315edo - 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"

2026-03-13T13:32:58Z

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
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	\| [[Ennealimmal]]		\| [[Ennealimmal]]
	\|}		\|}
	<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

Overthink: /* Theory */

2025-10-14T17:41:36Z

Theory

← Older revision		Revision as of 17:41, 14 October 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 315 factors into 3<sup>2</sup> × 5 × 7, 315edo has subset edos {{EDOs\| 3, 5, 7, 9, 15, 21, 35, 45, 63, and 105 }}. [[945edo]], which triples it, gives a good correction to the ~~harmonic~~ 11.		Since 315 factors into 3<sup>2</sup> × 5 × 7, 315edo has subset edos {{EDOs\| 3, 5, 7, 9, 15, 21, 35, 45, 63, and 105 }}. [[945edo]], which triples it, gives a good correction to the harmonics 3, 5, 7, and 11.

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

Francium: changed EDO intro to ED intro

2025-02-21T06:25:33Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:25, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|315~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:43, 15 January 2025

2025-01-15T17:43:58Z

← Older revision		Revision as of 17:43, 15 January 2025
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	\| {{monzo\|-499 315}}		\| {{monzo\|-499 315}}
	\| {{mapping\|315 499}}		\| {{mapping\|315 499}}
	\| 0.3163		\| +0.3163
	\| 0.3164		\| 0.3164
	\| 8.31		\| 8.31
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	\| {{monzo\| -27 -2 13 }}, {{monzo\| -28 25 -5 }}		\| {{monzo\| -27 -2 13 }}, {{monzo\| -28 25 -5 }}
	\| {{mapping\| 315 499 731 }}		\| {{mapping\| 315 499 731 }}
	\| 0.4337		\| +0.4337
	\| 0.3071		\| 0.3071
	\| 8.06		\| 8.06
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	\| 2401/2400, 4375/4374, {{monzo\| -21 6 11 -5 }}		\| 2401/2400, 4375/4374, {{monzo\| -21 6 11 -5 }}
	\| {{mapping\| 315 499 731 884 }}		\| {{mapping\| 315 499 731 884 }}
	\| 0.4328		\| +0.4328
	\| 0.2659		\| 0.2659
	\| 6.98		\| 6.98
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	\| [[Ennealimmal]]		\| [[Ennealimmal]]
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T13:08:54Z

Partial undo

← Older revision		Revision as of 13:08, 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
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	\| 0.2659		\| 0.2659
	\| 6.98		\| 6.98
	~~{{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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	\| 6/5<br />(36/35)		\| 6/5<br />(36/35)
	\| [[Ennealimmal]]		\| [[Ennealimmal]]
	~~{{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

ArrowHead294 at 02:25, 16 November 2024

2024-11-16T02:25:00Z

← Older revision		Revision as of 02:25, 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
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	\| 0.2659		\| 0.2659
	\| 6.98		\| 6.98
	\|}		{{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
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	\|-		\|-
	\| 5		\| 5
	\| 131\315<br>(5\315)		\| 131\315<br />(5\315)
	\| 499.05<br>(19.05)		\| 499.05<br />(19.05)
	\| 4/3<br>(81/80)		\| 4/3<br />(81/80)
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|-		\|-
	\| 9		\| 9
	\| 83\315<br>(13\315)		\| 83\315<br />(13\315)
	\| 316.19<br>(49.52)		\| 316.19<br />(49.52)
	\| 6/5<br>(36/35)		\| 6/5<br />(36/35)
	\| [[Ennealimmal]]		\| [[Ennealimmal]]
	\|}		{{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}}

Fredg999: Skip disambiguation

2024-09-09T02:01:06Z

Skip disambiguation

← Older revision		Revision as of 02:01, 9 September 2024
Line 63:		Line 63:
	\| 499.05<br>(19.05)		\| 499.05<br>(19.05)
	\| 4/3<br>(81/80)		\| 4/3<br>(81/80)
	\| [[Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|-		\|-
	\| 9		\| 9

FloraC: Review

2024-03-05T15:25:53Z

Review

← Older revision		Revision as of 15:25, 5 March 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~315et~~ is consistent to the [[7-odd-limit]], tempering out [[2401/2400]], [[4375/4374]] and 35595703125/35246833664. Using the 315e val in the 11-limit ({{val\|315 499 731 884 '''1089'''}}), it tempers out [[385/384]], 1375/1372, 4375/4374 and 644204/643125, [[support]]ing [[beyla]] and [[ennealiminal]].		315edo is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]]. The equal temperament [[tempering out\|tempers out]] [[2401/2400]], [[4375/4374]] and 35595703125/35246833664. Using the 315e [[val]] in the 11-limit ({{val\| 315 499 731 884 '''1089''' }}), it tempers out [[385/384]], 1375/1372, 4375/4374 and 644204/643125, [[support]]ing [[beyla]] and [[ennealiminal]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	315 factors into 3<sup>2</sup> × 5 × 7, ~~with~~ subset edos {{EDOs\|3, 5, 7, 9, 15, 21, 35, 45, 63, and 105}}. [[945edo]], which triples it, gives a good correction to the harmonic 11.		Since 315 factors into 3<sup>2</sup> × 5 × 7, 315edo has subset edos {{EDOs\| 3, 5, 7, 9, 15, 21, 35, 45, 63, and 105 }}. [[945edo]], which triples it, gives a good correction to the harmonic 11.

	== 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\|-499 315}}		\| {{monzo\|-499 315}}
	\|{{mapping\|315 499}}		\| {{mapping\|315 499}}
	\| 0.3163		\| 0.3163
	\| 0.3164		\| 0.3164
	\| 8.31		\| 8.31
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-27 -2 13}}, {{monzo\|-28 25 -5}}		\| {{monzo\| -27 -2 13 }}, {{monzo\| -28 25 -5 }}
	\|{{mapping\|315 499 731}}		\| {{mapping\| 315 499 731 }}
	\| 0.4337		\| 0.4337
	\| 0.3071		\| 0.3071
	\| 8.06		\| 8.06
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|2401/2400, 4375/4374, ~~35595703125/35246833664~~		\| 2401/2400, 4375/4374, {{monzo\| -21 6 11 -5 }}
	\|{{mapping\|315 499 731 884}}		\| {{mapping\| 315 499 731 884 }}
	\| 0.4328		\| 0.4328
	\| 0.2659		\| 0.2659
Line 53:		Line 53:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|107\315		\| 107\315
	\|407.62		\| 407.62
	\|15625/12288		\| 15625/12288
	\|[[Ditonic]]		\| [[Ditonic]]
	\|-		\|-
	\|5		\| 5
	\|131\315<br>(5\315)		\| 131\315<br>(5\315)
	\|499.05<br>(19.05)		\| 499.05<br>(19.05)
	\|4/3<br>(81/80)		\| 4/3<br>(81/80)
	\|[[Pental]]		\| [[Pental]] (5-limit)
	\|-		\|-
	\|9		\| 9
	\|83\315<br>(13\315)		\| 83\315<br>(13\315)
	\|316.19<br>(49.52)		\| 316.19<br>(49.52)
	\|6/5<br>(36/35)		\| 6/5<br>(36/35)
	\|[[Ennealimmal]]		\| [[Ennealimmal]]
	\|}		\|}

	<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

Francium: Created page with "{{Infobox ET}} {{EDO intro|315}} == Theory == 315et is consistent to the 7-odd-limit, tempering out 2401/2400, 4375/4374 and 35595703125/35246833664. Using the 31..."

2024-03-05T14:03:05Z

Created page with "{{Infobox ET}} {{EDO intro|315}} == Theory == 315et is consistent to the 7-odd-limit, tempering out 2401/2400, 4375/4374 and 35595703125/35246833664. Using the 31..."

New page

{{Infobox ET}}
{{EDO intro|315}}

== Theory ==
315et is consistent to the [[7-odd-limit]], tempering out [[2401/2400]], [[4375/4374]] and 35595703125/35246833664. Using the 315e val in the 11-limit ({{val|315 499 731 884 '''1089'''}}), it tempers out [[385/384]], 1375/1372, 4375/4374 and 644204/643125, [[support]]ing [[beyla]] and [[ennealiminal]].

=== Odd harmonics ===
{{Harmonics in equal|315}}

=== Subsets and supersets ===
315 factors into 32 × 5 × 7, with subset edos {{EDOs|3, 5, 7, 9, 15, 21, 35, 45, 63, and 105}}. [[945edo]], which triples it, gives a good correction to the harmonic 11.

== 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|-499 315}}
|{{mapping|315 499}}
| 0.3163
| 0.3164
| 8.31
|-
|2.3.5
|{{monzo|-27 -2 13}}, {{monzo|-28 25 -5}}
|{{mapping|315 499 731}}
| 0.4337
| 0.3071
| 8.06
|-
|2.3.5.7
|2401/2400, 4375/4374, 35595703125/35246833664
|{{mapping|315 499 731 884}}
| 0.4328
| 0.2659
| 6.98
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator*
! Cents*
! Associated Ratio*
! Temperaments
|-
|1
|107\315
|407.62
|15625/12288
|[[Ditonic]]
|-
|5
|131\315 (5\315)
|499.05 (19.05)
|4/3 (81/80)
|[[Pental]]
|-
|9
|83\315 (13\315)
|316.19 (49.52)
|6/5 (36/35)
|[[Ennealimmal]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct