EDT: Difference between revisions

| | [[50edt]]

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| | 50edt falls exactly halfway between 31 and 32 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\63 of an octave.

| | [[51edt]]

| | [[32edo]]

| | 51edt is 32edo with ~6.6 cent octave compression. Patent vals match through the 3-limit.

| | [[52edt]]

| | [[33edo]]

| | 52edt is 33edo with ~7 cent octave stretch. Patent vals match through the 11-limit, with the exception of 5.

| | [[53edt]]

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| | 53edt falls exactly halfway between 33 and 34 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\67 of an octave.

| | [[55edt]]

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| rowspan="2"| Neither 55edt nor 56edt is equivalent to [[35edo]].

| | [[56edt]]

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| | [[58edt]]

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| | 58edt falls exactly halfway between 36 and 37 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\73 of an octave.

| | [[59edt]]

| | [[37edo]]

| | 59edt is 37edo with~7.25 cent octave compression. Patent vals match through the 5-limit.

| | [[61edt]]

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| | 61edt falls exactly halfway between 38 and 39 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\77 of an octave.

| | [[63edt]]

| | [[40edo]]

| | 63edt is 40edo with ~7.6 cent stretched octaves. Patent vals match through the 7-limit, with the exception of 5.

| | [[64edt]]

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| | 64edt falls exactly halfway between 40 and 41 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\81 of an octave.

| | [[66edt]]

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| | 66edt falls exactly halfway between 41 and 42 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\83 of an octave.

| | [[67edt]]

| | [[42edo]]

| | 67edt is 42edo with ~7.3 cent compressed octaves. Patent vals match through the 5-limit, though the 5s cannot be said to match with a straight face.

| | [[69edt]]

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| | 69edt falls exactly halfway between 43 and 44 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\87 of an octave.

| | [[70edt]]

| | [[44edo]]

| | Same ~4.5 cent octave compression as 35edt~22edo. Patent vals match through the 7-limit, with the exception of 5, though the 7s cannot be said to match with a straight face.

| | [[71edt]]

| | [[45edo]]

| | 71edt is is 45edo with ~4.5 cent stretched octaves. Patent vals match through the 7-limit, with the exception of 5.

| | [[72edt]]

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| | 72edt falls exactly halfway between 45 and 46 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\91 of an octave.

| | [[74edt]]

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| rowspan="2"| Neither 74edt nor 75edt is equivalent to [[47edo]].  

| | [[75edt]]

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| | [[77edt]]

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| | 77edt falls exactly halfway between 48 and 49 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\97 of an octave.

| | [[78edt]]

| | [[49edo]]

| | 78edt is 49edo with ~5.2 cent compressed octaves.  Patent vals match through the 11-limit, though the 77s rather than either the 7s or 11s individually can be said to match with a straight face.  

| | [[80edt]]

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| | 80edt falls exactly halfway between 50 and 51 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\101 of an octave.

| | [[82edt]]

| | [[52edo]]

| | Same ~6.1 cent octave stretch as 41edt~26edo, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit.

| | [[83edt]]

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| | 83edt falls exactly halfway between 50 and 51 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\105 of an octave.

| | [[85edt]]

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| | 85edt falls exactly halfway between 53 and 54 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\107 of an octave.

| | [[86edt]]

| | [[54edo]]

| | Same ~5.7 cent octave compression as 43edt~27edo, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit.

| | [[88edt]]

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| | 88edt falls exactly halfway between 55 and 56 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\111 of an octave.

| | [[90edt]]

| | [[57edo]]

| | Same ~4.6 cent octave stretch as 30edt~19edo. Patent vals match through the 5-limit.

| | [[91edt]]

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| | 91edt falls exactly halfway between 57 and 58 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\115 of an octave.

| | [[93edt]]

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| rowspan="2"| Neither 93edt nor 94edt is equivalent to [[59edo]].

| | [[94edt]]

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| | [[96edt]]

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| | 96edt falls exactly halfway between 60 and 61 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\121 of an octave.

| | [[97edt]]

| | [[61edo]]

| | 97edt is 61edo with ~3.9 cent compressed octaves. Patent vals match through the 5-limit.

| | [[98edt]]

| | [[62edo]]

| | Same ~3.3 cent octave compression as 49edt~31edo. Patent vals match through the 23-limit.

| | [[99edt]]

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| | 99edt falls exactly halfway between 62 and 63 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\125 of an octave.

| | [[101edt]]

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| rowspan="2"| Neither 101edt nor 102edt is equivalent to [[64edo]].

| | [[102edt]]

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| | [[104edt]]

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| | 104edt falls exactly halfway between 65 and 66 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\131 of an octave.

| | [[105edt]]

| | [[66edo]]

| | Same ~4.5 cent octave compression as 35edt~22edo, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit.

| | [[107edt]]

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| | 107edt falls exactly halfway between 67 and 68 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\135 of an octave.

| | [[109edt]]

| | [[69edo]]

| | 109edt is 69edo with ~4 cent stretched octaves. Patent vals match through the 5-limit.

| | [[110edt]]

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| | 110edt falls exactly halfway between 69 and 70 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\139 of an octave.

| | [[112edt]]

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| rowspan="2"| Neither 112edt nor 113edt is equivalent to 71edo.

| | [[113edt]]

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| | [[115edt]]

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| | 115edt falls exactly halfway between 72 and 73 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\145 of an octave.

| | [[116edt]]

| | [[73edo]]

| | 116edt is 73edo with ~3.1 cent compressed octaves. Patent vals match through the 11-limit, though products of of any two of 5, 7 and 11 rather than 5, 7 and 11 themselves can be said to match with a straight face.

| | [[117edt]]

| | [[74edo]]

| | 117edt is 74edo with ~2.95 cent stretched octaves, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit.

| | [[118edt]]

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| | 118edt falls exactly halfway between 74 and 75 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\149 of an octave.

| | [[120edt]]

| | [[76edo]]

| | Same ~4.6 cent octave stretch as 30edt~19edo. Patent vals match through the 7-limit, though the 7s cannot be said to match with a straight face.

| | [[121edt]]

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| | 121edt falls exactly halfway between 76 and 77 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\153 of an octave.

| | [[123edt]]

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| | Same ~6.1 cent octave stretch as 41edt~26edo, but actually more strongly resembles the scale with generator 2\155 of an octave.

| | [[124edt]]

| | [[78edo]]

| | Same ~3.6 cent octave compression as 62edt~39edo, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit.

| | [[126edt]]

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| | 126edt falls exactly halfway between 79 and 80 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\159 of an octave.

| | [[128edt]]

| | [[81edo]]

| | 128edt is 81edo with ~3.6 cent stretched octaves. Patent vals match through the 5-limit, though the 5s cannot be said to match with a straight face.

| | [[129edt]]

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| | Same ~5.7 cent octave compression as 43edt~27edo, but actually more strongly resembles the scale with generator 2\163 of an octave.

| | [[131edt]]

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| | 131edt falls exactly halfway between 82 and 83 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\165 of an octave.

| | [[132edt]]

| | [[83edo]]

| | 132edt is 83edo with ~4.1 cent compressed octaves.

| | [[134edt]]

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| | 134edt falls exactly halfway between 84 and 85 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\169 of an octave.

| | [[135edt]]

| | [[85edo]]

| | Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 7-limit, with the exception of 5.

| | [[136edt]]

| | [[86edo]]

| | Same ~2.7 cent octave stretch as 68edt~43edo.

| | [[137edt]]

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| | 137edt falls exactly halfway between 86 and 87 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\173 of an octave.

| | [[139edt]]

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| | 139edt is 88edo with a ~4.1 cent stretched octave, but also 175ed4 with a ~5.55 cent compressed 4/1.

| | [[140edt]]

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| | Same ~4.5 cent octave compression as 35edt~22edo, but actually equally strongly resembles the scale with generator 2\177 of an octave.

| | [[142edt]]

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| | 142edt falls exactly halfway between 89 and 90 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\179 of an octave.

| | [[143edt]]

| | [[90edo]]

| | 143edt is 90edo with ~3 cent compressed octaves.

| | [[145edt]]

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| | 145edt falls exactly halfway between 91 and 92 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\183 of an octave.

| | [[147edt]]

| | [[93edo]]

| | Same ~3.3 cent octave compression as 49edt~31edo, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit.

| | [[148edt]]

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| | 148edt falls exactly halfway between 93 and 94 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\187 of an octave.

| | [[150edt]]

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| | Same ~4.6 cent octave stretch as 30edt~19edo, but actually equally strongly resembles the scale with generator 2\189 of an octave.

| | [[151edt]]

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| | 151edt is 95edo with a ~3.4 cent compressed octave, but also 191ed4 with a ~5.7 cent stretched 4/1.  

| | [[153edt]]

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| | 153edt falls exactly halfway between 96 and 97 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\193 of an octave.

| | [[154edt]]

| | [[97edo]]

| | 154edt is 97edo with ~2 cent compressed octaves.

| | [[155edt]]

| | [[98edo]]

| | 155edt is 98edo with ~2.5 cent stretched octaves.

| | [[156edt]]

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| | Same ~5.2 cent octave stretch as 78edt~49edo, but actually equally strongly resembles the scale with generator 2\197 of an octave.

| | [[158edt]]

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| | Same ~3.6 cent octave stretch as 79edt~50edo, but actually equally strongly resembles the scale with generator 2\199 of an octave.

| | [[159edt]]

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| | 159edt is 100edo with a ~3.8 cent compressed octave, but also 201ed4 with a ~4.4 cent stretched 4/1.