1609edo - 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"

2026-03-13T13:44:03Z

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]]		; [[Francium]]
	* "HAVE A HAM" from ''Things to Scream at People'' (2025) – [https://open.spotify.com/track/5mtAJXrW6Rb3IE2tIqYT4c Spotify] \| [https://francium223.bandcamp.com/track/have-a-ham Bandcamp] \| [https://www.youtube.com/watch?v=E-JO2ZvBjw8 YouTube]		* "HAVE A HAM" from ''Things to Scream at People'' (2025) – [https://open.spotify.com/track/5mtAJXrW6Rb3IE2tIqYT4c Spotify] \| [https://francium223.bandcamp.com/track/have-a-ham Bandcamp] \| [https://www.youtube.com/watch?v=E-JO2ZvBjw8 YouTube]

Francium: +music

2025-10-15T12:09:14Z

+music

← Older revision		Revision as of 12:09, 15 October 2025
Line 76:		Line 76:

	<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]]
			* "HAVE A HAM" from ''Things to Scream at People'' (2025) – [https://open.spotify.com/track/5mtAJXrW6Rb3IE2tIqYT4c Spotify] \| [https://francium223.bandcamp.com/track/have-a-ham Bandcamp] \| [https://www.youtube.com/watch?v=E-JO2ZvBjw8 YouTube]

Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 1609edo is consistent to the 15-odd-limit, tempering out 67392/67375, 160083/160000, 50193/50176, 91125/91091 and 557..."

2025-02-23T20:23:02Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 1609edo is consistent to the 15-odd-limit, tempering out 67392/67375, 160083/160000, 50193/50176, 91125/91091 and 557..."

New page

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

== Theory ==
1609edo is [[consistent]] to the [[15-odd-limit]], [[tempering out]] 67392/67375, [[160083/160000]], 50193/50176, 91125/91091 and 557568/557375 in the [[13-limit]]. It is a strong 2.5.7.13.19 [[subgroup]] tuning, tempering out 401408/401375, 739375/739328, 479199083125/479174066176 and 32005131723019/32000000000000. Using the 2.5.7.11.13.19.43 subgroup it tempers out [[5720/5719]]. The equal temperament [[support]]s [[exodia]].

=== Prime harmonics ===
{{Harmonics in equal|1609}}

=== Subsets and supersets ===
1609edo is the 254th [[prime edo]].

== 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|-2550 1609}}
| {{mapping|1609 2550}}
| 0.0482
| 0.0482
| 6.46
|-
| 2.3.5
| {{monzo|-68 18 17}}, {{monzo|-38 65 -28}}
| {{mapping|1609 2550 3736}}
| 0.0302
| 0.0468
| 6.28
|-
| 2.3.5.7
| 2460375/2458624, 1640558367/1638400000, {{monzo|29 14 -16 -5}}
| {{mapping|1609 2550 3736 4517}}
| 0.0249
| 0.0416
| 5.58
|-
| 2.3.5.7.11
| 160083/160000, 1240029/1239040, 151263/151250, 262766592/262609375
| {{mapping|1609 2550 3736 4517 5566}}
| 0.0297
| 0.0384
| 5.15
|-
| 2.3.5.7.11.13
| 67392/67375, 160083/160000, 50193/50176, 91125/91091, 557568/557375
| {{mapping|1609 2550 3736 4517 5566 5954}}
| 0.0250
| 0.0365
| 4.89
|}

=== 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
| 150\1609
| 111.871
| 16/15
| [[Vavoom]]
|}

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