User:Overthink/Sandbox

Scratchwork

The following tables show how 15-odd-limit intervals are represented in 5edo. Prime harmonics are in bold; inconsistent intervals are in italics.

15-odd-limit intervals in 5edo (direct approximation, even if inconsistent)

Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
15/13, 26/15	7.741	3.2
7/4, 8/7	8.826	3.7
3/2, 4/3	18.045	7.5
13/10, 20/13	25.786	10.7
7/6, 12/7	26.871	11.2
9/8, 16/9	36.090	15.0
9/7, 14/9	44.916	18.7
13/11, 22/13	49.210	20.5
15/11, 22/15	56.951	23.7
9/5, 10/9	57.596	24.0
11/7, 14/11	62.492	26.0
11/8, 16/11	71.318	29.7
11/10, 20/11	74.996	31.2
5/3, 6/5	75.641	31.5
13/9, 18/13	83.382	34.7
11/6, 12/11	89.363	37.2
5/4, 8/5	93.686	39.0
13/12, 24/13	101.427	42.3
7/5, 10/7	102.512	42.7
11/9, 18/11	107.408	44.8
13/7, 14/13	111.702	46.5
15/8, 16/15	111.731	46.6
15/14, 28/15	119.443	49.8
13/8, 16/13	119.472	49.8

15-odd-limit intervals in 5edo (patent val mapping)

Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
15/13, 26/15	7.741	3.2
7/4, 8/7	8.826	3.7
3/2, 4/3	18.045	7.5
13/10, 20/13	25.786	10.7
7/6, 12/7	26.871	11.2
9/8, 16/9	36.090	15.0
9/7, 14/9	44.916	18.7
9/5, 10/9	57.596	24.0
11/7, 14/11	62.492	26.0
11/8, 16/11	71.318	29.7
5/3, 6/5	75.641	31.5
13/9, 18/13	83.382	34.7
11/6, 12/11	89.363	37.2
5/4, 8/5	93.686	39.0
13/12, 24/13	101.427	42.3
7/5, 10/7	102.512	42.7
11/9, 18/11	107.408	44.8
15/8, 16/15	111.731	46.6
13/8, 16/13	119.472	49.8
15/14, 28/15	120.557	50.2
13/7, 14/13	128.298	53.5
11/10, 20/11	165.004	68.8
15/11, 22/15	183.049	76.3
13/11, 22/13	190.790	79.5

