385edo - 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"

2026-03-13T13:32:39Z

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 13:32, 13 March 2026
Line 100:		Line 100:
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|}		\|}
	<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

	[[Category:Hemipental]]		[[Category:Hemipental]]

Francium: changed EDO intro to ED intro

2025-02-21T06:30:45Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:30, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|385~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 19:45, 15 January 2025

2025-01-15T19:45:16Z

← Older revision		Revision as of 19:45, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out\|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.		385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out\|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/6655]], and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 54:		Line 54:
	\| 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000		\| 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000
	\| {{mapping\| 385 610 894 1081 1332 1425 }}		\| {{mapping\| 385 610 894 1081 1332 1425 }}
	\| ~~−0~~.0394		\| −0.0394
	\| 0.2207		\| 0.2207
	\| 7.08		\| 7.08
Line 61:		Line 61:
	\| 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095		\| 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095
	\| {{mapping\| 385 610 894 1081 1332 1425 1574 }}		\| {{mapping\| 385 610 894 1081 1332 1425 1574 }}
	\| ~~−0~~.0693		\| −0.0693
	\| 0.2171		\| 0.2171
	\| 6.97		\| 6.97
Line 100:		Line 100:
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|}		\|}
	<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

	[[Category:Hemipental]]		[[Category:Hemipental]]

ArrowHead294: Partial undo

2024-11-16T12:41:09Z

Partial undo

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

	== 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 55:		Line 64:
	\| 0.2171		\| 0.2171
	\| 6.97		\| 6.97
	~~{{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
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	\| 4/3<br />(81/80)		\| 4/3<br />(81/80)
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	~~{{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

	[[Category:Hemipental]]		[[Category:Hemipental]]

ArrowHead294 at 04:10, 16 November 2024

2024-11-16T04:10:47Z

← Older revision		Revision as of 04:10, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|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 53:		Line 45:
	\| 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000		\| 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000
	\| {{mapping\| 385 610 894 1081 1332 1425 }}		\| {{mapping\| 385 610 894 1081 1332 1425 }}
	\| -0.0394		\| −0.0394
	\| 0.2207		\| 0.2207
	\| 7.08		\| 7.08
Line 60:		Line 52:
	\| 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095		\| 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095
	\| {{mapping\| 385 610 894 1081 1332 1425 1574 }}		\| {{mapping\| 385 610 894 1081 1332 1425 1574 }}
	\| -0.0693		\| −0.0693
	\| 0.2171		\| 0.2171
	\| 6.97		\| 6.97
	\|}		{{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 87:		Line 73:
	\|-		\|-
	\| 5		\| 5
	\| 80\385<br>(3\385)		\| 80\385<br />(3\385)
	\| 249.35<br>(9.35)		\| 249.35<br />(9.35)
	\| 81/70<br>(176/175)		\| 81/70<br />(176/175)
	\| [[Hemipental]]		\| [[Hemipental]]
	\|-		\|-
	\| 5		\| 5
	\| 160\385<br>(6\385)		\| 160\385<br />(6\385)
	\| 498.70<br>(18.70)		\| 498.70<br />(18.70)
	\| 4/3<br>(81/80)		\| 4/3<br />(81/80)
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|}		{{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}}

	[[Category:Hemipental]]		[[Category:Hemipental]]

Fredg999: Skip disambiguation

2024-09-09T01:59:43Z

Skip disambiguation

← Older revision		Revision as of 01:59, 9 September 2024
Line 96:		Line 96:
	\| 498.70<br>(18.70)		\| 498.70<br>(18.70)
	\| 4/3<br>(81/80)		\| 4/3<br>(81/80)
	\| [[Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Hemipental]]		[[Category:Hemipental]]

FloraC: -typo; review the temp table; +hemipental

2023-11-06T17:21:12Z

-typo; review the temp table; +hemipental

← Older revision		Revision as of 17:21, 6 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out\|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/~~665~~]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.		385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out\|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 76:		Line 76:
	\| 1		\| 1
	\| 62\385		\| 62\385
	\| 193.~~247~~		\| 193.25
	\| ~~4096~~/~~3645~~		\| 262144/234375
	\| [[Luna]]		\| [[Luna]]
	\|-		\|-
	\| 1		\| 1
	\| 162/385		\| 162/385
	\| 504.~~935~~		\| 504.94
	\| 4/3		\| 4/3
	\| [[Countermeantone]]		\| [[Countermeantone]]
			\|-
			\| 5
			\| 80\385<br>(3\385)
			\| 249.35<br>(9.35)
			\| 81/70<br>(176/175)
			\| [[Hemipental]]
	\|-		\|-
	\| 5		\| 5
	\| 160\385<br>(6\385)		\| 160\385<br>(6\385)
	\| 498.~~701~~<br>(18.~~701~~)		\| 498.70<br>(18.70)
	\| 4/3<br>(81/80)		\| 4/3<br>(81/80)
	\| [[Pental]] (5-limit)		\| [[Pental]] (5-limit)

FloraC: Rework; cleanup; clarify the title row of the rank-2 temp table

2023-11-06T17:17:46Z

Rework; cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 17:17, 6 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~385et~~ tempers out ~~following commas:~~		385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out\|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/665]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.

	~~7-limit commas:~~ 589824/588245, ~~134217728/133984375,~~ [[703125/702464]]~~, 1959552/1953125, 5250987/5242880, 200120949/200000000~~

	11-limit ~~commas: 1073741824~~/~~1071794405~~, ~~161280~~/~~161051~~, ~~25165824~~/~~25109315~~, ~~234375~~/~~234256~~, ~~2097152~~/~~2096325, 1366875/1362944~~, 166698/166375, ~~496125~~/~~495616~~, ~~151263~~/~~151250~~, ~~104857600~~/~~104825259~~, [[~~540~~/~~539~~]], ~~172032~~/~~171875~~, ~~369140625~~/~~369098752, 825000~~/~~823543, 180224~~/~~180075~~, [[~~8019~~/~~8000~~]], ~~160083~~/~~160000~~, ~~539055~~/~~537824, 766656/765625, 202397184/201768035, 43923/43904, 20614528/20588575, 39135393/39062500, 781258401/781250000~~

	=== Prime harmonics ===		=== Prime harmonics ===
Line 13:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	385 factors into ~~5 x 7 x 11~~, ~~with~~ subset edos {{EDOs\| 5, 7, 11, 35, 55, and 77 }}.		Since 385 factors into {{factorization\|385}}, 385edo has subset edos {{EDOs\| 5, 7, 11, 35, 55, and 77 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 28:		Line 24:
	\| 2.3		\| 2.3
	\| {{monzo\| -122 77 }}		\| {{monzo\| -122 77 }}
	\| {{~~val~~\| 385 610 }}		\| {{mapping\| 385 610 }}
	\| +0.2070		\| +0.2070
	\| 0.2071		\| 0.2071
Line 35:		Line 31:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| -28 25 -5 }}, {{monzo\| 38 -2 -15 }}		\| {{monzo\| -28 25 -5 }}, {{monzo\| 38 -2 -15 }}
	\| {{~~val~~\| 385 610 894 }}		\| {{mapping\| 385 610 894 }}
	\| +0.1122		\| +0.1122
	\| 0.2158		\| 0.2158
Line 42:		Line 38:
	\| 2.3.5.7		\| 2.3.5.7
	\| 19683/19600, 589824/588245, 703125/702464		\| 19683/19600, 589824/588245, 703125/702464
	\| {{~~val~~\| 385 610 894 1081 }}		\| {{mapping\| 385 610 894 1081 }}
	\| +0.0374		\| +0.0374
	\| 0.2274		\| 0.2274
Line 48:		Line 44:
	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 540/539, 8019/8000, ~~496125~~/~~495616~~, 172032/171875		\| 540/539, 8019/8000, 151263/151250, 172032/171875
	\| {{~~val~~\| 385 610 894 1081 1332 }}		\| {{mapping\| 385 610 894 1081 1332 }}
	\| +0.0085		\| +0.0085
	\| 0.2114		\| 0.2114
Line 55:		Line 51:
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 540/539, ~~1716~~/~~1715~~, ~~8019~~/~~8000~~, 4096/4095, ~~81675~~/~~81536~~		\| 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000
	\| {{~~val~~\| 385 610 894 1081 1332 1425 }}		\| {{mapping\| 385 610 894 1081 1332 1425 }}
	\| -0.0394		\| -0.0394
	\| 0.2207		\| 0.2207
Line 62:		Line 58:
	\|-		\|-
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 540/539, 936/935, 1377/1375, ~~1716~~/~~1715~~, 4096/4095~~, 13365/13328~~		\| 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095
	\| {{~~val~~\| 385 610 894 1081 1332 1425 1574 }}		\| {{mapping\| 385 610 894 1081 1332 1425 1574 }}
	\| -0.0693		\| -0.0693
	\| 0.2171		\| 0.2171
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	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 96:		Line 92:
	\| [[Pental]] (5-limit)		\| [[Pental]] (5-limit)
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	~~{{Todo\| review }}~~		[[Category:Hemipental]]

