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{{Editable user page}}
{{Editable user page}}


== Pages that are in the greatest need of fixes (Sadbox) ==
== Sadbox ==
Importance of fixing the page is scored out of 5 because i can't stop myself from ranking things. Some reasonably good pages, like [[31edo]], can still have a high score because they get so much attention.


=== Overly mathematical ===
=== Impractical ===
3 [[Wedgies and multivals]]
3 Wedgies


5 [[Tenney–Euclidean]]
5 TE


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


2 [[Balanced word]]
2 Balanced word


2 [[43edo]]
2 43ed2


3 [[31edo]] (needs to be especially accessible to beginners, which it is not)
3 31ed2 (beginner-friendliness)


=== Terribly written ===
=== 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)


4 [[Concordance]]
4 Concordance


2 [[29edo]] (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)
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 [[Fokker block]]
4 Periodicity block


3 [[FAQ]]
3 FAQ


=== Unnecessary ===
=== Unnecessary ===
1 [[Oodako]]
1 Oodako


1 [[Augmented_family#Trug]]
1 Trug


1 [[Oviminor]]
1 Oviminor


2 A bunch of stub pages
2 A bunch of stub pages


=== Terrible names ===
=== Badly named ===
1 [[1025/1024]]
1 1025/1024


=== Terrible concepts or designs ===
=== Badly designed ===
2 [[Ploidacot]] (this is a matter of opinion, so remove if this is too controversial--but we're forcing people to learn new number names for absolutely no reason)
2 Ploidacot (why the number names?)


=== Bad 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 ==
We take all of the fractions greater than 1 within the temperament subgroup and map them to orthogonal Kronecker vectors in an infinite-dimensional vector space (because there are infinitely many fractions within the temperament subgroup). We plot all of our infinitely many commas on this vector space (for example, if our comma basis contains elements that generate 80/81, the vector [-4 1] in the subgroup with first coordinate corresponding to 3/2 and second coordinate 5/1 is plotted here because (3/2)^-4 * 5/1 = 80/81). We then stretch each axis (which is a linear transformation where the eigenvectors are the kronecker vectors) to have length equal to (min_axis_length + the square root of the cent error) * the sum of the numerator and denominator of the basis element, where min_axis_length is a constant and the cent error is the difference between the tempered cent value (using the tempered generators) and the real cent value. Then the score of a comma is score_persistence to the power of its 1-norm (taxicab norm), where score_persistence < 1.
{| class="wikitable sortable" style="text-align: right;"
 
|+ Temperament Rankings
The score for a temperament is the sum of the scores of all the commas.
! 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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