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14 November 2026

• diffhist 311edo 21:35 +1,334 Eufalesio talk contribs (WIP commas, TBA deleted commas) Tag: Visual edit
• diffhist Talk:Keyboard 20:34 +1,036 Lucius Chiaraviglio talk contribs (→Miso modular isomorphic keyboard: new section)
• diffhist 13/7 18:40 +511 DesertFreeze talk contribs (Added info) Tag: Visual edit
• diffhist 13/10 17:55 +25 DesertFreeze talk contribs (Added third-fourth naming) Tag: Visual edit
• User creation log 17:12 User account SomeDee talk contribs was created by Fredg999 talk contribs and password was sent by email
• User creation log 17:11 User account Avi talk contribs was created by Fredg999 talk contribs and password was sent by email
• diffhist Catalog of temperaments by wedgie 14:10 +279 FloraC talk contribs (+++)
• diffhist m 31st-octave temperaments 13:52 +34 FloraC talk contribs (+ links)
• diffhist m 2573edo 13:49 −20 FloraC talk contribs (Update)
• diffhist N Euphrosynean 13:49 +159 FloraC talk contribs (Redirected page to Ragismic microtemperaments#Euphrosynean) Tag: New redirect
• diffhist m Hemimean clan 13:47 +94 FloraC talk contribs (→Birds: + link to 5-limit)
• diffhist Syntonic–31 equivalence continuum 13:45 +223 FloraC talk contribs
• diffhist 31st-octave temperaments 13:42 −1,030 FloraC talk contribs (- 31-commatic / 31-5-commatic)
• diffhist Syntonic–31 equivalence continuum 13:35 +1,080 FloraC talk contribs (Move 31-commatic and 5-limit birds (31-5-commatic) here)
• diffhist 31st-octave temperaments 13:26 −5,114 FloraC talk contribs (- birds, - euphrosynean (covered in hemimean clan and ragismic microtemperaments))
• diffhist Ragismic microtemperaments 13:25 +2,701 FloraC talk contribs (Move euphrosynean here)
• diffhist m 2.5.7 subgroup 13:22 −29 FloraC talk contribs (Update)
• diffhist m Undecimal birds node 13:19 −13 FloraC talk contribs (Changed redirect target from 31st-octave temperaments#11-limit to Hemimean clan#Birds) Tag: Redirect target changed
• diffhist m Birds node 13:19 −10 FloraC talk contribs (Changed redirect target from 31st-octave temperaments#Birds to Hemimean clan#Birds) Tag: Redirect target changed
• diffhist m Birds 13:18 +10 FloraC talk contribs (Update) Tag: Redirect target changed
• diffhist Hemimean clan 13:17 +2,525 FloraC talk contribs (Move birds here)
• diffhist 31st-octave temperaments 12:59 +816 FloraC talk contribs (Switch to Sintel's badness, WE & CWE tunings (4/4))
• diffhist 31st-octave temperaments 12:37 +565 FloraC talk contribs (Switch to Sintel's badness, WE & CWE tunings (3/))
• diffhist 31st-octave temperaments 10:35 +568 FloraC talk contribs (Complete data; switch to Sintel's badness, WE & CWE tunings (2/))
• diffhist 31st-octave temperaments 10:17 +1,102 FloraC talk contribs (Cleanup; switch to Sintel's badness, WE & CWE tunings (1/))
• diffhist N 1-11-13-17 hexany 09:43 +742 Yourmusic Productions talk contribs (Create Page.)
• diffhist m No-fives subgroup temperaments 09:38 −9 FloraC talk contribs (→Nimbus: monzify the ultralong comma)
• diffhist No-fives subgroup temperaments 09:37 +66 FloraC talk contribs (→Nimbus: note relation to sedecic)
• diffhist 16th-octave temperaments 09:32 0 FloraC talk contribs (Move ntiscifer to the top as it will permanently be here (if deemed worth documenting), while sulfur is temporary)
• Upload log 09:32 Yourmusic Productions talk contribs uploaded File:1-11-13-17 hexany.png (Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by Nick Vuci.)
• diffhist 16th-octave temperaments 09:30 −2,159 FloraC talk contribs (- nimbus (covered in no-5's))
• diffhist No-fives subgroup temperaments 09:30 +2,258 FloraC talk contribs (Move nimbus here)
• diffhist m 16th-octave temperaments 09:28 −46 FloraC talk contribs (→Nimbus: style and fix mapping)
• diffhist m No-fives subgroup temperaments 09:17 +46 FloraC talk contribs (→Hemif: +1 missing extension)
• diffhist Miscellaneous 7-limit temperaments 09:13 +546 FloraC talk contribs (→Tolerant: + intro)
• diffhist 12th-octave temperaments 09:00 +6 CompactStar talk contribs (I doubt atomic was "hugely" known)
• diffhist m Archytas clan 08:57 0 FloraC talk contribs (→Archy: fixes)
• diffhist Flutterpyth 08:55 −16 FloraC talk contribs (Changed redirect target from No-fives subgroup temperaments#Flutterpyth to Archytas clan#Flutterpyth) Tag: Redirect target changed
• diffhist No-fives subgroup temperaments 08:52 −1,011 FloraC talk contribs (- archy extensions (covered in archytas clan))
• diffhist Archytas clan 08:52 +1,351 FloraC talk contribs (+ preflutterpyth to complete the move)
• diffhist User:CompactStar/sandbox 08:45 +14 CompactStar talk contribs
• diffhist Aldebaran 08:43 +41 CompactStar talk contribs
• diffhist 47edo 08:35 +97 CompactStar talk contribs (→Scales)
• diffhist m 66th-octave temperaments 08:09 +145 FloraC talk contribs (+ todo notice)
• diffhist 73edo 08:06 +182 Lucius Chiaraviglio talk contribs (→Music: Add ABBA's ''Dancing Queen'' (1976) — microtonal cover by Bryan Deister (2026) (had to add Modern renderings section for this))
• diffhist Lumatone mapping for 61edo 06:29 +382 Lucius Chiaraviglio talk contribs (→Diatonic: Add demo video for sharp fifth version)
• diffhist 61edo 05:46 +357 Lucius Chiaraviglio talk contribs (→Music: Add Sam Haft and Andrew Underberg's ''Wilting'' via ''Dandy's World'' (2025) — microtonal cover by Bryan Deister (2026) (had to add Modern renderings section for this))

13 November 2026

• diffhist N Dysprosium 21:39 +49 Eliora talk contribs (Redirected page to 66th-octave temperaments#Dysprosium) Tag: New redirect
• diffhist 1650edo 21:39 +262 Eliora talk contribs (expand clarify)
• diffhist 20th-octave temperaments 20:58 +24 Eliora talk contribs (clarify)