FloraC: Doesn't support septimal pental so the limit must be specified

2023-05-16T14:20:55Z

Doesn't support septimal pental so the limit must be specified

← Older revision		Revision as of 14:20, 16 May 2023
Line 9:		Line 9:
	11-limit commas: 1073741824/1071794405, 161280/161051, 25165824/25109315, 234375/234256, 2097152/2096325, 1366875/1362944, 166698/166375, 496125/495616, 151263/151250, 104857600/104825259, [[540/539]], 172032/171875, 369140625/369098752, 825000/823543, 180224/180075, [[8019/8000]], 160083/160000, 539055/537824, 766656/765625, 202397184/201768035, 43923/43904, 20614528/20588575, 39135393/39062500, 781258401/781250000		11-limit commas: 1073741824/1071794405, 161280/161051, 25165824/25109315, 234375/234256, 2097152/2096325, 1366875/1362944, 166698/166375, 496125/495616, 151263/151250, 104857600/104825259, [[540/539]], 172032/171875, 369140625/369098752, 825000/823543, 180224/180075, [[8019/8000]], 160083/160000, 539055/537824, 766656/765625, 202397184/201768035, 43923/43904, 20614528/20588575, 39135393/39062500, 781258401/781250000

	===Prime harmonics===		=== Prime harmonics ===
	{{Harmonics in equal\|385}}		{{Harmonics in equal\|385}}

	===Subsets and supersets===		=== Subsets and supersets ===
	385 factors into 5 x 7 x 11, with subset edos {{EDOs\| 5, 7, 11, 35, 55, and 77}}.		385 factors into 5 x 7 x 11, with subset edos {{EDOs\| 5, 7, 11, 35, 55, and 77 }}.

	==Regular temperament properties==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|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
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|-122 77}}		\| {{monzo\| -122 77 }}
	\|{{val\|385 610}}		\| {{val\| 385 610 }}
	\| +0.2070		\| +0.2070
	\| 0.2071		\| 0.2071
	\| 6.64		\| 6.64
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-28 25 -5}}, {{monzo\|38 -2 -15}}		\| {{monzo\| -28 25 -5 }}, {{monzo\| 38 -2 -15 }}
	\|{{val\|385 610 894}}		\| {{val\| 385 610 894 }}
	\| +0.1122		\| +0.1122
	\| 0.2158		\| 0.2158
	\| 6.92		\| 6.92
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|19683/19600, 703125/702464~~, 589824/588245~~		\| 19683/19600, 589824/588245, 703125/702464
	\|{{val\|385 610 894 1081}}		\| {{val\| 385 610 894 1081 }}
	\| +0.0374		\| +0.0374
	\| 0.2274		\| 0.2274
	\| 7.30		\| 7.30
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|540/539, 8019/8000, 496125/495616, 172032/171875		\| 540/539, 8019/8000, 496125/495616, 172032/171875
	\|{{val\|385 610 894 1081 1332}}		\| {{val\| 385 610 894 1081 1332 }}
	\| +0.0085		\| +0.0085
	\| 0.2114		\| 0.2114
	\| 6.78		\| 6.78
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|540/539, 1716/1715, 8019/8000, 4096/4095, 81675/81536		\| 540/539, 1716/1715, 8019/8000, 4096/4095, 81675/81536
	\|{{val\|385 610 894 1081 1332 1425}}		\| {{val\| 385 610 894 1081 1332 1425 }}
	\| -0.0394		\| -0.0394
	\| 0.2207		\| 0.2207
	\| 7.08		\| 7.08
	\|-		\|-
	\|2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\|540/539, 936/935, 1377/1375, 1716/1715, 4096/4095, 13365/13328		\| 540/539, 936/935, 1377/1375, 1716/1715, 4096/4095, 13365/13328
	\|{{val\|385 610 894 1081 1332 1425 1574}}		\| {{val\| 385 610 894 1081 1332 1425 1574 }}
	\| -0.0693		\| -0.0693
	\| 0.2171		\| 0.2171
Line 73:		Line 73:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator<br>(~~reduced~~)		! Generator<br>(Reduced)
	! Cents<br>(~~reduced~~)		! Cents<br>(Reduced)
	! Associated<br>~~ratio~~		! Associated<br>Ratio
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|62\385		\| 62\385
	\|193.247		\| 193.247
	\|4096/3645		\| 4096/3645
	\|[[Luna]]		\| [[Luna]]
	\|-		\|-
	\|1		\| 1
	\|162/385		\| 162/385
	\|504.935		\| 504.935
	\|4/3		\| 4/3
	\|[[Countermeantone]]		\| [[Countermeantone]]
	\|-		\|-
	\|5		\| 5
	\|160\385<br>(6\385)		\| 160\385<br>(6\385)
	\|498.701<br>(18.701)		\| 498.701<br>(18.701)
	\|4/3<br>(81/80)		\| 4/3<br>(81/80)
	\|[[Pental]]		\| [[Pental]] (5-limit)
	\|}		\|}

			{{Todo\| review }}

Francium: Created page because the category already existed

2023-05-15T12:27:14Z

Created page because the category already existed

New page

{{Infobox ET}}
{{EDO intro|385}}

== Theory ==
385et tempers out following commas:

7-limit commas: 589824/588245, 134217728/133984375, [[703125/702464]], 1959552/1953125, 5250987/5242880, 200120949/200000000

11-limit commas: 1073741824/1071794405, 161280/161051, 25165824/25109315, 234375/234256, 2097152/2096325, 1366875/1362944, 166698/166375, 496125/495616, 151263/151250, 104857600/104825259, [[540/539]], 172032/171875, 369140625/369098752, 825000/823543, 180224/180075, [[8019/8000]], 160083/160000, 539055/537824, 766656/765625, 202397184/201768035, 43923/43904, 20614528/20588575, 39135393/39062500, 781258401/781250000

===Prime harmonics===
{{Harmonics in equal|385}}

===Subsets and supersets===
385 factors into 5 x 7 x 11, with subset edos {{EDOs| 5, 7, 11, 35, 55, and 77}}.

==Regular temperament properties==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|-122 77}}
|{{val|385 610}}
| +0.2070
| 0.2071
| 6.64
|-
|2.3.5
|{{monzo|-28 25 -5}}, {{monzo|38 -2 -15}}
|{{val|385 610 894}}
| +0.1122
| 0.2158
| 6.92
|-
|2.3.5.7
|19683/19600, 703125/702464, 589824/588245
|{{val|385 610 894 1081}}
| +0.0374
| 0.2274
| 7.30
|-
|2.3.5.7.11
|540/539, 8019/8000, 496125/495616, 172032/171875
|{{val|385 610 894 1081 1332}}
| +0.0085
| 0.2114
| 6.78
|-
|2.3.5.7.11.13
|540/539, 1716/1715, 8019/8000, 4096/4095, 81675/81536
|{{val|385 610 894 1081 1332 1425}}
| -0.0394
| 0.2207
| 7.08
|-
|2.3.5.7.11.13.17
|540/539, 936/935, 1377/1375, 1716/1715, 4096/4095, 13365/13328
|{{val|385 610 894 1081 1332 1425 1574}}
| -0.0693
| 0.2171
| 6.97
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator (reduced)
! Cents (reduced)
! Associated ratio
! Temperaments
|-
|1
|62\385
|193.247
|4096/3645
|[[Luna]]
|-
|1
|162/385
|504.935
|4/3
|[[Countermeantone]]
|-
|5
|160\385 (6\385)
|498.701 (18.701)
|4/3 (81/80)
|[[Pental]]
|}