374edo - Revision history

ArrowHead294 at 12:14, 21 February 2025

2025-02-21T12:14:17Z

← Older revision		Revision as of 12:14, 21 February 2025
Line 15:		Line 15:
	== 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\| 593 -374 }}		\| {{monzo\| 593 -374 }}
	\| {{mapping\| 374 593 }}		\| {{mapping\| 374 593 }}
	\| -0.2268		\| −0.2268
	\| 0.2267		\| 0.2267
	\| 7.07		\| 7.07
Line 34:		Line 35:
	\| {{monzo\| 4 -22 11 }}, {{monzo\| 51 -18 -8 }}		\| {{monzo\| 4 -22 11 }}, {{monzo\| 51 -18 -8 }}
	\| {{mapping\| 374 593 1050 }}		\| {{mapping\| 374 593 1050 }}
	\| -0.1699		\| −0.1699
	\| 0.2018		\| 0.2018
	\| 6.29		\| 6.29
Line 41:		Line 42:
	\| 41503/41472, 1362944/1361367, 70493667328/70027449129		\| 41503/41472, 1362944/1361367, 70493667328/70027449129
	\| {{mapping\| 374 593 1050 1294 }}		\| {{mapping\| 374 593 1050 1294 }}
	\| -0.1675		\| −0.1675
	\| 0.1748		\| 0.1748
	\| 5.45		\| 5.45
Line 48:		Line 49:
	\| 10648/10647, 20449/20412, 41503/41472, 652288/649539		\| 10648/10647, 20449/20412, 41503/41472, 652288/649539
	\| {{mapping\| 374 593 1050 1294 138 4}}		\| {{mapping\| 374 593 1050 1294 138 4}}
	\| -0.1401		\| −0.1401
	\| 0.1656		\| 0.1656
	\| 5.16		\| 5.16
Line 55:		Line 56:
	\| 2058/2057, 8281/8262, 8624/8619, 22528/22491, 34816/34749		\| 2058/2057, 8281/8262, 8624/8619, 22528/22491, 34816/34749
	\| {{mapping\| 374 593 1050 1294 1384 1529 }}		\| {{mapping\| 374 593 1050 1294 1384 1529 }}
	\| -0.1546		\| −0.1546
	\| 0.1546		\| 0.1546
	\| 4.82		\| 4.82
Line 62:		Line 63:
	\| 1729/1728, 2058/2057, 2912/2907, 5929/5928, 22528/22491, 34816/34749		\| 1729/1728, 2058/2057, 2912/2907, 5929/5928, 22528/22491, 34816/34749
	\| {{mapping\| 374 593 1050 1294 1384 1529 1589 }}		\| {{mapping\| 374 593 1050 1294 1384 1529 1589 }}
	\| -0.1622		\| −0.1622
	\| 0.1444		\| 0.1444
	\| 4.50		\| 4.50
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T06:23:56Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:23, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|374~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC at 13:53, 14 January 2024

2024-01-14T13:53:57Z

← Older revision		Revision as of 13:53, 14 January 2024
Line 5:		Line 5:
	374et is in[[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[5/1\|5]] is about halfway between its steps. Omitting the harmonic 5, it is consistent to the [[31-odd-limit]].		374et is in[[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[5/1\|5]] is about halfway between its steps. Omitting the harmonic 5, it is consistent to the [[31-odd-limit]].

	Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[5120/5103]], 1071875/1062882, 1500625/1492992 ~~and~~ [[2100875/2097152]], 9765625/9680832 in the 7-limit; 1375/1372, 4375/4356, 12005/11979, and [[41503/41472]] in the 11-limit. It [[support]]s [[quintakwai]] and [[quartemka]].		Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[5120/5103]], 1071875/1062882, 1500625/1492992, [[2100875/2097152]], and 9765625/9680832 in the 7-limit; 1375/1372, 4375/4356, 12005/11979, and [[41503/41472]] in the 11-limit. It [[support]]s [[quintakwai]] and [[quartemka]].

