monzo\| -69 45 -1 }} ([[counterschisma]]), {{monzo\| -16 35 -17 }} (minortone comma), {{monzo\| -53 10 16 }} ([[kwazy comma]]), {{monzo\| 37 25 -33 }} (whoosh comma), and {{monzo\| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.		730edo is a very strong 5-limit system, but is also [[consistency\|distinctly consistent]] up to the [[15-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the {{monzo\| -69 45 -1 }} ([[counterschisma]]), {{monzo\| -16 35 -17 }} (minortone comma), {{monzo\| -53 10 16 }} ([[kwazy comma]]), {{monzo\| 37 25 -33 }} (whoosh comma), and {{monzo\| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.

	{{W\|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure\|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.		{{W\|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure\|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|730~~\|columns=11~~}}		{{Harmonics in equal\|730}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 730 factors into ~~{{factorization\|730}}~~, 730edo has subset edos {{EDOs\| 2, 5, 10, 73, 146, and 365 }}. 1460edo, which doubles it, gives alternative approximations to harmonics 7, 11, and 13. [[2190edo]], which triples it, corrects these harmonics to near-just levels of accuracy. [[4380edo]] gives a possible full 31-limit system.		Since 730 factors into 2 × 5 × 73, 730edo has subset edos {{EDOs\| 2, 5, 10, 73, 146, and 365 }}. 1460edo, which doubles it, gives alternative approximations to harmonics 7, 11, and 13. [[2190edo]], which triples it, corrects these harmonics to near-just levels of accuracy. [[4380edo]] gives a possible full 31-limit system.

	== Intervals ==		== Intervals ==

ArrowHead294 at 15:28, 16 January 2025

2025-01-16T15:28:06Z

← Older revision		Revision as of 15:28, 16 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	730edo is a very strong 5-limit system, but is also [[consistency\|distinctly consistent]] up to the [[15-odd-limit]]. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] the {{monzo\| -69 45 -1 }} ([[counterschisma]]), {{monzo\| -16 35 -17 }} (minortone comma), {{monzo\| -53 10 16 }} ([[kwazy comma]]), {{monzo\| 37 25 -33 }} (whoosh comma), and {{monzo\| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.		730edo is a very strong 5-limit system, but is also [[consistency\|distinctly consistent]] up to the [[15-odd-limit]]. It [[tempers out]] the {{monzo\| -69 45 -1 }} ([[counterschisma]]), {{monzo\| -16 35 -17 }} (minortone comma), {{monzo\| -53 10 16 }} ([[kwazy comma]]), {{monzo\| 37 25 -33 }} (whoosh comma), and {{monzo\| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.

	{{W\|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure\|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.		{{W\|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure\|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.
Line 140:		Line 140:
	\| [[Deca]]		\| [[Deca]]
	\|}		\|}
	<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 12:02, 16 November 2024

2024-11-16T12:02:28Z

← Older revision		Revision as of 12:02, 16 November 2024
Line 41:		Line 41:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{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]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 77:		Line 86:
	\| 0.0884		\| 0.0884
	\| 5.38		\| 5.38
	~~{{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*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 123:		Line 139:
	\| 6/5<br />(40/39)		\| 6/5<br />(40/39)
	\| [[Deca]]		\| [[Deca]]
	~~{{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 at 05:44, 16 November 2024

2024-11-16T05:44:21Z

← Older revision		Revision as of 05:44, 16 November 2024
Line 41:		Line 41:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal 8ve<br>stretch (¢)~~
	~~! colspan="2" \| Tuning error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 85:		Line 77:
	\| 0.0884		\| 0.0884
	\| 5.38		\| 5.38
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 133:		Line 119:
	\|-		\|-
	\| 10		\| 10
	\| 192\730<br>(27\730)		\| 192\730<br />(27\730)
	\| 315.62<br>(44.38)		\| 315.62<br />(44.38)
	\| 6/5<br>(40/39)		\| 6/5<br />(40/39)
	\| [[Deca]]		\| [[Deca]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Scales ==		== Scales ==
Line 171:		Line 157:

	{\| class="wikitable"		{\| class="wikitable"
	\|+Woolhouse 730EDO diatonic scale		\|+ style="font-size: 105%;" \| Woolhouse 730EDO diatonic scale
	\|-
	~~!Sequence!!Mode (suggested name)!!I1!!I2!!I3!!I4!!I5!!I6!!I7~~
	\|-		\|-
	~~\|LMsLMLs\|\|Woolhouse Ionian\|\|P1\|\|[[9/8\|M2]]\|\|[[5/4\|M3<sup>5</sup>]]\|\|[[4/3\|P4]]\|\|[[3/2\|P5]]\|\|[[5/3\|M6<sup>5</sup>]]\|\|[[15/8\|M7<sup>5</sup>]]~~		! Sequence !! Mode (suggested name) !! I1 !! I2 !! I3 !! I4 !! I5 !! I6 !! I7
	\|-		\|-
	\|~~MsLMLsL~~\|\|Woolhouse ~~Dorian~~\|\|P1\|\|~~m2<sub>~~5</~~sub>\|~~\|m3<~~sub~~>5</~~sub~~>\|\|P4\|\|P5\|\|m6<~~sub~~>5</~~sub~~>\|\|m7<~~sub~~>5</~~sub~~>		\| LMsLMLs \|\| Woolhouse Ionian \|\| P1 \|\| [[9/8\|M2]] \|\| [[5/4\|M3<sup>5</sup>]] \|\| [[4/3\|P4]] \|\| [[3/2\|P5]] \|\| [[5/3\|M6<sup>5</sup>]] \|\| [[15/8\|M7<sup>5</sup>]]
	\|-		\|-
	\|~~sLMLsLM~~\|\|Woolhouse ~~Phrygian~~\|\|P1\|\|M2<~~sup~~>5</~~sup~~>\|\|M3<~~sup~~>5</~~sup~~>\|\|P4\|\|P5\|\|M6<~~sup~~>5</~~sup~~>\|\|m7		\| MsLMLsL \|\| Woolhouse Dorian \|\| P1 \|\| m2<sub>5</sub> \|\| m3<sub>5</sub> \|\| P4 \|\| P5 \|\| m6<sub>5</sub> \|\| m7<sub>5</sub>
	\|-		\|-
	\|~~LMLsLMs~~\|\|Woolhouse ~~Lydian~~\|\|P1\|\|m2<~~sub~~>5</~~sub~~>\|\|m3<~~sub~~>5</~~sub~~>\|\|P4\|\|~~d5<sup>17</sup>~~\|\|m6<~~sub~~>5</~~sub~~>\|\|m7		\| sLMLsLM \|\| Woolhouse Phrygian \|\| P1 \|\| M2<sup>5</sup> \|\| M3<sup>5</sup> \|\| P4 \|\| P5 \|\| M6<sup>5</sup> \|\| m7
	\|-		\|-
	\|~~MLsLMsL~~\|\|Woolhouse ~~Mixolydian~~\|\|P1\|\|M2<~~sup~~>5</~~sup~~>\|\|m3<~~sup~~>19</~~sup~~>\|\|P4\|\|-\|\|M6<~~sup~~>5</~~sup~~>\|\|m7		\| LMLsLMs \|\| Woolhouse Lydian \|\| P1 \|\| m2<sub>5</sub> \|\| m3<sub>5</sub> \|\| P4 \|\| d5<sup>17</sup> \|\| m6<sub>5</sub> \|\| m7
	\|-		\|-
	\|~~LsLMsLM~~\|\|Woolhouse ~~Aeolian~~\|\|P1\|\|M2~~\|\|M3~~<sup>5</sup>\|\|A4<sup>5</sup>\|\|P5\|\|~~d7<sup>17</sup><sub>5</sub>~~\|\|M7<sup>5</sup>		\| MLsLMsL \|\| Woolhouse Mixolydian \|\| P1 \|\| M2<sup>5</sup> \|\| m3<sup>19</sup> \|\| P4 \|\| — \|\| M6<sup>5</sup> \|\| m7
	\|-		\|-
	\|~~sLMsLML~~\|\|Woolhouse ~~Locrian~~\|\|P1\|\|M2\|\|m3<~~sub~~>5</~~sub~~>\|\|P4<sup>19</sup><~~sub~~>7</~~sub~~>~~\|\|P5\|\|m6~~<sub>5</sub>\|\|m7<~~sub~~>5</~~sub~~>		\| LsLMsLM \|\| Woolhouse Aeolian \|\| P1 \|\| M2 \|\| M3<sup>5</sup> \|\| A4<sup>5</sup> \|\| P5 \|\| d7<sup>17</sup><sub>5</sub> \|\| M7<sup>5</sup>
	\|-		\|-
			\| sLMsLML \|\| Woolhouse Locrian \|\| P1 \|\| M2 \|\| m3<sub>5</sub> \|\| P4<sup>19</sup><sub>7</sub> \|\|P5 \|\| m6<sub>5</sub> \|\| m7<sub>5</sub>
	\|}		\|}

Fredg999: External link

2024-07-05T04:17:06Z

External link

← Older revision		Revision as of 04:17, 5 July 2024
Line 193:		Line 193:
	== References ==		== References ==
	<references />		<references />

			== External links ==
			* [http://tonalsoft.com/enc/w/woolhouse-unit.aspx woolhouse-unit] on [[Tonalsoft Encyclopedia]]

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

FloraC: Cleanup and +links

2024-04-23T13:57:54Z

Cleanup and +links

← Older revision		Revision as of 13:57, 23 April 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	730edo is a very strong 5-limit system, but is also [[consistency\|distinctly consistent]] up to the [[15-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the {{monzo\| -69 45 -1 }} ([[counterschisma]]), {{monzo\| -16 35 -17 }} (minortone comma), {{monzo\| -53 10 16 }} (kwazy comma), {{monzo\| 37 25 -33 }} (whoosh comma), and {{monzo\| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.		730edo is a very strong 5-limit system, but is also [[consistency\|distinctly consistent]] up to the [[15-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the {{monzo\| -69 45 -1 }} ([[counterschisma]]), {{monzo\| -16 35 -17 }} (minortone comma), {{monzo\| -53 10 16 }} ([[kwazy comma]]), {{monzo\| 37 25 -33 }} (whoosh comma), and {{monzo\| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.

	[[W. S. B. Woolhouse]] proposed 730edo as a [[interval size measure\|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.		{{W\|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure\|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 93:		Line 93:
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T12:24:33Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 12:24, 2 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	730edo is a very strong 5-limit system, but is also [[~~Consistency~~\|distinctly consistent]] up to the [[15-odd-limit]]. The equal temperament [[~~Tempering~~ out\|tempers out]] the ~~[[counterschisma]],~~ {{monzo\| -69 45 -1 }}~~, the minortone comma~~, {{monzo\| -16 35 -17 }}~~, the kwazy~~ comma, {{monzo\| -53 10 16 }}~~, the whoosh~~ comma, {{monzo\| 37 25 -33 }}, and ~~the pirate comma,~~ {{monzo\| -90 -15 49 }}. In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.		730edo is a very strong 5-limit system, but is also [[consistency\|distinctly consistent]] up to the [[15-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the {{monzo\| -69 45 -1 }} ([[counterschisma]]), {{monzo\| -16 35 -17 }} (minortone comma), {{monzo\| -53 10 16 }} (kwazy comma), {{monzo\| 37 25 -33 }} (whoosh comma), and {{monzo\| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo\| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo\| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.

	[[W. S. B. Woolhouse]] proposed 730edo<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref> ~~as a [[Interval size measure\|logarithmic measure of interval size]]~~, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.		[[W. S. B. Woolhouse]] proposed 730edo as a [[interval size measure\|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 730 factors into ~~2 × 5 × 73~~, 730edo has subset edos {{EDOs\| 2, 5, 10, 73, 146, and 365 }}. 1460edo, which doubles it, gives alternative approximations to harmonics 7, 11, and 13. [[2190edo]], which triples it, corrects these harmonics to near-just levels of accuracy. [[4380edo]] gives a possible full 31-limit system.		Since 730 factors into {{factorization\|730}}, 730edo has subset edos {{EDOs\| 2, 5, 10, 73, 146, and 365 }}. 1460edo, which doubles it, gives alternative approximations to harmonics 7, 11, and 13. [[2190edo]], which triples it, corrects these harmonics to near-just levels of accuracy. [[4380edo]] gives a possible full 31-limit system.

	== Intervals ==		== Intervals ==