3361edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:44:00Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:44, 13 March 2026
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	\|}		\|}

	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

Francium: /* Music */ +links

2025-06-06T12:02:33Z

Music: +links

← Older revision		Revision as of 12:02, 6 June 2025
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	* from ''Microtonal Six-Dimensional Cats'' (2025)		* from ''Microtonal Six-Dimensional Cats'' (2025)
	** "Cat In My Yard" – [https://open.spotify.com/track/1oZOuXz4O2EBQuXEpmInzH Spotify] \| [https://francium223.bandcamp.com/track/cat-in-my-yard Bandcamp] \| [https://www.youtube.com/watch?v=4jPCR9cVUbI YouTube]		** "Cat In My Yard" – [https://open.spotify.com/track/1oZOuXz4O2EBQuXEpmInzH Spotify] \| [https://francium223.bandcamp.com/track/cat-in-my-yard Bandcamp] \| [https://www.youtube.com/watch?v=4jPCR9cVUbI YouTube]
	** "Spicy Kitties" – [https://open.spotify.com/track/0nqQuPSwbMIctvHAAPXyb2 Spotify] \| [https://francium223.bandcamp.com/track/spicy-kitties Bandcamp]		** "Spicy Kitties" – [https://open.spotify.com/track/0nqQuPSwbMIctvHAAPXyb2 Spotify] \| [https://francium223.bandcamp.com/track/spicy-kitties Bandcamp] \| [https://www.youtube.com/watch?v=H8citdRcy1U YouTube]

Francium: +music

2025-06-04T11:32:43Z

+music

← Older revision		Revision as of 11:32, 4 June 2025
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	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			== Music ==
			; [[Francium]]
			* from ''Microtonal Six-Dimensional Cats'' (2025)
			** "Cat In My Yard" – [https://open.spotify.com/track/1oZOuXz4O2EBQuXEpmInzH Spotify] \| [https://francium223.bandcamp.com/track/cat-in-my-yard Bandcamp] \| [https://www.youtube.com/watch?v=4jPCR9cVUbI YouTube]
			** "Spicy Kitties" – [https://open.spotify.com/track/0nqQuPSwbMIctvHAAPXyb2 Spotify] \| [https://francium223.bandcamp.com/track/spicy-kitties Bandcamp]

Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 3361edo is consistent to the 5-odd-limit, with an almost perfect harmonic 5, its relative error is only 0.1%. Its..."

2025-03-04T10:54:17Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 3361edo is consistent to the 5-odd-limit, with an almost perfect harmonic 5, its relative error is only 0.1%. Its..."

New page

{{Infobox ET}}
{{ED intro}}

== Theory ==
3361edo is [[consistent]] to the [[5-odd-limit]], with an almost perfect [[harmonic]] [[5/1|5]], its relative error is only 0.1%. Its harmonic [[7/1|7]] is about halfway its steps though, hence the consistency of this edo. As a temperament, 3361edo is strong in the 2.3.5.11.13.17.31 [[subgroup]], [[tempering out]] [[37180/37179]], 10881/10880, 196625/196608, 3025269/3025000, 492804/492745 and 131769/131750. Using the 2.3.5.13.17.37.43 subgroup, it tempers out [[7956/7955]].

=== Prime harmonics ===
{{Harmonics in equal|3361}}

=== Subsets and supersets ===
3361edo is the 474th [[prime edo]]. [[6722edo]], which doubles it, gives a good correction to the harmonic 7.

== 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|-5327 3361}}
| {{mapping|3361 5327}}
| 0.0066
| 0.0066
| 1.85
|-
| 2.3.5
| {{monzo|37 25 -33}}, {{monzo|-176 92 13}}
| {{mapping|3361 5327 7804}}
| 0.0044
| 0.0063
| 1.76
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
| 1
| 1570\3361
| 560.547
| 864/625
| [[Whoosh]]
|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct