659edo - Revision history

ArrowHead294 at 13:02, 21 February 2025

2025-02-21T13:02:23Z

← Older revision		Revision as of 13:02, 21 February 2025
Line 13:		Line 13:
	== 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" \|[[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \|Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| [[Mapping]]
	! colspan="2" \|Tuning ~~Error~~		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	\|-		! colspan="2" \| Tuning error
	![[TE error\|Absolute]] (¢)		\|-
	![[TE simple badness\|Relative]] (%)		! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.9		\| 2.9
	\| {{monzo\|2089 -659}}		\| {{monzo\|2089 -659}}
	\| {{mapping\|659 2089}}		\| {{mapping\|659 2089}}
	\| -0.0056		\| −0.0056
	\| 0.0056		\| 0.0056
	\| 1.02		\| 1.02
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	\| 1575/1573, 4096/4095, 86625/86528, 31250/31213, 650000/649539		\| 1575/1573, 4096/4095, 86625/86528, 31250/31213, 650000/649539
	\| {{mapping\|659 2089 1530 1850 2280 2439}}		\| {{mapping\|659 2089 1530 1850 2280 2439}}
	\| -0.0313		\| −0.0313
	\| 0.1042		\| 0.1042
	\| 18.97		\| 18.97

Francium: changed EDO intro to ED intro

2025-02-21T05:49:11Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:49, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|659~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: +music

2024-09-30T13:03:12Z

+music

← Older revision		Revision as of 13:03, 30 September 2024
Line 57:		Line 57:
	\| 18.97		\| 18.97
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "In My Wildest Dreams" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/1RQsBF3qi9n13jVfCUgbN7 Spotify] \| [https://francium223.bandcamp.com/track/in-my-wildest-dreams Bandcamp] \| [https://www.youtube.com/watch?v=NDciaAdI44g YouTube]

Francium: typo

2024-08-13T13:39:24Z

typo

← Older revision		Revision as of 13:39, 13 August 2024
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	\| 2.9		\| 2.9
	\| {{monzo\|2089 -659}}		\| {{monzo\|2089 -659}}
	\| {{mapping 659 2089}}		\| {{mapping\|659 2089}}
	\| -0.0056		\| -0.0056
	\| 0.0056		\| 0.0056
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	\| 2.9.5		\| 2.9.5
	\| {{monzo\|10 -20 23}}, {{monzo\|-83 13 18}}		\| {{monzo\|10 -20 23}}, {{monzo\|-83 13 18}}
	\| {{mapping 659 2089 1530}}		\| {{mapping\|659 2089 1530}}
	\| +0.0357		\| +0.0357
	\| 0.0585		\| 0.0585
Line 38:		Line 38:
	\| 2.9.5.7		\| 2.9.5.7
	\| 420175/419904, 703125/702464, {{monzo\|44 -14 5 -4}}		\| 420175/419904, 703125/702464, {{monzo\|44 -14 5 -4}}
	\| {{mapping 659 2089 1530 1850}}		\| {{mapping\|659 2089 1530 1850}}
	\| +0.0343		\| +0.0343
	\| 0.0507		\| 0.0507
Line 45:		Line 45:
	\| 2.9.5.7.11		\| 2.9.5.7.11
	\| 496125/495616, 420175/419904, 151263/151250, 2097152/2096325		\| 496125/495616, 420175/419904, 151263/151250, 2097152/2096325
	\| {{mapping 659 2089 1530 1850 2280}}		\| {{mapping\|659 2089 1530 1850 2280}}
	\| +0.0028		\| +0.0028
	\| 0.0777		\| 0.0777
Line 52:		Line 52:
	\| 2.9.5.7.11.13		\| 2.9.5.7.11.13
	\| 1575/1573, 4096/4095, 86625/86528, 31250/31213, 650000/649539		\| 1575/1573, 4096/4095, 86625/86528, 31250/31213, 650000/649539
	\| {{mapping 659 2089 1530 1850 2280 2439}}		\| {{mapping\|659 2089 1530 1850 2280 2439}}
	\| -0.0313		\| -0.0313
	\| 0.1042		\| 0.1042
	\| 18.97		\| 18.97
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|659}} == Theory == 659edo is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. Using the 2.9.5.7.11...."

2024-08-13T13:38:31Z

Created page with "{{Infobox ET}} {{EDO intro|659}} == Theory == 659edo is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. Using the 2.9.5.7.11...."

New page

{{Infobox ET}}
{{EDO intro|659}}

== Theory ==
659edo is [[consistent]] to the [[7-odd-limit]] and its [[harmonic]] [[3/1|3]] is about halfway its steps. Using the 2.9.5.7.11.17.23.31 [[subgroup]], it [[tempering out|tempers out]] [[1225/1224]], [[2025/2024]], [[5832/5831]], 3520/3519, [[3969/3968]], 790625/790272 and 1740800/1740123. It [[support]]s [[counterultrakleismic]].

=== Odd harmonics ===
{{Harmonics in equal|659}}

=== Subsets and supersets ===
659edo is the 120th [[prime EDO]]. [[1318edo]], 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|2089 -659}}
| {{mapping 659 2089}}
| -0.0056
| 0.0056
| 1.02
|-
| 2.9.5
| {{monzo|10 -20 23}}, {{monzo|-83 13 18}}
| {{mapping 659 2089 1530}}
| +0.0357
| 0.0585
| 10.65
|-
| 2.9.5.7
| 420175/419904, 703125/702464, {{monzo|44 -14 5 -4}}
| {{mapping 659 2089 1530 1850}}
| +0.0343
| 0.0507
| 9.23
|-
| 2.9.5.7.11
| 496125/495616, 420175/419904, 151263/151250, 2097152/2096325
| {{mapping 659 2089 1530 1850 2280}}
| +0.0028
| 0.0777
| 14.15
|-
| 2.9.5.7.11.13
| 1575/1573, 4096/4095, 86625/86528, 31250/31213, 650000/649539
| {{mapping 659 2089 1530 1850 2280 2439}}
| -0.0313
| 0.1042
| 18.97
|}