EDT: Difference between revisions
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| | [[9edt]] | | | [[9edt]] | ||
| | | | | | ||
| rowspan="2"| Neither 9edt nor 10edt is equivalent to [[6edo]]. | | rowspan="2" | Neither 9edt nor 10edt is equivalent to [[6edo]]. | ||
|- | |- | ||
| | [[10edt]] | | | [[10edt]] | ||
| Line 445: | Line 445: | ||
| | [[17edt]] | | | [[17edt]] | ||
| | | | | | ||
| rowspan="2"| Neither 17edt nor 18edt is equivalent to [[11edo]]. | | rowspan="2" | Neither 17edt nor 18edt is equivalent to [[11edo]]. | ||
|- | |- | ||
| | [[18edt]] | | | [[18edt]] | ||
| Line 456: | Line 456: | ||
| | [[20edt]] | | | [[20edt]] | ||
| | | | | | ||
| rowspan="2"| Neither 20edt nor 21edt is equivalent to [[13edo]]. | | rowspan="2" | Neither 20edt nor 21edt is equivalent to [[13edo]]. | ||
|- | |- | ||
| | [[21edt]] | | | [[21edt]] | ||
| Line 487: | Line 487: | ||
| | [[28edt]] | | | [[28edt]] | ||
| | | | | | ||
| rowspan="2"| Neither 28edt nor 29edt is equivalent to [[18edo]]. | | rowspan="2" | Neither 28edt nor 29edt is equivalent to [[18edo]]. | ||
|- | |- | ||
| | [[29edt]] | | | [[29edt]] | ||
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| | [[36edt]] | | | [[36edt]] | ||
| | | | | | ||
| rowspan="2"| Neither 36edt nor 37edt is equivalent to [[23edo]]. | | rowspan="2" | Neither 36edt nor 37edt is equivalent to [[23edo]]. | ||
|- | |- | ||
| | [[37edt]] | | | [[37edt]] | ||
| Line 529: | Line 529: | ||
| | [[39edt]] | | | [[39edt]] | ||
| | | | | | ||
| rowspan="2"| Neither 39edt (Triple BP scale) nor 40edt is equivalent to [[25edo]]. | | rowspan="2" | Neither 39edt (Triple BP scale) nor 40edt is equivalent to [[25edo]]. | ||
|- | |- | ||
| | [[40edt]] | | | [[40edt]] | ||
| Line 548: | Line 548: | ||
| | [[44edt]] | | | [[44edt]] | ||
| | | | | | ||
| rowspan="2"| Neither 44edt nor 45edt is equivalent to [[28edo]]. | | rowspan="2" | Neither 44edt nor 45edt is equivalent to [[28edo]]. | ||
|- | |- | ||
| | [[45edt]] | | | [[45edt]] | ||
| Line 559: | Line 559: | ||
| | [[47edt]] | | | [[47edt]] | ||
| | | | | | ||
| rowspan="2"| Neither 47edt nor 48edt is equivalent to [[30edo]]. | | rowspan="2" | Neither 47edt nor 48edt is equivalent to [[30edo]]. | ||
|- | |- | ||
| | [[48edt]] | | | [[48edt]] | ||
| Line 567: | Line 567: | ||
| | [[31edo]] | | | [[31edo]] | ||
| | 49edt is 31edo with ~3.3 cent stretched octaves. Patent vals match through the 11-limit. | | | 49edt is 31edo with ~3.3 cent stretched octaves. Patent vals match through the 11-limit. | ||
|- | |||
|[[50edt]] | |||
| | |||
|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]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[54edt]] | | | [[54edt]] | ||
| | [[34edo]] | | | [[34edo]] | ||
| | Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 17-limit, with the exception of 7. | | | Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 17-limit, with the exception of 7. | ||
|- | |||
|[[55edt]] | |||
| | |||
| rowspan="2" |Neither 55edt nor 56edt is equivalent to [[35edo]] | |||
|- | |||
|56edt | |||
| | |||
|- | |- | ||
| | [[57edt]] | | | [[57edt]] | ||
| | [[36edo]] | | | [[36edo]] | ||
| | Same ~1.2 cent octave stretch as 19edt~12edo. Patent vals match through the 31-limit, with the exception of 11. | | | Same ~1.2 cent octave stretch as 19edt~12edo. Patent vals match through the 31-limit, with the exception of 11. | ||
|- | |||
|[[58edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[60edt]] | | | [[60edt]] | ||
| | [[38edo]] | | | [[38edo]] | ||
| | Same ~4.6 cent octave stretch as 30edt~19edo. Patent vals match through the 5-limit. | | | Same ~4.6 cent octave stretch as 30edt~19edo. Patent vals match through the 5-limit. | ||
|- | |||
|[[61edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[62edt]] | | | [[62edt]] | ||
| | [[39edo]] | | | [[39edo]] | ||
| | 62edt is 39edo with ~3.6 cent compressed octaves. Patent vals match through the 5-limit. | | | 62edt is 39edo with ~3.6 cent compressed octaves. Patent vals match through the 5-limit. | ||
|- | |||
|[[63edt]] | |||
|40edo | |||
|63edt is 40edo with ~7.6 cent stretched octaves. Patent vals match through the 7-limit, with the exception of 5. | |||
|- | |||
|[[64edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[65edt]] | | | [[65edt]] | ||
| | [[41edo]] | | | [[41edo]] | ||
| | 65edt is 41edo with ~0.31 cent compressed octaves. Patent vals match through the 19-limit. | | | 65edt is 41edo with ~0.31 cent compressed octaves. Patent vals match through the 19-limit. | ||
|- | |||
|[[66edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[68edt]] | | | [[68edt]] | ||
| | [[43edo]] | | | [[43edo]] | ||
| | 68edt is 43edo with ~2.7 cent stretched octaves. Patent vals match through the 5-limit. | | | 68edt is 43edo with ~2.7 cent stretched octaves. Patent vals match through the 5-limit. | ||
|- | |||
|[[69edt]] | |||
| | |||
|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]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[73edt]] | | | [[73edt]] | ||
| | [[46edo]] | | | [[46edo]] | ||
| | 73edt is 46edo with ~1.5 cent compressed octaves. Patent vals match through the 17-limit. | | | 73edt is 46edo with ~1.5 cent compressed octaves. Patent vals match through the 17-limit. | ||
|- | |||
|[[74edt]] | |||
| | |||
| rowspan="2" |Neither 74edt nor 75edt is equivalent to [[47edo]]. | |||
|- | |||
|[[75edt]] | |||
| | |||
|- | |- | ||
| | [[76edt]] | | | [[76edt]] | ||
| | [[48edo]] | | | [[48edo]] | ||
| | Same ~1.2 cent octave stretch as 19edt~12edo. Patent vals match through the 11-limit. | | | Same ~1.2 cent octave stretch as 19edt~12edo. Patent vals match through the 11-limit. | ||
|- | |||
|[[77edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[79edt]] | | | [[79edt]] | ||
| | [[50edo]] | | | [[50edo]] | ||
| | 79edt is 50edo with ~3.8 cent stretched octaves. Patent vals match through the 7-limit. | | | 79edt is 50edo with ~3.8 cent stretched octaves. Patent vals match through the 7-limit. | ||
|- | |||
|[[80edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[81edt]] | | | [[81edt]] | ||
| | [[51edo]] | | | [[51edo]] | ||
| | Same ~2.5 cent octave compression as 27edt~17edo, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit. | | | Same ~2.5 cent octave compression as 27edt~17edo, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit. | ||
|- | |||
|[[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]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[84edt]] | | | [[84edt]] | ||
| | [[53edo]] | | | [[53edo]] | ||
| | 84edt is 53edo with ~0.04 cent stretched octaves. Patent vals match through the 61-limit. | | | 84edt is 53edo with ~0.04 cent stretched octaves. Patent vals match through the 61-limit. | ||
|- | |||
|[[85edt]] | |||
| | |||
|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.. | |||
|- | |- | ||
| | [[87edt]] | | | [[87edt]] | ||
| | [[55edo]] | | | [[55edo]] | ||
| | 87edt is 55edo with ~2.4 cent stretched octaves. Patent vals match through the 11-limit, with the exception of 5. | | | 87edt is 55edo with ~2.4 cent stretched octaves. Patent vals match through the 11-limit, with the exception of 5. | ||
|- | |||
|[[88edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[89edt]] | | | [[89edt]] | ||
| | [[56edo]] | | | [[56edo]] | ||
| | 89edt is 56edo with ~3.3 cent compressed octaves. Patent vals match through the 5-limit. | | | 89edt is 56edo with ~3.3 cent compressed octaves. Patent vals match through the 5-limit. | ||
|- | |||
|[[90edt]] | |||
|[[57edo]] | |||
|Same ~4.6 cent octave stretch as 30edt~19edo. Patent vals match through the 5-limit. | |||
|- | |||
|[[91edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[92edt]] | | | [[92edt]] | ||
| | [[58edo]] | | | [[58edo]] | ||
| | Same ~0.94 cent octave compression as 46edt~29edo. Patent vals match through the 17-limit. | | | Same ~0.94 cent octave compression as 46edt~29edo. Patent vals match through the 17-limit. | ||
|- | |||
|[[93edt]] | |||
| | |||
| rowspan="2" |Neither 93edt nor 94edt is equivalent to [[59edo]]. | |||
|- | |||
|[[94edt]] | |||
| | |||
|- | |- | ||
| | [[95edt]] | | | [[95edt]] | ||
| | [[60edo]] | | | [[60edo]] | ||
| | Same ~1.2 cent octave stretch as 19edt~12edo. Patent vals match through the 7-limit. | | | Same ~1.2 cent octave stretch as 19edt~12edo. Patent vals match through the 7-limit. | ||
|- | |||
|[[96edt]] | |||
| | |||
|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]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[100edt]] | | | [[100edt]] | ||
| | [[63edo]] | | | [[63edo]] | ||
| | 100edt is 63edo with ~1.8 cent compressed octaves. Patent vals match through the 23-limit. | | | 100edt is 63edo with ~1.8 cent compressed octaves. Patent vals match through the 23-limit. | ||
|- | |||
|[[101edt]] | |||
| | |||
| rowspan="2" |Neither 101edt nor 102edt is equivalent to [[64edo]]. | |||
|- | |||
|[[102edt]] | |||
| | |||
|- | |- | ||
| | [[103edt]] | | | [[103edt]] | ||
| | [[65edo]] | | | [[65edo]] | ||
| | 103edt is 65edo with ~2.4 cent stretched octaves. Patent vals match through the 181-limit, with the exception of 13. | | | 103edt is 65edo with ~2.4 cent stretched octaves. Patent vals match through the 181-limit, with the exception of 13. | ||
|- | |||
|[[104edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[106edt]] | | | [[106edt]] | ||
| | [[67edo]] | | | [[67edo]] | ||
| | 106edt is 67edo with ~2.2 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. | | | 106edt is 67edo with ~2.2 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. | ||
|- | |||
|[[107edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[108edt]] | | | [[108edt]] | ||
| | [[68edo]] | | | [[68edo]] | ||
| | Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 7-limit. | | | Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 7-limit. | ||
|- | |||
|[[109edt]] | |||
|69edo | |||
|109edt is 69edo with ~4 cent stretched octaves. Patent vals match through the 5-limit. | |||
|- | |||
|[[110edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[111edt]] | | | [[111edt]] | ||
| | [[70edo]] | | | [[70edo]] | ||
| | 111edt is 70edo with ~0.57 cent compressed octaves. Patent vals match through the 67-limit. | | | 111edt is 70edo with ~0.57 cent compressed octaves. Patent vals match through the 67-limit. | ||
|- | |||
|[[112edt]] | |||
| | |||
| rowspan="2" |Neither 112edt nor 113edt is equivalent to 71edo. | |||
|- | |||
|[[113edt]] | |||
| | |||
|- | |- | ||
| | [[114edt]] | | | [[114edt]] | ||
| | [[72edo]] | | | [[72edo]] | ||
| | Same ~1.2 cent octave stretch as 19edt~12edo. Patent vals match through the 19-limit. | | | Same ~1.2 cent octave stretch as 19edt~12edo. Patent vals match through the 19-limit. | ||
|- | |||
|[[115edt]] | |||
| | |||
|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]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[119edt]] | | | [[119edt]] | ||
| | [[75edo]] | | | [[75edo]] | ||
| | 119edt is 75edo with ~1.3 cent compressed octaves. Patent vals match through the 19-limit, with the exception of 11. | | | 119edt is 75edo with ~1.3 cent compressed octaves. Patent vals match through the 19-limit, with the exception of 11. | ||
|- | |||
|[[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]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[122edt]] | | | [[122edt]] | ||
| | [[77edo]] | | | [[77edo]] | ||
| | 122edt is 77edo with ~0.41 cent stretched octaves. Patent vals match through the 37-limit. | | | 122edt is 77edo with ~0.41 cent stretched octaves. Patent vals match through the 37-limit. | ||
|- | |||
|[[123edt]] | |||
| | |||
|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.. | |||
|- | |- | ||
| | [[125edt]] | | | [[125edt]] | ||
| | [[79edo]] | | | [[79edo]] | ||
| | 125edt is 79edo with ~2.0 cent stretched octaves. Patent vals match through the 13-limit, with the exception of 7. | | | 125edt is 79edo with ~2.0 cent stretched octaves. Patent vals match through the 13-limit, with the exception of 7. | ||
|- | |||
|[[126edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[127edt]] | | | [[127edt]] | ||
| | [[80edo]] | | | [[80edo]] | ||
| | 127edt is 80edo with ~1.9 cent compressed octaves. Patent vals match through the 11-limit. | | | 127edt is 80edo with ~1.9 cent compressed octaves. Patent vals match through the 11-limit. | ||
|- | |||
|[[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]] | |||
| | |||
|Same ~5.7 cent octave compression as 43edt~27edo, but actually more strongly resembles the scale with generator 2\163 of an octave. | |||
|- | |- | ||
| | [[130edt]] | | | [[130edt]] | ||
| | [[82edo]] | | | [[82edo]] | ||
| | Same ~0.31 cent octave compression as 65edt~41edo. | | | Same ~0.31 cent octave compression as 65edt~41edo. | ||
|- | |||
|[[131edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[133edt]] | | | [[133edt]] | ||
| | [[84edo]] | | | [[84edo]] | ||
| | Same ~1.2 cent octave stretch as 19edt~12edo. | | | Same ~1.2 cent octave stretch as 19edt~12edo. | ||
|- | |||
|[[134edt]] | |||
| | |||
|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]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[138edt]] | | | [[138edt]] | ||
| | [[87edo]] | | | [[87edo]] | ||
| | Same ~0.94 cent octave compression as 46edt~29edo. | | | Same ~0.94 cent octave compression as 46edt~29edo. | ||
|- | |||
|[[139edt]] | |||
| | |||
|139edt is 88edo with a ~4.1 cent stretched octave, but also 175ed4 with a ~5.55 cent compressed 4/1. | |||
|- | |||
|[[140edt]] | |||
| | |||
|Same ~4.5 cent octave compression as 35edt~22edo, but actually equally strongly resembles the scale with generator 2\177 of an octave. | |||
|- | |- | ||
| | [[141edt]] | | | [[141edt]] | ||
| | [[89edo]] | | | [[89edo]] | ||
| | 141edt is 89edo with ~0.52 cent stretched octaves. | | | 141edt is 89edo with ~0.52 cent stretched octaves. | ||
|- | |||
|[[142edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[144edt]] | | | [[144edt]] | ||
| | [[91edo]] | | | [[91edo]] | ||
| | 144edt is 91edo with ~1.9 cent stretched octaves. | | | 144edt is 91edo with ~1.9 cent stretched octaves. | ||
|- | |||
|[[145edt]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[146edt]] | | | [[146edt]] | ||
| | [[92edo]] | | | [[92edo]] | ||
| | Same ~1.5 cent octave compression as 73edt~46edo. | | | Same ~1.5 cent octave compression as 73edt~46edo. | ||
|- | |||
|[[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]] | |||
| | |||
|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. | |||
|- | |- | ||
| | [[149edt]] | | | [[149edt]] | ||
| | [[94edo]] | | | [[94edo]] | ||
| | 149edt is 94edo with ~0.11 cent compressed octaves. | | | 149edt is 94edo with ~0.11 cent compressed octaves. | ||
|- | |||
|[[150edt]] | |||
| | |||
|Same ~4.6 cent octave stretch as 30edt~19edo, but actually equally strongly resembles the scale with generator 2\189 of an octave. | |||
|- | |||
|[[151edt]] | |||
| | |||
|151edt is 95edo with a ~3.4 cent compressed octave, but also 191ed4 with a ~5.7 cent stretched 4/1. | |||
|- | |- | ||
| | [[152edt]] | | | [[152edt]] | ||
| | [[96edo]] | | | [[96edo]] | ||
| | Same ~1.2 cent octave stretch as 19edt~12edo. | | | Same ~1.2 cent octave stretch as 19edt~12edo. | ||
|- | |||
|[[153edt]] | |||
| | |||
|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 97edo with ~2.5 cent stretched octaves. | |||
|- | |||
|[[156edt]] | |||
| | |||
|Same ~5.2 cent octave stretch as 78edt~49edo, but actually equally strongly resembles the scale with generator 2\197 of an octave. | |||
|- | |- | ||
| | [[157edt]] | | | [[157edt]] | ||
| | [[99edo]] | | | [[99edo]] | ||
| | 157edt is 99edo with ~0.68 cent compressed octaves. | | | 157edt is 99edo with ~0.68 cent compressed octaves. | ||
|- | |||
|[[158edt]] | |||
| | |||
|Same ~3.6 cent octave stretch as 79edt~50edo, but actually equally strongly resembles the scale with generator 2\199 of an octave. | |||
|- | |||
|[[159edt]] | |||
| | |||
|159edt is 100edo with a ~3.8 cent compressed octave, but also 201ed4 with a ~4.4 cent stretched 4/1. | |||
|- | |- | ||
| | [[160edt]] | | | [[160edt]] | ||
| Line 782: | Line 1,081: | ||
=Multiples of 13EDT which approximate EDO= | =Multiples of 13EDT which approximate EDO= | ||
Also, on the topic of multiples of 13edt, 26 (double) and 39 (triple) offer very good harmonic approximations, the former of the 8th, 13th and 17th partials, and the latter of the 11th and 13th. However, quadruple | Also, on the topic of multiples of 13edt, 26 (double) and 39 (triple) offer very good harmonic approximations, the former of the 8th, 13th and 17th partials, and the latter of the 11th and 13th. However, quadruple through sextuple, ie. 52, 65 and 78edt, also exist offering good approximations of the octave. 52edt is very nearly [[33edo]], 65edt is practically identical to [[41edo]] and 78edt is very nearly 49edo. | ||
=See also= | =See also= | ||
| Line 788: | Line 1,087: | ||
* [[Consistency levels of small EDTs]] | * [[Consistency levels of small EDTs]] | ||
* [[Tritave Reduced Harmonics]] | * [[Tritave Reduced Harmonics]] | ||
* Heinz Bohlen's work: http://www.huygens-fokker.org/bpsite/otherscales.html | * Heinz Bohlen's work: http://www.huygens-fokker.org/bpsite/otherscales.html [[Category:Edt| ]] <!-- main article --> | ||
[[Category:Edt| ]] <!-- main article --> | |||
[[Category:3/1]] | [[Category:3/1]] | ||
[[category:nonoctave]] | [[category:nonoctave]] | ||