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Line 3: Line 3:
== Sadbox ==
== Sadbox ==


=== Practicality ===
=== Impractical ===
3 Wedgies
3 Wedgies


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3 31ed2 (beginner-friendliness)
3 31ed2 (beginner-friendliness)


=== Writing ===
=== Badly written ===
5 Intro to Xenharmonics (can be supplemented with user:hkm/Intro_page)
5 Intro to Xenharmonics (can be supplemented with user:hkm/Intro_page)


Line 27: Line 27:
3 FAQ
3 FAQ


=== Criticality ===
=== Unnecessary ===
1 Oodako
1 Oodako


Line 36: Line 36:
2 A bunch of stub pages
2 A bunch of stub pages


=== Naming ===
=== Badly named ===
1 1025/1024
1 1025/1024


=== Design ===
=== Badly designed ===
2 Ploidacot (why the number names?)
2 Ploidacot (why the number names?)


=== Formatting ===
=== Badly formatted ===
2 Practically all edo pages <50 (algorithmically generated material, like GPVs and sagittal notations, should be moved to the GPV and sagittal pages, for example. The interval table gets to stay though)
2 Practically all edo pages <50 (algorithmically generated material, like GPVs and sagittal notations, should be moved to the GPV and sagittal pages, for example. The interval table gets to stay though)


== Badness ==
== Badness ==
Let min_cents ~ 35, error_power ~ 1.5, complexity_fondness ~ 0.93, and magic_number ~ 2.
{| class="wikitable sortable" style="text-align: right;"
 
