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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24 September 2026

• diffhist Template:Mapping/doc 12:30 +96 FloraC talk contribs (Update)
• diffhist Template:Mapping 12:28 +4 FloraC talk contribs (+ an option for an unlinked legend)
• diffhist Gallery of just intervals 12:25 +6 FloraC talk contribs (Update)
• diffhist 63/40 12:24 +402 FloraC talk contribs (Update the name; 198edo -> 99edo; + see also; + categories)
• diffhist m 80/63 12:18 +42 FloraC talk contribs (+ link to octave complement)
• diffhist 80/63 12:17 −64 FloraC talk contribs (And we don't need the other name anymore)
• diffhist Xenharmonic Wiki talk:Introduction 12:15 +335 FloraC talk contribs
• diffhist m 18ifdo 11:39 +638 BudjarnLambeth talk contribs (→Modes: 11/8 is increasingly important in higher octaves as 11/4, 11/2, etc so worth including)
• diffhist m 18ifdo 11:21 −448 BudjarnLambeth talk contribs (→Modes: highlight only major third not supermajor third cells because supermajor thirds are significantly less consonant)
• diffhist 80/63 11:17 +4 Hotcrystal0 talk contribs (This.)
• diffhist User:Hotcrystal0 11:13 +30 Hotcrystal0 talk contribs
• diffhist User:Hotcrystal0 11:13 +52 Hotcrystal0 talk contribs
• diffhist User:Hotcrystal0/Proposed search program names 11:13 +43 Hotcrystal0 talk contribs
• diffhist N User:Hotcrystal0/Proposed search program names 11:12 +584 Hotcrystal0 talk contribs (Created page with "'''Disclaimer: This page is a joke.''' Some search programs for Conway's Game of Life and other cellular automata have names consisting of L's and S's. Since this can be very confusing, I've proposed the following names for them, using MOS scales as the basis: * LLS → Trial/Fibotonic * LSS → Antrial/Lucatonic * LSSS → Antetric * LLSSS → Pentatonic * LLLSSSSSSSS (Lattice Life Logic Slice Satisfiability Search for Smallest Spaceships Supporting Specific Speeds) (...")
• diffhist m 18ifdo 11:06 −16 BudjarnLambeth talk contribs
• diffhist m 18ifdo 11:05 −946 BudjarnLambeth talk contribs (→Modes: added major sixths and changed colour scheme to loosely reflect consonance)
• diffhist m 18ifdo 10:56 +790 BudjarnLambeth talk contribs (→Modes)
• diffhist m Monthly Tunings 10:44 +161 BudjarnLambeth talk contribs (→2026: add new)
• diffhist Gallery of combination product sets 10:43 +23 BudjarnLambeth talk contribs (→1.n: add new)
• diffhist N 1-5-13-17 hexany 08:23 +743 Yourmusic Productions talk contribs (Create Page.)
• diffhist 18ifdo 06:59 +170 Lucius Chiaraviglio talk contribs (→Music: Add Claudi Meneghin's ''A 2-in-1 canon in F for organ (short version), in 18-IFDO, for baroque oboe and bassoon'' (2026))
• Upload log 06:46 Yourmusic Productions talk contribs uploaded File:1-5-13-17 Hexany.png (Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by Nick Vuci.)
• diffhist Xenharmonic Wiki talk:Introduction 05:59 +255 BudjarnLambeth talk contribs (Should we link Xen concepts for beginners somewhere on this page?)
• diffhist m Frequently asked questions 05:53 +8 BudjarnLambeth talk contribs (→About the wiki)
• diffhist m 43edo 05:30 0 Lucius Chiaraviglio talk contribs (→Modern renderings: Last entry is actually from 2026, not 2024)
• diffhist 41edo/Music 05:29 +199 Lucius Chiaraviglio talk contribs (→Modern renderings: Add Modest Mussorgsky's ''«Gnomus» from «Pictures at an Exhibition»'' (1874) – arranged for harpsichord and rendered by Claudi Meneghin (2026))
• diffhist 43edo 05:26 +199 Lucius Chiaraviglio talk contribs (→Modern renderings: Add Modest Mussorgsky's ''«Gnomus» from «Pictures at an Exhibition»'' (1874) – arranged for harpsichord and rendered by Claudi Meneghin (2024))
• diffhist 31edo/Music 05:17 +143 Lucius Chiaraviglio talk contribs (→Modern renderings: Add Ween's ''Birthday Boy'' (1990) – microtonal cover in 31edo by Bryan Deister (2026))
• diffhist 13edo/Music 04:53 +162 Lucius Chiaraviglio talk contribs (→21st century: Add Noah Jordan's ''Microtonal Ambient Music in 13-EDO | Endless Wind Over the Grass (Tottori, Japan)'' (2026))
• diffhist Gallery of combination product sets 03:07 +53 BudjarnLambeth talk contribs (→In no-3s subgroups: add new)

23 September 2026

• diffhist Interval family 23:14 +703 Currywurst44 talk contribs (Interval set family table completed) Tag: Visual edit: Switched
• diffhist m 253389edo 22:11 +140 Royalmilktea talk contribs (more harmonics)
• diffhist Talk:Minimal consistent EDOs 21:26 +118 Currywurst44 talk contribs (Changes applied)
• diffhist m Minimal consistent EDOs 21:21 +49 Currywurst44 talk contribs (Use visual edit to add links to new edos in columns that were mentioned elsewhere but whose previous mention isn't already in the same row.) Tag: Visual edit
• diffhist Talk:Minimal consistent EDOs 17:15 +359 Currywurst44 talk contribs (Suggest linking the first mention of each edo in every column)
• diffhist Fluid piano 17:08 +2,110 Lucius Chiaraviglio talk contribs (Add web site for performer Utsav Lal; add web site for Geoffrey Smith; add the aforementioned Google Gemini search (dynamic output — may change over time))
• diffhist Fluid piano 16:51 +52 Lucius Chiaraviglio talk contribs (→Description: The old fluid piano web site (dubious to start with, so never linked here) disappeared; Gemini found a new web site for the fluid piano — add link; this also has links to some more performances, although at least one of them duplicates an already-linked video)
• diffhist m History and philosophy of xenharmonic music 16:21 −1 Xenjacob talk contribs (→Setting the Stage: it's -> its) Tag: Visual edit
• diffhist m Template:Monzo/doc 15:48 −22 FloraC talk contribs (Left-align variable-length table contents)
• diffhist m Template:Val/doc 15:48 −22 FloraC talk contribs (Left-align variable-length table contents)
• diffhist User:Lucius Chiaraviglio/Keyboard Layout Lab/Various rank-3 temperament Lumatone mappings 15:47 +1,791 Lucius Chiaraviglio talk contribs (→Biyatismic family rank-3 variant with Magic (Witchcraft) generator Lumatone mappings: Insert Porwell Lumatone mappings (temporarily moved up for visibility) above this, starting with Bryan Deister's Lumatone mapping for 84edo)
• diffhist Template:Multival/doc 15:46 −181 FloraC talk contribs (Update; left-align variable-length table contents)
• diffhist m Template:Multimonzo/doc 15:46 −11 FloraC talk contribs (Left-align variable-length table contents)
• diffhist Lumatone mapping for 84edo 15:45 +1,603 Lucius Chiaraviglio talk contribs (→Orwell: Insert Bryan Deister's Porwell mapping after this)
• diffhist Template:Multival 15:44 −68 FloraC talk contribs (No longer need the functionality of a legend. Match it with Template: Multimonzo)
• diffhist m Template:Multimonzo 15:42 0 FloraC talk contribs (There was another decimal HTML)
• diffhist m Template:Ket/doc 15:40 +16 FloraC talk contribs (Partial undo)
• diffhist m Template:Bra/doc 15:39 +16 FloraC talk contribs (Partial undo)
• diffhist m Template:Multimonzo 15:34 −27 FloraC talk contribs (- monzo class (has no effects))
• diffhist Template:Multival 15:29 −41 FloraC talk contribs (- badass invalid character; - val class (has no effects))