User:FloraC/Sandbox: Difference between revisions

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{{Flat}} {{natural}} {{sharp}}
== Accidentals ==
 
; Wiki templates : {{Flat}} {{natural}} {{sharp}}
♭ ♮ ♯
; Unicode characters : ♭ ♮ ♯
 
; Bravura font : <span class="bravura">&#xE260;</span> <span class="bravura">&#xE261;</span> <span class="bravura">&#xE262;</span>
<span class="bravura">&#xE260;</span> <span class="bravura">&#xE261;</span> <span class="bravura">&#xE262;</span>
; Heji font : <span class="heji">e</span> <span class="heji">n</span> <span class="heji">v</span>  
 
<span class="heji">n</span>


== Template: Temperament data ==
== Template: Temperament data ==

Revision as of 15:02, 25 November 2025

Accidentals

Wiki templates
Unicode characters
♭ ♮ ♯
Bravura font
Heji font
e n v

Template: Temperament data

Subgroup: 2.3.5.7

Comma list: 81/80, 126/125

Mapping: [⟨1 0 -4 -13], ⟨0 1 4 10]]

mapping generators: ~2, ~3

Wedgie: ⟨⟨ 1 4 10 4 13 12 ]]

Optimal tuning (CTE): ~3/2 = 696.9521

Optimal ET sequence: 12, 19, 31, 81, 112b, 143b

Badness: 0.0137

5-limit rank-2 temperaments by TE simple badness

Breed's simple badness.

Junk temperaments

High-badness temperaments

Temperament Complexity Error (¢) Badness (moct) Mapping Comma list
Yo .367 26.0 7.95 [⟨1 0 -1], ⟨0 1 -2]] 10/9
Antitonic .395 27.0 8.89 [⟨2 3 0], ⟨0 0 1]] 9/8
Father .443 13.2 4.87 [⟨1 0 4], ⟨0 1 -1]] 16/15
Bug .602 11.6 5.81 [⟨1 0 0], ⟨0 2 3]] 27/25
Supersharp 1.06 7.94 7.01 [⟨2 0 -5], ⟨0 1 3]] 800/729
Laconic 1.24 6.52 6.74 [⟨1 1 1], ⟨0 3 7]] 2187/2000
Lafayette 1.30 7.00 7.60 [⟨1 1 2], ⟨0 5 3]] 3456/3125
Symbolic 1.31 6.09 6.66 [⟨1 3 4], ⟨0 -5 -6]] 2048/1875
Sixix 1.37 4.57 5.22 [⟨1 3 2], ⟨0 -4 1]] 3125/2916
Uncle 1.40 7.53 8.80 [⟨1 0 12], ⟨0 1 -6]] 4096/3645
Whitewood 1.42 4.20 4.95 [⟨7 11 0], ⟨0 0 1]] 2187/2048
1.66 4.13 5.72 [⟨1 0 5], ⟨0 3 -5]] 32768/30375

Main sequence

Temperament Complexity Error (¢) Badness (moct) Mapping Comma list
Dicot .521 7.09 3.08 [⟨1 1 2], ⟨0 2 1]] 25/24
Meantone .711 1.58 .937 [⟨1 0 -4], ⟨0 1 4]] 81/80
Mavila .795 6.06 4.02 [⟨1 0 7], ⟨0 1 -3]] 135/128
Augmented .894 2.40 1.79 [⟨3 0 7], ⟨0 1 0]] 128/125
Porcupine .960 2.68 2.14 [⟨1 2 3], ⟨0 -3 -5]] 250/243
Blackwood 1.02 4.63 3.93 [⟨5 8 0], ⟨0 0 1]] 256/243
Diminished 1.05 3.10 2.73 [⟨4 0 3], ⟨0 1 1]] 648/625
Srutal 1.22 .835 .852 [⟨2 0 11], ⟨0 1 -2]] 2048/2025
Magic 1.40 1.11 1.29 [⟨1 0 2], ⟨0 5 1]] 3125/3072
Hanson 1.55 .274 .353 [⟨1 0 1], ⟨0 6 5]] 15625/15552
Ripple 1.56 2.82 3.66 [⟨1 2 3], ⟨0 -5 -8]] 6561/6250
Negri 1.58 1.69 2.23 [⟨1 2 2], ⟨0 -4 3]] 16875/16384
Tetracot 1.61 .900 1.21 [⟨1 1 1], ⟨0 4 9]] 20000/19683
Superpyth 1.70 2.11 2.99 [⟨1 0 -12], ⟨0 1 9]] 20480/19683
Helmholtz 1.79 .0570 .0851 [⟨1 0 15], ⟨0 1 -8]] 32805/32768
Wesley 1.91 2.75 4.37 [⟨1 4 3], ⟨0 -7 -2]] 78125/73728
Sensipent 1.97 .356 .584 [⟨1 6 8], ⟨0 7 9]] 78732/78125
Stump 2.02 1.88 3.16 [⟨1 0 6], ⟨0 3 -7]] 273375/262144
Passion 2.02 1.57 2.64 [⟨1 2 2], ⟨0 -5 4]] 262144/253125
Doublewide 2.06 2.00 3.43 [⟨2 1 3], ⟨0 4 3]] 390625/373248
Würschmidt 2.29 .262 .499 [⟨1 7 3], ⟨0 8 1]] 393216/390625
Amity 2.29 .140 .268 [⟨1 3 6], ⟨0 -5 -13]] 1600000/1594323
Valentine 2.34 .736 1.44 [⟨1 1 2], ⟨0 9 5]] 1990656/1953125
Immunity 2.40 1.03 2.06 [⟨1 0 -8], ⟨0 2 13]] 1638400/1594323
Shibboleth 2.42 1.24 2.50 [⟨1 4 5], ⟨0 -9 -10]] 1953125/1889568
Compton 2.44 .504 1.02 [⟨12 19 0], ⟨0 0 1]] 531441/524288
Orson 2.44 .215 .438 [⟨1 0 3], ⟨0 7 -3]] 2109375/2097152
Unicorn 2.52 .725 1.52 [⟨1 2 3], ⟨0 -8 -13]] 1594323/1562500
Mynic 2.60 1.10 2.37 [⟨1 9 9], ⟨0 -10 -9]] 10077696/9765625
Ampersand 2.78 .594 1.38 [⟨1 1 3], ⟨0 6 -7]] 34171875/33554432
Fifive 2.91 .643 1.56 [⟨2 2 3], ⟨0 5 7]] 9765625/9565938
Misty 2.99 .308 .767 [⟨3 0 26], ⟨0 1 -4]] 67108864/66430125
Gravity 2.99 .269 .669 [⟨1 5 12], ⟨0 -6 -17]] 129140163/128000000
Rodan 3.10 .433 1.12 [⟨1 1 -1], ⟨0 3 17]] [20 -17 3⟩
3.11 .757 1.96 [⟨1 0 -23], ⟨0 1 16]] [-23 16 -1⟩
Mabila 3.32 .488 1.35 [⟨1 6 1], ⟨0 -10 3]] [28 -3 -10⟩
Parakleismic 3.47 .0798 .231 [⟨1 5 6], ⟨0 -13 -14]] [8 14 -13⟩
Quartonic 3.48 .214 .621 [⟨1 2 3], ⟨0 -11 -18]] [3 -18 11⟩
Escapade 3.60 .138 .414 [⟨1 2 2], ⟨0 -9 7]] [32 -7 -9⟩
Ditonic 3.68 .258 .792 [⟨1 6 3], ⟨0 -13 -2]] [-27 -2 13⟩
Vishnuzmic 3.71 .0471 .145 [⟨2 4 5], ⟨0 -7 -3]] [23 6 -14⟩
Vulture 3.81 .0576 .183 [⟨1 0 -6], ⟨0 4 21]] [24 -21 4⟩
Trisedodge 3.87 .336 1.08 [⟨5 1 7], ⟨0 3 2]] [19 10 -15⟩
4.00 .157 .524 [⟨1 4 -1], ⟨0 -8 11]] [-36 11 8⟩