|+ Temperament Rankings
Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)**error_power) * complexity_fondness**(the complexity of the step) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign a JI interpretation to each pair of notes and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.
! style="width: 25%;" | EDO
! style="width: 25%;" | GPV
! style="width: 25%;" | Goodness
! style="width: 25%;" | Octave stretch
|-
| 1 || 0.91 || 11.8 ||  +0.00
|-
| 2 || 1.88 || 12.4 ||  +0.05
|-
| 3 || 2.91 || 14.2 ||  -5.13
|-
| 4 || 3.97 || 13.2 ||  -0.01
|-
| 5 || 5.12 || 14.8 ||  -0.00
|-
| 6 || 6.00 || 14.3 ||  -0.22
|-
| 7 || 6.91 || 16.7 ||  -0.31
|-
| 8 || 8.03 || 16.2 ||  -18.36
|-
| 9 || 9.03 || 18.0 ||  -0.12
|-
| 10 || 10.03 || 20.1 ||  +0.27
|-
| 11 || 11.00 || 16.2 ||  -2.52
|-
| 12 || 12.03 || 27.2 ||  -0.01
|-
| 13 || 12.88 || 17.9 ||  +0.43
|-
| 14 || 13.91 || 24.3 ||  +9.75
|-
| 15 || 15.06 || 26.4 ||  -4.16
|-
| 16 || 15.91 || 24.0 ||  +0.14
|-
| 17 || 17.06 || 28.7 ||  -2.47
|-
| 18 || 18.12 || 23.2 ||  -8.80
|-
| 19 || 19.03 || 32.8 ||  +3.38
|-
| 20 || 19.97 || 22.5 ||  +1.02
|-
| 21 || 20.97 || 26.5 ||  -0.73
|-
| 22 || 22.09 || 34.0 ||  -1.50
|-
| 23 || 22.88 || 25.2 ||  +8.60
|-
| 24 || 24.00 || 33.9 ||  +0.03
|-
| 25 || 25.03 || 26.0 ||  +0.69
|-
| 26 || 25.94 || 34.4 ||  +2.77
|-
| 27 || 27.12 || 36.2 ||  -4.24
|-
| 28 || 27.88 || 27.4 ||  +7.01
|-
| 29 || 28.94 || 35.5 ||  +3.21
|-
| 30 || 30.06 || 27.5 ||  -2.51
|-
| 31 || 31.00 || 40.2 ||  +0.33
|-
| 32 || 32.03 || 31.8 ||  -2.37
|-
| 33 || 32.88 || 29.6 ||  +4.40
|-
| 34 || 34.03 || 39.6 ||  -1.75
|-
| 35 || 34.94 || 32.0 ||  +2.81
|-
| 36 || 36.03 || 37.3 ||  +0.29
|-
| 37 || 37.06 || 35.9 ||  -1.00
|-
| 38 || 37.88 || 38.1 ||  +3.88
|-
| 39 || 39.06 || 38.3 ||  -3.89
|-
| 40 || 39.94 || 33.6 ||  +1.23
|-
| 41 || 41.00 || 42.7 ||  +0.14
|-
| 42 || 42.12 || 34.4 ||  -4.29
|-
| 43 || 43.09 || 39.9 ||  -1.04
|-
| 44 || 44.00 || 36.5 ||  -0.76
|-
| 45 || 44.88 || 38.4 ||  +4.01
|-
| 46 || 46.00 || 42.9 ||  +0.14
|-
| 47 || 46.91 || 33.3 ||  +1.42
|-
| 48 || 47.97 || 38.4 ||  +0.35
|-
| 49 || 49.12 || 40.1 ||  -3.48
|-
| 50 || 49.94 || 41.6 ||  +1.41
|-
| 51 || 51.06 || 37.5 ||  -2.05
|-
| 52 || 51.91 || 34.1 ||  +0.50
|-
| 53 || 53.00 || 44.1 ||  +0.08
|-
| 54 || 54.06 || 36.9 ||  -2.68
|-
| 55 || 54.88 || 38.6 ||  +2.81
|-
| 56 || 55.94 || 40.8 ||  -0.07
|-
| 57 || 56.94 || 39.3 ||  +0.72
|-
| 58 || 58.09 || 43.5 ||  -1.55
|-
| 59 || 59.09 || 35.6 ||  -1.95
|-
| 60 || 59.97 || 42.6 ||  +1.54
|-
| 61 || 61.12 || 38.5 ||  -2.54
|-
| 62 || 61.97 || 42.0 ||  +1.42
|-
| 63 || 63.03 || 42.2 ||  -0.33
|-
| 64 || 63.88 || 38.8 ||  +3.49
|-
| 65 || 65.06 || 43.2 ||  -0.56
|-
| 66 || 66.12 || 37.8 ||  -3.38
|-
| 67 || 67.09 || 40.0 ||  -0.37
|-
| 68 || 68.06 || 43.4 ||  -0.79
|-
| 69 || 68.91 || 39.5 ||  +1.86
|-
| 70 || 70.09 || 40.6 ||  -0.63
|-
| 71 || 71.12 || 38.6 ||  -2.08
|-
| 72 || 71.97 || 45.0 ||  +0.71
|-
| 73 || 73.12 || 40.6 ||  -2.32
|-
| 74 || 74.00 || 40.1 ||  -0.00
|-
| 75 || 75.09 || 41.7 ||  -1.46
|-
| 76 || 75.88 || 39.4 ||  +2.03
|-
| 77 || 76.97 || 44.0 ||  +0.21
|-
| 78 || 78.09 || 40.8 ||  -0.80
|-
| 79 || 78.91 || 41.3 ||  +1.19
|-
| 80 || 80.09 || 43.9 ||  -1.02
|-
| 81 || 80.88 || 41.2 ||  +1.28
|-
| 82 || 82.00 || 42.3 ||  +0.57
|-
| 83 || 83.12 || 39.3 ||  -2.12
|-
| 84 || 84.03 || 43.6 ||  -0.05
|-
| 85 || 85.12 || 40.8 ||  -1.89
|-
| 86 || 85.88 || 41.2 ||  +1.99
|-
| 87 || 87.00 || 44.3 ||  -0.26
|-
| 88 || 87.91 || 40.2 ||  +1.70
|-
| 89 || 89.03 || 43.2 ||  -0.33
|-
| 90 || 90.06 || 41.2 ||  -1.07
|-
| 91 || 90.88 || 42.6 ||  +1.97
|-
| 92 || 92.00 || 42.0 ||  +0.00
|-
| 93 || 92.88 || 40.9 ||  +0.86
|-
| 94 || 94.03 || 44.3 ||  +0.15
|-
| 95 || 95.09 || 42.1 ||  -1.55
|-
| 96 || 95.94 || 43.0 ||  +0.65
|-
| 97 || 97.00 || 40.9 ||  -0.03
|-
| 98 || 97.91 || 41.5 ||  +1.25
|-
| 99 || 99.06 || 44.2 ||  -0.71
|-
| 100 || 99.91 || 41.2 ||  +1.41
|-
| 101 || 100.91 || 42.0 ||  +1.52
|-
| 102 || 102.09 || 42.1 ||  -1.33
|-
| 103 || 102.94 || 44.2 ||  +0.75
|-
| 104 || 104.06 || 42.9 ||  -0.73
|-
| 105 || 104.94 || 40.1 ||  +0.39
|-
| 106 || 106.00 || 43.1 ||  +0.09
|-
| 107 || 107.12 || 40.9 ||  -1.88
|-
| 108 || 108.00 || 42.1 ||  -0.13
|-
| 109 || 109.03 || 43.0 ||  -0.03
|-
| 110 || 109.88 || 41.5 ||  +1.48
|-
| 111 || 111.00 || 44.1 ||  -0.61
|-
| 112 || 111.91 || 41.1 ||  +1.43
|-
| 113 || 112.97 || 43.8 ||  +0.39
|-
| 114 || 114.12 || 42.4 ||  -0.88
|-
| 115 || 114.97 || 42.3 ||  +0.28
|-
| 116 || 116.09 || 42.1 ||  -1.34
|-
| 117 || 116.88 || 40.5 ||  +1.62
|-
| 118 || 117.97 || 44.3 ||  +0.20
|-
| 119 || 119.12 || 40.7 ||  -1.35
|-
| 120 || 120.09 || 42.5 ||  -0.19
|-
| 121 || 121.09 || 44.1 ||  -0.74
|-
| 122 || 121.91 || 42.6 ||  +1.17
|-
| 123 || 123.09 || 42.2 ||  -0.88
|-
| 124 || 124.12 || 41.4 ||  -0.39
|-
| 125 || 124.94 || 43.8 ||  +0.54
|-
| 126 || 126.12 || 42.4 ||  -1.35
|-
| 127 || 126.91 || 42.2 ||  +0.62
|-
| 128 || 127.97 || 43.0 ||  -0.03
|-
| 129 || 128.91 || 41.4 ||  +0.94
|-
| 130 || 130.00 || 44.2 ||  -0.00
|-
| 131 || 131.03 || 41.7 ||  -0.59
|-
| 132 || 131.94 || 42.9 ||  +1.23
|-
| 133 || 133.06 || 42.9 ||  -0.50
|-
| 134 || 133.91 || 42.4 ||  +0.73
|-
| 135 || 135.12 || 42.9 ||  -0.39
|-
| 136 || 136.12 || 42.1 ||  -0.97
|-
| 137 || 137.03 || 43.5 ||  -0.06
|-
| 138 || 138.09 || 42.4 ||  -1.25
|-
| 139 || 139.00 || 41.9 ||  +0.31
|-
| 140 || 139.97 || 43.9 ||  +0.12
|}
== 128::256 ==
Retrieved from "https://en.xen.wiki/w/User:Hkm/Sandbox"