Testing

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 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))
diffhist m User:Lucius Chiaraviglio/Keyboard Layout Lab/Various other Lumatone mappings 14:41 0 Lucius Chiaraviglio talk contribs (→Sensipent (1/5-Octave) + Malcolmismic Pseudo-Pinetone (1/5-Octave) Lumatone mappings: Move down to the proper place)
diffhist m Lumatone mapping for 100edo 14:27 +17 Lucius Chiaraviglio talk contribs (→Submerged-related rank-2 temperament: Add the interval corresponding to the flat fourth)
diffhist Lumatone mapping for 100edo 14:25 +222 Lucius Chiaraviglio talk contribs (→Unnamed rank-2 temperament: --> Submerged-related rank-2 temperament)
diffhist Lumatone mapping for 100edo 14:13 +2,010 Lucius Chiaraviglio talk contribs (→Other Mappings: --> Unnamed rank-2 temperament; flesh out description a bit; insert Bryan Deister's unnamed rank-3 temperament mapping after this)
diffhist User:Lucius Chiaraviglio/Keyboard Layout Lab/Unnamed rank-3 temperament Lumatone mappings 08:17 +120 Lucius Chiaraviglio talk contribs (→100edo (demonstrated to work but awaiting approval): Got approval with instructions to fix note 0 position)
diffhist Lumatone mapping for 99edo 08:04 +675 Lucius Chiaraviglio talk contribs (→Diatonic: Insert Bryan Deister's 49L 1s MOS subset pseudo-isomorphic pseudo-diatonic mapping after this)
diffhist m User:Lucius Chiaraviglio/Keyboard Layout Lab/Non-Isomorphic Lumatone mappings 08:02 +16 Lucius Chiaraviglio talk contribs (→99edo 49L 1s MOS subset (demonstrated to work): Fix section heading)
diffhist User:Lucius Chiaraviglio/Keyboard Layout Lab/Non-Isomorphic Lumatone mappings 08:01 +802 Lucius Chiaraviglio talk contribs (→94edo (demonstrated to work): Insert Bryan Deister's Lumatone mapping for 99edo after this)
diffhist m Kleismic 07:48 +43 FloraC talk contribs (→Music: fix a dead link)
diffhist Kleismic 07:47 +84 FloraC talk contribs (→Music: arrangement of nonmicrotonal work)
diffhist Talk:Septischismic family 07:46 +278 FloraC talk contribs
diffhist m Lumatone mapping for 11edo 07:45 −2 Lucius Chiaraviglio talk contribs (Fix section headings)
diffhist Kleismic 07:40 +308 Naren talk contribs (Add to music and external links)
diffhist 11edo 07:30 +91 Lucius Chiaraviglio talk contribs (→21st century: Add Bryan Deister's ''11edo groove'' (2026))
Deletion log 06:20 FloraC talk contribs deleted page User:Hotcrystal0/Talk:Septischismic family archive (Author request)
diffhist Regular temperament 02:13 −152 Sintel talk contribs (single pitch tuning is not of any practical interest)
diffhist User:Eliora/Intentionally idiosyncratic concepts 02:11 +294 Eliora talk contribs
diffhist User:Eliora/Intentionally idiosyncratic concepts 02:09 +100 Eliora talk contribs
diffhist N User:Eliora/137th-octave temperaments 00:31 +111 Eliora talk contribs (Created page with "== Untriseptium == Untriseptium is named after a chemical element 137. Described as the 822 & 6713 temperament.")
diffhist Interval family 00:12 +934 Currywurst44 talk contribs (Create more compact table in preparation of merger. Remove primodality as it's main purpose is as an overtone scale.)

22 September 2026

diffhist Talk:Septischismic family 22:09 +10 Hotcrystal0 talk contribs (add an actual title)
diffhist Talk:Septischismic family 22:04 +720 Hotcrystal0 talk contribs (→Rename androschismic?: new section)