390edo - Revision history

ArrowHead294 at 12:28, 21 February 2025

2025-02-21T12:28:45Z

← Older revision		Revision as of 12:28, 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]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
Line 27:		Line 28:
	\| 118098/117649, 34451725707/34359738368		\| 118098/117649, 34451725707/34359738368
	\| {{mapping\| 390 618 1095 }}		\| {{mapping\| 390 618 1095 }}
	\| 0.0395		\| +0.0395
	\| 0.1685		\| 0.1685
	\| 5.48		\| 5.48
Line 34:		Line 35:
	\| 118098/117649, 1362944/1361367, 235782657/234881024		\| 118098/117649, 1362944/1361367, 235782657/234881024
	\| {{mapping\| 390 618 1095 1349 }}		\| {{mapping\| 390 618 1095 1349 }}
	\| 0.0693		\| +0.0693
	\| 0.1548		\| 0.1548
	\| 5.03		\| 5.03
Line 41:		Line 42:
	\| 729/728, 10648/10647, 16848/16807, 1574573/1572864		\| 729/728, 10648/10647, 16848/16807, 1574573/1572864
	\| {{mapping\| 390 618 1095 1349 1443 }}		\| {{mapping\| 390 618 1095 1349 1443 }}
	\| 0.0839		\| +0.0839
	\| 0.1415		\| 0.1415
	\| 4.60		\| 4.60
Line 48:		Line 49:
	\| 729/728, 1089/1088, 16848/16807, 65637/65536, 95823/95744		\| 729/728, 1089/1088, 16848/16807, 65637/65536, 95823/95744
	\| {{mapping\| 390 618 1095 1349 1443 1594 }}		\| {{mapping\| 390 618 1095 1349 1443 1594 }}
	\| 0.0838		\| +0.0838
	\| 0.1292		\| 0.1292
	\| 4.20		\| 4.20
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T06:15:56Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:15, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|390~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2024-01-16T14:36:38Z

Review

← Older revision		Revision as of 14:36, 16 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	390et is ~~only consistent to the~~ [[~~3-odd~~-limit]]. ~~It can be used~~ in the 2.3.7.11.13.17.23.31.41 [[subgroup]]. Using the patent val, it tempers out [[~~32805~~/~~32768~~]] ~~in the 5-limit; 283115520/282475249, 184528125/184473632, [[589824/588245]], 2460375/2458624, 67108864/66976875, [[6144/6125]], 102760448/102515625,~~ [[3136/3125]]~~, [[2401/2400]] and 5250987/5242880~~ in the 7-limit~~. It~~ [[support]]s [[~~trilobite~~]].		390et is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[65edo]]. But its approximation to higher [[harmonic]]s are improved, so that it is suitable for use in the 2.3.7.11.13.17.23.31.41 [[subgroup]].

			Using the [[patent val]] nonetheless, it tempers out [[2401/2400]] and [[3136/3125]] in the 7-limit, [[support]]ing [[hemiwürschmidt]].

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	390 factors into 2 × 3 × 5 × 13 ~~with~~ subset edos {{EDOs\|2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, and 195}}. [[780edo]], which doubles it, gives a good correction to the harmonic 5.		Since 390 factors into 2 × 3 × 5 × 13, 390edo has subset edos {{EDOs\| 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, and 195 }}. [[780edo]], which doubles it, gives a good correction to the harmonic 5.

	== 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~~
	~~\|{{monzo\|-103 65}}~~
	~~\|{{mapping\|390 618}}~~
	~~\| 0.1314~~
	~~\| 0.1314~~
	~~\| 4.27~~
	\|-		\|-
	\|2.3.7		\| 2.3.7
	\|118098/117649, 34451725707/34359738368		\| 118098/117649, 34451725707/34359738368
	\|{{mapping\|390 618 1095}}		\| {{mapping\| 390 618 1095 }}
	\| 0.0395		\| 0.0395
	\| 0.1685		\| 0.1685
	\| 5.48		\| 5.48
	\|-		\|-
	\|2.3.7.11		\| 2.3.7.11
	\|118098/117649, 1362944/1361367, 235782657/234881024		\| 118098/117649, 1362944/1361367, 235782657/234881024
	\|{{mapping\|390 618 1095 1349}}		\| {{mapping\| 390 618 1095 1349 }}
	\| 0.0693		\| 0.0693
	\| 0.1548		\| 0.1548
	\| 5.03		\| 5.03
	\|-		\|-
	\|2.3.7.11.13		\| 2.3.7.11.13
	\|729/728, 16848/16807~~, 10648/10647~~, 1574573/1572864		\| 729/728, 10648/10647, 16848/16807, 1574573/1572864
	\|{{mapping\|390 618 1095 1349 1443}}		\| {{mapping\| 390 618 1095 1349 1443 }}
	\| 0.0839		\| 0.0839
	\| 0.1415		\| 0.1415
	\| 4.60		\| 4.60
	\|-		\|-
	\|2.3.7.11.13.17		\| 2.3.7.11.13.17
	\|729/728, 1089/1088, 16848/16807, 95823/95744~~, 65637/65536~~		\| 729/728, 1089/1088, 16848/16807, 65637/65536, 95823/95744
	\|{{mapping\|390 618 1095 1349 1443 1594}}		\| {{mapping\| 390 618 1095 1349 1443 1594 }}
	\| 0.0838		\| 0.0838
	\| 0.1292		\| 0.1292
	\| 4.20		\| 4.20
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|390}} == Theory == 390et is only consistent to the 3-odd-limit. It can be used in the 2.3.7.11.13.17.23.31.41 subgroup. Using the patent va..."

2024-01-05T08:57:45Z

Created page with "{{Infobox ET}} {{EDO intro|390}} == Theory == 390et is only consistent to the 3-odd-limit. It can be used in the 2.3.7.11.13.17.23.31.41 subgroup. Using the patent va..."

New page

{{Infobox ET}}
{{EDO intro|390}}

== Theory ==
390et is only consistent to the [[3-odd-limit]]. It can be used in the 2.3.7.11.13.17.23.31.41 [[subgroup]]. Using the patent val, it tempers out [[32805/32768]] in the 5-limit; 283115520/282475249, 184528125/184473632, [[589824/588245]], 2460375/2458624, 67108864/66976875, [[6144/6125]], 102760448/102515625, [[3136/3125]], [[2401/2400]] and 5250987/5242880 in the 7-limit. It [[support]]s [[trilobite]].

=== Prime harmonics ===
{{Harmonics in equal|390}}

=== Subsets and supersets ===
390 factors into 2 × 3 × 5 × 13 with subset edos {{EDOs|2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, and 195}}. [[780edo]], 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|-103 65}}
|{{mapping|390 618}}
| 0.1314
| 0.1314
| 4.27
|-
|2.3.7
|118098/117649, 34451725707/34359738368
|{{mapping|390 618 1095}}
| 0.0395
| 0.1685
| 5.48
|-
|2.3.7.11
|118098/117649, 1362944/1361367, 235782657/234881024
|{{mapping|390 618 1095 1349}}
| 0.0693
| 0.1548
| 5.03
|-
|2.3.7.11.13
|729/728, 16848/16807, 10648/10647, 1574573/1572864
|{{mapping|390 618 1095 1349 1443}}
| 0.0839
| 0.1415
| 4.60
|-
|2.3.7.11.13.17
|729/728, 1089/1088, 16848/16807, 95823/95744, 65637/65536
|{{mapping|390 618 1095 1349 1443 1594}}
| 0.0838
| 0.1292
| 4.20
|}