375edo - Revision history

ArrowHead294 at 12:19, 21 February 2025

2025-02-21T12:19:04Z

← Older revision		Revision as of 12:19, 21 February 2025
Line 17:		Line 17:
	== 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]]
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	\| {{monzo\| 1189 -375 }}		\| {{monzo\| 1189 -375 }}
	\| {{mapping\| 375 1189 }}		\| {{mapping\| 375 1189 }}
	\| -0.1404		\| −0.1404
	\| 0.1404		\| 0.1404
	\| 4.39		\| 4.39
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	\| {{monzo\| 8 7 -13 }}, {{monzo\| 97 -24 -9 }}		\| {{monzo\| 8 7 -13 }}, {{monzo\| 97 -24 -9 }}
	\| {{mapping\| 375 1189 871 }}		\| {{mapping\| 375 1189 871 }}
	\| -0.2208		\| −0.2208
	\| 0.1615		\| 0.1615
	\| 5.05		\| 5.05
Line 43:		Line 44:
	\| 250047/250000, 589824/588245, {{monzo\| 8 7 -13 }}		\| 250047/250000, 589824/588245, {{monzo\| 8 7 -13 }}
	\| {{mapping\| 375 1189 871 1053 }}		\| {{mapping\| 375 1189 871 1053 }}
	\| -0.2345		\| −0.2345
	\| 0.1418		\| 0.1418
	\| 4.43		\| 4.43
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T06:19:27Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:19, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|375~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2024-01-14T14:08:35Z

Review

← Older revision		Revision as of 14:08, 14 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~375et~~ is ~~only~~ consistent to the [[3-odd-limit]] and ~~the~~ harmonic 3 is about halfway between its steps. It can be used in the 2.9.5.7.13.17.19 [[subgroup]]~~. Using the patent val~~, it tempers out ~~40500000~~/~~40353607~~, ~~52734375~~/~~52706752~~ and [[~~6144/6125~~]] in the 7-limit~~; 100663296/100656875~~, ~~10333575/10307264~~, ~~166698~~/~~166375, 759375~~/~~758912~~, ~~151263~~/~~151250,~~ [[~~540~~/~~539~~]], ~~4302592/4296875, 825000/823543~~, [[~~5632~~/~~5625~~]]~~, 16808715/16777216, 1362944/1361367, 4108797~~/~~4096000~~, ~~67110351/67108864, 805255/802816 and~~ [[~~1771561/1769472~~]] in the 11-limit~~. It~~ [[~~support~~]]s [[aufic]] and [[persephone]].		375edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. It can be used as a temperament in the 2.9.5.7.13.17.19 [[subgroup]], in which it [[tempering out\|tempers out]] [[250047/250000]], 589824/588245, and {{monzo\| 8 7 -13 }} ([[parakleisma]]).

			For the full 7-limit, the 375cd [[val]] is the best, where it tempers out [[1029/1024]] and [[15625/15552]], [[support]]ing [[tritikleismic]]. In the 11-limit it tempers out [[385/384]] and [[441/440]], supporting undecimal tritikleismic.

			Using the [[patent val]], it tempers out [[6144/6125]] and 177147/175616, supporting [[aufo]]. In the 11-limit it tempers out [[540/539]] and [[5632/5625]], supporting [[aufic]] and [[persephone]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 13:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	375 factors into 3 × 5<sup>3</sup> ~~with~~ subset edos {{EDOs\|3, 5, 15, 25, 75, and 125}}. [[1175edo]], which triples it, gives a good correction to the harmonic 3 and is consistent to the [[15-odd-limit]].		Since 375 factors into 3 × 5<sup>3</sup>, 375edo has subset edos {{EDOs\| 3, 5, 15, 25, 75, and 125 }}. [[1175edo]], which triples it, gives a good correction to the harmonic 3 and is consistent to the [[15-odd-limit]].

	== 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]] (%)
	\|-		\|-
	\|2.9		\| 2.9
	\|{{monzo\|1189 -375}}		\| {{monzo\| 1189 -375 }}
	\|{{mapping\|375 1189}}		\| {{mapping\| 375 1189 }}
	\| -0.1404		\| -0.1404
	\| 0.1404		\| 0.1404
	\| 4.39		\| 4.39
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|{{monzo\|8 7 -13}}, {{monzo\|97 -24 -9}}		\| {{monzo\| 8 7 -13 }}, {{monzo\| 97 -24 -9 }}
	\|{{mapping\|375 1189 871}}		\| {{mapping\| 375 1189 871 }}
	\| -0.2208		\| -0.2208
	\| 0.1615		\| 0.1615
	\| 5.05		\| 5.05
	\|-		\|-
	\|2.9.5.7		\| 2.9.5.7
	\|250047/250000, ~~26873856~~/~~26796875~~, ~~26985857024/26904200625~~		\| 250047/250000, 589824/588245, {{monzo\| 8 7 -13 }}
	\|{{mapping\|375 1189 871 1053}}		\| {{mapping\| 375 1189 871 1053 }}
	\| -0.2345		\| -0.2345
	\| 0.1418		\| 0.1418
	\| 4.43		\| 4.43
	\|}		\|}

Francium: /* Subsets and supersets */ typo

2024-01-04T22:02:25Z

Subsets and supersets: typo

← Older revision		Revision as of 22:02, 4 January 2024
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	375 factors into 3 × 5<sup>3<sup> with subset edos {{EDOs\|3, 5, 15, 25, 75, and 125}}. [[1175edo]], which triples it, gives a good correction to the harmonic 3 and is consistent to the [[15-odd-limit]].		375 factors into 3 × 5<sup>3</sup> with subset edos {{EDOs\|3, 5, 15, 25, 75, and 125}}. [[1175edo]], which triples it, gives a good correction to the harmonic 3 and is consistent to the [[15-odd-limit]].

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

Francium: Created page with "{{Infobox ET}} {{EDO intro|375}} == Theory == 375et is only consistent to the 3-odd-limit and the harmonic 3 is about halfway between its steps. It can be used in the 2.9..."

2024-01-04T22:01:54Z

Created page with "{{Infobox ET}} {{EDO intro|375}} == Theory == 375et is only consistent to the 3-odd-limit and the harmonic 3 is about halfway between its steps. It can be used in the 2.9..."

New page

{{Infobox ET}}
{{EDO intro|375}}

== Theory ==
375et is only consistent to the [[3-odd-limit]] and the harmonic 3 is about halfway between its steps. It can be used in the 2.9.5.7.13.17.19 [[subgroup]]. Using the patent val, it tempers out 40500000/40353607, 52734375/52706752 and [[6144/6125]] in the 7-limit; 100663296/100656875, 10333575/10307264, 166698/166375, 759375/758912, 151263/151250, [[540/539]], 4302592/4296875, 825000/823543, [[5632/5625]], 16808715/16777216, 1362944/1361367, 4108797/4096000, 67110351/67108864, 805255/802816 and [[1771561/1769472]] in the 11-limit. It [[support]]s [[aufic]] and [[persephone]].

=== Odd harmonics ===
{{Harmonics in equal|375}}

=== Subsets and supersets ===
375 factors into 3 × 5<sup>3<sup> with subset edos {{EDOs|3, 5, 15, 25, 75, and 125}}. [[1175edo]], which triples it, gives a good correction to the harmonic 3 and is consistent to the [[15-odd-limit]].

== 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<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.9
|{{monzo|1189 -375}}
|{{mapping|375 1189}}
| -0.1404
| 0.1404
| 4.39
|-
|2.9.5
|{{monzo|8 7 -13}}, {{monzo|97 -24 -9}}
|{{mapping|375 1189 871}}
| -0.2208
| 0.1615
| 5.05
|-
|2.9.5.7
|250047/250000, 26873856/26796875, 26985857024/26904200625
|{{mapping|375 1189 871 1053}}
| -0.2345
| 0.1418
| 4.43
|}