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

Whatever

List of abbreviations:

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23 September 2026

m   22:11

253389edo diffhist +140 Royalmilktea talk contribs (more harmonics)

			21:26		Talk:Minimal consistent EDOs 2 changes history +477 [Currywurst44 (2×)]
					21:26 (cur | prev) +118 Currywurst44 talk contribs (Changes applied)
					17:15 (cur | prev) +359 Currywurst44 talk contribs (Suggest linking the first mention of each edo in every column)

m   21:21

Minimal consistent EDOs diffhist +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

			17:08		Fluid piano 2 changes history +2,162 [Lucius Chiaraviglio (2×)]
					17:08 (cur | prev) +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))
					16:51 (cur | prev) +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)

m   16:21

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15:47

User:Lucius Chiaraviglio/Keyboard Layout Lab/Various rank-3 temperament Lumatone mappings diffhist +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)

15:46

Template:Multival/doc diffhist −181 FloraC talk contribs (Update; left-align variable-length table contents)

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15:45

Lumatone mapping for 84edo diffhist +1,603 Lucius Chiaraviglio talk contribs (→Orwell: Insert Bryan Deister's Porwell mapping after this)

			15:44		Template:Multival 2 changes history −109 [FloraC (2×)]
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			m   15:42		Template:Multimonzo 2 changes history −27 [FloraC (2×)]
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Template:Bra/doc diffhist +16 FloraC talk contribs (Partial undo)

m   14:41

User:Lucius Chiaraviglio/Keyboard Layout Lab/Various other Lumatone mappings diffhist 0 Lucius Chiaraviglio talk contribs (→Sensipent (1/5-Octave) + Malcolmismic Pseudo-Pinetone (1/5-Octave) Lumatone mappings: Move down to the proper place)

			14:27		Lumatone mapping for 100edo 3 changes history +2,249 [Lucius Chiaraviglio (3×)]
			m		14:27 (cur | prev) +17 Lucius Chiaraviglio talk contribs (→Submerged-related rank-2 temperament: Add the interval corresponding to the flat fourth)
					14:25 (cur | prev) +222 Lucius Chiaraviglio talk contribs (→Unnamed rank-2 temperament: --> Submerged-related rank-2 temperament)
					14:13 (cur | prev) +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)

08:17

User:Lucius Chiaraviglio/Keyboard Layout Lab/Unnamed rank-3 temperament Lumatone mappings diffhist +120 Lucius Chiaraviglio talk contribs (→100edo (demonstrated to work but awaiting approval): Got approval with instructions to fix note 0 position)

08:04

Lumatone mapping for 99edo diffhist +675 Lucius Chiaraviglio talk contribs (→Diatonic: Insert Bryan Deister's 49L 1s MOS subset pseudo-isomorphic pseudo-diatonic mapping after this)

			08:02		User:Lucius Chiaraviglio/Keyboard Layout Lab/Non-Isomorphic Lumatone mappings 2 changes history +818 [Lucius Chiaraviglio (2×)]
			m		08:02 (cur | prev) +16 Lucius Chiaraviglio talk contribs (→99edo 49L 1s MOS subset (demonstrated to work): Fix section heading)
					08:01 (cur | prev) +802 Lucius Chiaraviglio talk contribs (→94edo (demonstrated to work): Insert Bryan Deister's Lumatone mapping for 99edo after this)

			07:48		Kleismic 3 changes history +435 [Naren; FloraC (2×)]
			m		07:48 (cur | prev) +43 FloraC talk contribs (→Music: fix a dead link)
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07:46

Talk:Septischismic family diffhist +278 FloraC talk contribs

m   07:45

Lumatone mapping for 11edo diffhist −2 Lucius Chiaraviglio talk contribs (Fix section headings)

07:30

11edo diffhist +91 Lucius Chiaraviglio talk contribs (→21st century: Add Bryan Deister's ''11edo groove'' (2026))

06:20

Deletion log FloraC talk contribs deleted page User:Hotcrystal0/Talk:Septischismic family archive (Author request)

02:13

Regular temperament diffhist −152 Sintel talk contribs (single pitch tuning is not of any practical interest)

			02:11		User:Eliora/Intentionally idiosyncratic concepts 2 changes history +394 [Eliora (2×)]
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N    00:31

User:Eliora/137th-octave temperaments diffhist +111 Eliora talk contribs (Created page with "== Untriseptium == Untriseptium is named after a chemical element 137. Described as the 822 & 6713 temperament.")

00:12

Interval family diffhist +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

			22:09		Talk:Septischismic family 7 changes history +8,509 [FloraC; Hotcrystal0 (6×)]
					22:09 (cur | prev) +10 Hotcrystal0 talk contribs (add an actual title)
					22:04 (cur | prev) +720 Hotcrystal0 talk contribs (→Rename androschismic?: new section)
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					21:15 (cur | prev) +2,433 FloraC talk contribs (Restore the poll & re)
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21:26

Minimal consistent EDOs diffhist +718 Royalmilktea talk contribs (linked first mentions of edos) Tag: Visual edit

19:52

Circular temperament diffhist +52 Hotcrystal0 talk contribs (those were deleted)

			19:48		Comptonesque 2 changes history +99 [Hotcrystal0 (2×)]
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					19:47 (cur | prev) +45 Hotcrystal0 talk contribs (This)