User:Hkm/Sandbox: Difference between revisions

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== Sadbox ==
== Sadbox ==


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


Line 16: Line 16:
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 a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the motion's error in cents)**error_power) * complexity_fondness**(the complexity of the motion) / 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 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 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.)
{| class="wikitable sortable" style="text-align: right;"
|+ Temperament Rankings
! 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 ==

Latest revision as of 01:30, 17 August 2025

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Sadbox

Impractical

3 Wedgies

5 TE

5 Otonality and utonality (what are the musical implications?)

2 Balanced word

2 43ed2

3 31ed2 (beginner-friendliness)

Badly written

5 Intro to Xenharmonics (can be supplemented with user:hkm/Intro_page)

4 Concordance

2 29ed2 (needs a clearer focus on essentially tempered chords in the 2.3.7/5.11/5.13/5 subgroup, less focus on temperaments of 29edo, and less trivia)

4 Periodicity block

3 FAQ

Unnecessary

1 Oodako

1 Trug

1 Oviminor

2 A bunch of stub pages

Badly named

1 1025/1024

Badly designed

2 Ploidacot (why the number names?)

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)

Badness

Temperament Rankings
EDO GPV Goodness 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

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