Tunings

5-limit norm-based tunings
Manhattan Euclidean Chebyshevian
Constrained Constrained & skewed
Equilateral CEOP: ~3/2 = 697.654 ¢
(1/5-comma) 		CEE: ~3/2 = 696.895 ¢
(4/17-comma) 		CSEE: ~3/2 = 696.453 ¢
(11/43-comma) 		CEC: ~3/2 = 696.578 ¢
(1/4-comma)
Tenney CTOP: ~3/2 = 698.020 ¢ CTE: ~3/2 = 697.214 ¢ CWE: ~3/2 = 696.651 ¢ CTC: ~3/2 = 696.578 ¢
(1/4-comma)
Benedetti,
Wilson 		CBOP: ~3/2 = 698.160 ¢
(3/17-comma) 		CBE: ~3/2 = 697.374 ¢
(36/169-comma) 		CSBE: ~3/2 = 696.787 ¢
(31/129-comma) 		CBC: ~3/2 = 696.578 ¢
(1/4-comma)
7-limit norm-based tunings
Manhattan Euclidean Chebyshevian
Constrained Constrained & skewed
Equilateral CEOP: ~3/2 = 697.344 ¢ CEE: ~3/2 = 696.884 ¢ CSEE: ~3/2 = 696.725 ¢ CEC: ~3/2 = 696.883 ¢
Tenney CTOP: ~3/2 = 696.646 ¢ CTE: ~3/2 = 696.952 ¢ CWE: ~3/2 = 696.656 ¢ CTC: ~3/2 = 696.883 ¢
Benedetti,
Wilson 		CBOP: ~3/2 = 697.842 ¢ CBE: ~3/2 = 697.015 ¢ CSBE: ~3/2 = 696.631 ¢ CBC: ~3/2 = 696.883 ¢

Temperament pages

Note:

  1. Order: subgroup, comma list, mapping, mapping generators, (subgroup-val mapping, gencom mapping), lattice basis, optimal tunings (WE and CWE), minimax tuning, tuning ranges, algebraic generator (?), optimal ET sequence, badness, complexity spectrum, and others.
  2. Comma list should be the Tenney-minimal commas sufficient to define the temperament, stated in Normal forms #Normal forms for commas.
  3. Mapping generators should show all the ratios as used in the mapping, including the period.
  4. For subgroup temperaments, "mapping" becomes "subgroup-val mapping" and "gencom mapping"".
  • If the subgroup is trivial, simply show "WE"/"CWE", otherwise show "subgroup/inharmonic WE/CWE" instead.
  1. Cent symbol in tunings.
  2. Since minimax tunings are based on tonality diamonds, it should explicitly state the odd limit, or a diamond function of ratios.
  3. Algebraic generators are to be discussed later.

Get a family for:

  • Ripple (3 different 7-limit extensions) done
  • Smate (2 different 7-limit extensions) done
  • Passion (4 different 7-limit extensions, 3 strong and 1 weak) done
  • Undim done
  • Quintaleap done
  • Quindromeda done
  • Parakleismic (many reasonable but unnamed 7-limit extensions)
  • Schismatic rank-3 family (perhaps)

Progress:

Scale tree

6-tone
1L 5s, 2L 4s, 3L 3s, 4L 2s, 5L 1s
7-tone
1L 6s, 2L 5s, 3L 4s, 4L 3s, 5L 2s, 6L 1s
8-tone
1L 7s, 2L 6s, 3L 5s, 4L 4s, 5L 3s, 6L 2s, 7L 1s
9-tone
1L 8s, 2L 7s, 3L 6s, 4L 5s, 5L 4s, 6L 3s, 7L 2s, 8L 1s
10-tone
1L 9s, 2L 8s, 3L 7s, 4L 6s, 5L 5s, 6L 4s, 7L 3s, 8L 2s, 9L 1s
11-tone
1L 10s, 2L 9s, 3L 8s, 4L 7s, 5L 6s, 6L 5s, 7L 4s, 8L 3s, 9L 2s, 10L 1s
12-tone
1L 11s, 2L 10s, 3L 9s, 4L 8s, 5L 7s, 6L 6s, 7L 5s, 8L 4s, 9L 3s, 10L 2s, 11L 1s
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