348edo - Revision history

Contribution at 14:41, 15 December 2025

2025-12-15T14:41:19Z

← Older revision		Revision as of 14:41, 15 December 2025
Line 7:		Line 7:
	Using the [[patent val]], it tempers out [[2401/2400]], [[15625/15552]], [[390625/388962]] and 156250000/155649627 and in the 7-limit. It [[support]]s [[quadritikleismic]] and [[subneutral]].		Using the [[patent val]], it tempers out [[2401/2400]], [[15625/15552]], [[390625/388962]] and 156250000/155649627 and in the 7-limit. It [[support]]s [[quadritikleismic]] and [[subneutral]].

	In 348edo, the prime harmonics up to 13 map the same way as in 87edo, except the 7th harmonic, which is corrected.		In 348edo, the prime harmonics up to 13 map the same way as in [[87edo]], except the 7th harmonic, which is corrected.

	=== Odd harmonics ===		=== Odd harmonics ===

Contribution at 14:40, 15 December 2025

2025-12-15T14:40:51Z

← Older revision		Revision as of 14:40, 15 December 2025
Line 6:		Line 6:

	Using the [[patent val]], it tempers out [[2401/2400]], [[15625/15552]], [[390625/388962]] and 156250000/155649627 and in the 7-limit. It [[support]]s [[quadritikleismic]] and [[subneutral]].		Using the [[patent val]], it tempers out [[2401/2400]], [[15625/15552]], [[390625/388962]] and 156250000/155649627 and in the 7-limit. It [[support]]s [[quadritikleismic]] and [[subneutral]].

			In 348edo, the prime harmonics up to 13 map the same way as in 87edo, except the 7th harmonic, which is corrected.

	=== Odd harmonics ===		=== Odd harmonics ===

ArrowHead294 at 12:23, 21 February 2025

2025-02-21T12:23:13Z

← Older revision		Revision as of 12:23, 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]]
	! 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]] (¢)
Line 55:		Line 56:
	\| 729/728, 1575/1573, 2200/2197, 32805/32768, 31250/31213		\| 729/728, 1575/1573, 2200/2197, 32805/32768, 31250/31213
	\| {{mapping\| 348 1103 808 977 1204 1288 }}		\| {{mapping\| 348 1103 808 977 1204 1288 }}
	\| -0.0343		\| −0.0343
	\| 0.1194		\| 0.1194
	\| 3.46		\| 3.46
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T06:17:36Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:17, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|348~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2023-12-05T14:46:11Z

Review

← Older revision		Revision as of 14:46, 5 December 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	348et is consistent to the 7-limit, but the error of the harmonic 3 is quite large, commending itself as a 2.9.5.7.11.13 subgroup temperament. Using the patent val, it tempers out ~~156250000/155649627 and~~ [[2401/2400]] in the 7-limit. It ~~provides the~~ [[~~optimal patent val~~]] ~~for~~ [[subneutral]].		348et is [[consistent]] to the [[7-odd-limit]], but the error of the [[harmonic]] [[3/1\|3]] is quite large, commending itself as a 2.9.5.7.11.13 [[subgroup]] temperament.

			Using the [[patent val]], it tempers out [[2401/2400]], [[15625/15552]], [[390625/388962]] and 156250000/155649627 and in the 7-limit. It [[support]]s [[quadritikleismic]] and [[subneutral]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	348 factors into 2<sup>2</sup> × 3 × 29, ~~with~~ subset edos {{EDOs\|2, 3, 4, 6, 12, 29, 58, 87, 116, and 174}}. [[696edo]], which doubles it, gives a good correction to the harmonic 3.		Since 348 factors into 2<sup>2</sup> × 3 × 29, 348edo has subset edos {{EDOs\| 2, 3, 4, 6, 12, 29, 58, 87, 116, and 174 }}. [[696edo]], which doubles it, gives a good correction to the harmonic 3.

	== 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\|-1103 348}}		\| {{monzo\| -1103 348 }}
	\|{{mapping\|348 1103}}		\| {{mapping\| 348 1103 }}
	\| +0.0728		\| +0.0728
	\| 0.0728		\| 0.0728
	\| 2.11		\| 2.11
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|32805/32768, {{monzo\|52 40 -77}}		\| 32805/32768, {{monzo\| 7 52 -74 }}
	\|{{mapping\|348 1103 808}}		\| {{mapping\| 348 1103 808 }}
	\| +0.0639		\| +0.0639
	\| 0.0608		\| 0.0608
	\|1.76		\| 1.76
	\|-		\|-
	\|2.9.5.7		\| 2.9.5.7
	\|32805/32768, 250047/250000, ~~247669456896/247165842875~~		\| 32805/32768, 250047/250000, {{monzo\| 7 9 -2 -11 }}
	\|{{mapping\|348 1103 808 977}}		\| {{mapping\| 348 1103 808 977 }}
	\| +0.0355		\| +0.0355
	\| 0.0721		\| 0.0721
	\| 2.09		\| 2.09
	\|-		\|-
	\|2.9.5.7.11		\| 2.9.5.7.11
	\|9801/9800, 32805/32768, 46656/46585, ~~250047~~/~~250000~~		\| 9801/9800, 32805/32768, 46656/46585, 151263/151250
	\|{{mapping\|348 1103 808 977 1204}}		\| {{mapping\| 348 1103 808 977 1204 }}
	\| +0.0049		\| +0.0049
	\| 0.0889		\| 0.0889
	\| 2.58		\| 2.58
	\|-		\|-
	\|2.9.5.7.11.13		\| 2.9.5.7.11.13
	\|729/728, 1575/1573, ~~4096~~/~~4095~~, ~~67392~~/~~67375~~, ~~250047~~/~~250000~~		\| 729/728, 1575/1573, 2200/2197, 32805/32768, 31250/31213
	\|{{mapping\|348 1103 808 977 1204 1288}}		\| {{mapping\| 348 1103 808 977 1204 1288 }}
	\| -0.0343		\| -0.0343
	\| 0.1194		\| 0.1194
	\| 3.46		\| 3.46
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|348}} == Theory == 348et is consistent to the 7-limit, but the error of the harmonic 3 is quite large, commending itself as a 2.9.5.7.11.13 subgrou..."

2023-12-01T20:16:26Z

Created page with "{{Infobox ET}} {{EDO intro|348}} == Theory == 348et is consistent to the 7-limit, but the error of the harmonic 3 is quite large, commending itself as a 2.9.5.7.11.13 subgrou..."

New page

{{Infobox ET}}
{{EDO intro|348}}

== Theory ==
348et is consistent to the 7-limit, but the error of the harmonic 3 is quite large, commending itself as a 2.9.5.7.11.13 subgroup temperament. Using the patent val, it tempers out 156250000/155649627 and [[2401/2400]] in the 7-limit. It provides the [[optimal patent val]] for [[subneutral]].

=== Odd harmonics ===
{{Harmonics in equal|348}}

=== Subsets and supersets ===
348 factors into 2<sup>2</sup> × 3 × 29, with subset edos {{EDOs|2, 3, 4, 6, 12, 29, 58, 87, 116, and 174}}. [[696edo]], which doubles it, gives a good correction to the harmonic 3.

== 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|-1103 348}}
|{{mapping|348 1103}}
| +0.0728
| 0.0728
| 2.11
|-
|2.9.5
|32805/32768, {{monzo|52 40 -77}}
|{{mapping|348 1103 808}}
| +0.0639
| 0.0608
|1.76
|-
|2.9.5.7
|32805/32768, 250047/250000, 247669456896/247165842875
|{{mapping|348 1103 808 977}}
| +0.0355
| 0.0721
| 2.09
|-
|2.9.5.7.11
|9801/9800, 32805/32768, 46656/46585, 250047/250000
|{{mapping|348 1103 808 977 1204}}
| +0.0049
| 0.0889
| 2.58
|-
|2.9.5.7.11.13
|729/728, 1575/1573, 4096/4095, 67392/67375, 250047/250000
|{{mapping|348 1103 808 977 1204 1288}}
| -0.0343
| 0.1194
| 3.46
|}