Francium: +music

2026-01-30T12:36:55Z

+music

← Older revision		Revision as of 12:36, 30 January 2026
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			== Music ==
			; [[Francium]]
			* "Fungie" from ''Bumbos'' (2026) – [https://open.spotify.com/track/2Uni7EpVdAVX3YAG0JcGnt Spotify] \| [https://francium223.bandcamp.com/track/fungie Bandcamp] \| [https://www.youtube.com/watch?v=8RPHiFdm88w YouTube] – in Unicorn, 2423edo tuning

Francium: /* Theory */

2025-12-02T19:33:01Z

Theory

← Older revision		Revision as of 19:33, 2 December 2025
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	== Theory ==		== Theory ==
	2423edo is [[consistent]] to the [[7-limit]], although the error of its [[harmonic]] [[3/1\|3]] is quite high. As an equal temperament, it [[tempers out]] [[160083/160000]], [[2460375/2458624]], 3750705/3748096 and 107495424/107421875 in the [[11-limit]] and 67392/67375, 160083/160000, 50193/50176, 91125/91091 and 3750705/3748096 in the [[13-limit]].		2423edo is [[consistent]] to the [[7-limit]], although the error of its [[harmonic]] [[3/1\|3]] is quite high. As an equal temperament, it [[temper out\|tempers out]] [[160083/160000]], [[2460375/2458624]], 3750705/3748096 and 107495424/107421875 in the [[11-limit]] and 67392/67375, 160083/160000, 50193/50176, 91125/91091 and 3750705/3748096 in the [[13-limit]].

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

Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 2423edo is consistent to the 7-limit, although the error of its harmonic 3 is quite high. As an equal temperament, it tempers out 160083/160000, 2460375/2458624, 3750705/3748096 and 107495424/107421875 in the 11-limit and 67392/67375, 160083/160000, 50193/50176, 91125/91091 and 3750705/3748096 in the 13-limit. === Odd harmonics === {{Harmonics in equal|2423}} === Subsets and supersets ===..."

2025-12-02T19:32:19Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 2423edo is consistent to the 7-limit, although the error of its harmonic 3 is quite high. As an equal temperament, it tempers out 160083/160000, 2460375/2458624, 3750705/3748096 and 107495424/107421875 in the 11-limit and 67392/67375, 160083/160000, 50193/50176, 91125/91091 and 3750705/3748096 in the 13-limit. === Odd harmonics === {{Harmonics in equal|2423}} === Subsets and supersets ===..."

New page

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

== Theory ==
2423edo is [[consistent]] to the [[7-limit]], although the error of its [[harmonic]] [[3/1|3]] is quite high. As an equal temperament, it [[tempers out]] [[160083/160000]], [[2460375/2458624]], 3750705/3748096 and 107495424/107421875 in the [[11-limit]] and 67392/67375, 160083/160000, 50193/50176, 91125/91091 and 3750705/3748096 in the [[13-limit]].

=== Odd harmonics ===
{{Harmonics in equal|2423}}

=== Subsets and supersets ===
2423edo is the 360th [[prime edo]]. [[4846edo]], which doubles it, gives a good correction to its harmonic 3, but is only consistent to the [[5-limit]]. To ensure the consistency of 2423edo, [[7269edo]], which triples it, is a better choice.

== 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|7681 -2423}}
| {{mapping|2423 7681}}
| −0.0212
| 0.0212
| 4.28
|-
| 2.9.5
| {{monzo|-13 -23 37}}, {{monzo|222 -40 -41}}
| {{mapping|2423 7681 5626}}
| −0.0119
| 0.0218
| 4.40
|-
| 2.9.5.7
| 420175/419904, {{monzo|44 -14 5 -4}}, {{monzo|39 -3 -26 11}}
| {{mapping|2423 7681 5626 6802}}
| +0.0008
| 0.0290
| 5.86
|-
| 2.9.5.7.11
| 420175/419904, 151263/151250, 2791309312/2790703125, 4194304000000/4193866120059
| {{mapping|2423 7681 5626 6802 8382}}
| +0.0065
| 0.0283
| 5.71
|-
| 2.9.5.7.11.13
| 10648/10647, 1146880/1146717, 105644/105625, 1890625/1889568, 167518208/167403915
| {{mapping|2423 7681 5626 6802 8382 8966}}
| +0.0091
| 0.0265
| 5.35
|-
| 2.9.5.7.11.13.17
| 12376/12375, 131648/131625, 194481/194480, 1146880/1146717, 4685824/4685625, 2127125/2125764
| {{mapping|2423 7681 5626 6802 8382 8966 9904}}
| +0.0064
| 0.0254
| 5.13
|}

User:Francium/2423edo - Revision history

Francium: +music

Francium: /* Theory */