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

FloraC: Review

2024-01-14T13:53:33Z

Review

← Older revision		Revision as of 13:53, 14 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	374et is ~~only~~ consistent to the [[3-odd-limit]]. Omitting the harmonic 5, it is consistent to the [[31-odd-limit]]. Using the patent val, it tempers out ~~40500000/40353607, 184528125/184473632,~~ [[5120/5103]] and [[2100875/2097152]] in the 7-limit; ~~1073741824~~/~~1071794405, 161280/161051~~, ~~820125~~/~~819896, 2097152/2096325~~, 12005/11979, ~~2621440/2614689, 496125/495616, 1296000/1294139, 1265625/1261568, [[200704/200475]], 5767168/5764801, 1375/1372, 184549376/184528125, 1479016/1476225, 275653125/275365888,~~ [[41503/41472]]~~, 1362944/1361367, 166375/165888, 3294225/3294172 and 322102/321489~~ in the 11-limit. It [[support]]s [[quintakwai]] and [[quartemka]].		374et is in[[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[5/1\|5]] is about halfway between its steps. Omitting the harmonic 5, it is consistent to the [[31-odd-limit]].

			Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[5120/5103]], 1071875/1062882, 1500625/1492992 and [[2100875/2097152]], 9765625/9680832 in the 7-limit; 1375/1372, 4375/4356, 12005/11979, and [[41503/41472]] in the 11-limit. It [[support]]s [[quintakwai]] and [[quartemka]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	374 factors into 2 × 11 × 17, ~~with~~ subset edos {{EDOs\|2, 11, 17, 22, 34, and 187}}. [[748edo]], which doubles it, gives a good correction to the harmonic 5.		Since 374 factors into 2 × 11 × 17, 374edo has subset edos {{EDOs\| 2, 11, 17, 22, 34, and 187 }}. [[748edo]], which doubles it, gives a good correction to the harmonic 5, but its approximation of harmonic 3 has drifted too far to render it inconsistent in the [[9-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]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|593 -374}}		\| {{monzo\| 593 -374 }}
	\|{{mapping\|374 593}}		\| {{mapping\| 374 593 }}
	\| -0.2268		\| -0.2268
	\| 0.2267		\| 0.2267
	\| 7.07		\| 7.07
	\|-		\|-
	\|2.3.7		\| 2.3.7
	\|{{monzo\|4 -22 11}}, {{monzo\|51 -18 -8}}		\| {{monzo\| 4 -22 11 }}, {{monzo\| 51 -18 -8 }}
	\|{{mapping\|374 593 1050}}		\| {{mapping\| 374 593 1050 }}
	\| -0.1699		\| -0.1699
	\| 0.2018		\| 0.2018
	\| 6.29		\| 6.29
	\|-		\|-
	\|2.3.7.11		\| 2.3.7.11
	\|41503/41472, 1362944/1361367, 70493667328/70027449129		\| 41503/41472, 1362944/1361367, 70493667328/70027449129
	\|{{mapping\|374 593 1050 1294}}		\| {{mapping\| 374 593 1050 1294 }}
	\| -0.1675		\| -0.1675
	\| 0.1748		\| 0.1748
	\| 5.45		\| 5.45
	\|-		\|-
	\|2.3.7.11.13		\| 2.3.7.11.13
	\|~~41503~~/~~41472~~, 20449/20412, 652288/649539~~, 10648/10647~~		\| 10648/10647, 20449/20412, 41503/41472, 652288/649539
	\|{{mapping\|374 593 1050 1294 ~~1384~~}}		\| {{mapping\| 374 593 1050 1294 138 4}}
	\| -0.1401		\| -0.1401
	\| 0.1656		\| 0.1656
	\| 5.16		\| 5.16
	\|-		\|-
	\|2.3.7.11.13.17		\| 2.3.7.11.13.17
	\|~~22528/22491,~~ 2058/2057, ~~34816~~/~~34749~~, 8624/8619, ~~8281~~/~~8262~~		\| 2058/2057, 8281/8262, 8624/8619, 22528/22491, 34816/34749
	\|{{mapping\|374 593 1050 1294 1384 1529}}		\| {{mapping\| 374 593 1050 1294 1384 1529 }}
	\| -0.1546		\| -0.1546
	\| 0.1546		\| 0.1546
	\| 4.82		\| 4.82
	\|-		\|-
	\|2.3.7.11.13.17.19		\| 2.3.7.11.13.17.19
	\|1729/1728, 2912/2907, 22528/22491~~, 2058/2057, 5929/5928~~, 34816/34749		\| 1729/1728, 2058/2057, 2912/2907, 5929/5928, 22528/22491, 34816/34749
	\|{{mapping\|374 593 1050 1294 1384 1529 1589}}		\| {{mapping\| 374 593 1050 1294 1384 1529 1589 }}
	\| -0.1622		\| -0.1622
	\| 0.1444		\| 0.1444
	\| 4.50		\| 4.50
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|374}} == Theory == 374et is only consistent to the 3-odd-limit. Omitting the harmonic 5, it is consistent to the 31-odd-limit. Using the pa..."

2024-01-04T21:06:13Z

Created page with "{{Infobox ET}} {{EDO intro|374}} == Theory == 374et is only consistent to the 3-odd-limit. Omitting the harmonic 5, it is consistent to the 31-odd-limit. Using the pa..."

New page

{{Infobox ET}}
{{EDO intro|374}}

== Theory ==
374et is only consistent to the [[3-odd-limit]]. Omitting the harmonic 5, it is consistent to the [[31-odd-limit]]. Using the patent val, it tempers out 40500000/40353607, 184528125/184473632, [[5120/5103]] and [[2100875/2097152]] in the 7-limit; 1073741824/1071794405, 161280/161051, 820125/819896, 2097152/2096325, 12005/11979, 2621440/2614689, 496125/495616, 1296000/1294139, 1265625/1261568, [[200704/200475]], 5767168/5764801, 1375/1372, 184549376/184528125, 1479016/1476225, 275653125/275365888, [[41503/41472]], 1362944/1361367, 166375/165888, 3294225/3294172 and 322102/321489 in the 11-limit. It [[support]]s [[quintakwai]] and [[quartemka]].

=== Prime harmonics ===
{{Harmonics in equal|374}}

=== Subsets and supersets ===
374 factors into 2 × 11 × 17, with subset edos {{EDOs|2, 11, 17, 22, 34, and 187}}. [[748edo]], which doubles it, gives a good correction to the harmonic 5.

== 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]] (%)
|-
|2.3
|{{monzo|593 -374}}
|{{mapping|374 593}}
| -0.2268
| 0.2267
| 7.07
|-
|2.3.7
|{{monzo|4 -22 11}}, {{monzo|51 -18 -8}}
|{{mapping|374 593 1050}}
| -0.1699
| 0.2018
| 6.29
|-
|2.3.7.11
|41503/41472, 1362944/1361367, 70493667328/70027449129
|{{mapping|374 593 1050 1294}}
| -0.1675
| 0.1748
| 5.45
|-
|2.3.7.11.13
|41503/41472, 20449/20412, 652288/649539, 10648/10647
|{{mapping|374 593 1050 1294 1384}}
| -0.1401
| 0.1656
| 5.16
|-
|2.3.7.11.13.17
|22528/22491, 2058/2057, 34816/34749, 8624/8619, 8281/8262
|{{mapping|374 593 1050 1294 1384 1529}}
| -0.1546
| 0.1546
| 4.82
|-
|2.3.7.11.13.17.19
|1729/1728, 2912/2907, 22528/22491, 2058/2057, 5929/5928, 34816/34749
|{{mapping|374 593 1050 1294 1384 1529 1589}}
| -0.1622
| 0.1444
| 4.50
|}