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| | [[55edt]]
| | [[55edt]]
| |  
| |  
| rowspan="2"| Neither 55edt nor 56edt is equivalent to [[35edo]].
| rowspan="2" | Neither 55edt nor 56edt is equivalent to [[35edo]].
|-
|-
| | [[56edt]]
| | [[56edt]]
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| | [[74edt]]
| | [[74edt]]
| |  
| |  
| rowspan="2"| Neither 74edt nor 75edt is equivalent to [[47edo]].  
| rowspan="2" | Neither 74edt nor 75edt is equivalent to [[47edo]].  
|-
|-
| | [[75edt]]
| | [[75edt]]
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| | [[93edt]]
| | [[93edt]]
| |  
| |  
| rowspan="2"| Neither 93edt nor 94edt is equivalent to [[59edo]].
| rowspan="2" | Neither 93edt nor 94edt is equivalent to [[59edo]].
|-
|-
| | [[94edt]]
| | [[94edt]]
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| | [[101edt]]
| | [[101edt]]
| |  
| |  
| rowspan="2"| Neither 101edt nor 102edt is equivalent to [[64edo]].
| rowspan="2" | Neither 101edt nor 102edt is equivalent to [[64edo]].
|-
|-
| | [[102edt]]
| | [[102edt]]
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| | [[112edt]]
| | [[112edt]]
| |  
| |  
| rowspan="2"| Neither 112edt nor 113edt is equivalent to 71edo.
| rowspan="2" | Neither 112edt nor 113edt is equivalent to 71edo.
|-
|-
| | [[113edt]]
| | [[113edt]]
Line 1,006: Line 1,006:
| | [[101edo]]
| | [[101edo]]
| | 160edt is 101edo with ~0.61 cent stretched octaves.
| | 160edt is 101edo with ~0.61 cent stretched octaves.
|-
|[[161edt]]
|
|161edt falls exactly halfway between 101 and 102 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\203 of an octave.
|-
|[[162edt]]
|[[102edo]]
|Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 5-limit.
|-
|[[163edt]]
|[[103edo]]
|163edt is 103edo with ~1.85 cent stretched octaves
|-
|[[164edt]]
|
|Same ~6.1 cent octave stretch as 41edt~26edo, but actually more strongly resembles the scale with generator 2\207 of an octave.
|-
|-
| | [[165edt]]
| | [[165edt]]
| | [[104edo]]
| | [[104edo]]
| | 165edt is 104edo with ~1.2 cent compressed octaves.
| | 165edt is 104edo with ~1.2 cent compressed octaves.
|-
|[[166edt]]
|[[105edo]]
|166edt is 105edo with ~3 cent stretched octaves.
|-
|[[167edt]]
|
|167edt falls exactly halfway between 105 and 106 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\211 of an octave.
|-
|-
| | [[168edt]]
| | [[168edt]]
| | [[106edo]]
| | [[106edo]]
| | Same ~0.04 cent octave stretch as 84edt~53edo.
| | Same ~0.04 cent octave stretch as 84edt~53edo.
|-
|[[169edt]]
|
|169edt falls exactly halfway between 106 and 107 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\213 of an octave.
|-
|[[170edt]]
|[[107edo]]
|170edt is 107edo with ~2.9 cent compressed octaves.
|-
|-
| | [[171edt]]
| | [[171edt]]
| | [[108edo]]
| | [[108edo]]
| | Same ~1.2 cent octave stretch as 19edt~12edo.
| | Same ~1.2 cent octave stretch as 19edt~12edo.
|-
|[[172edt]]
|
|172edt falls exactly halfway between 108 and 109 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\217 of an octave.
|-
|-
| | [[173edt]]
| | [[173edt]]
| | [[109edo]]
| | [[109edo]]
| | 173edt is 109edo with ~1.7 cent compressed octaves.
| | 173edt is 109edo with ~1.7 cent compressed octaves.
|-
|[[174edt]]
|[[110edo]]
|174edt is 110edo with ~2.4 cent stretched octaves.
|-
|[[175edt]]
|
|Same ~4.5 cent octave compression as 35edt~22edo, but actually more strongly resembles the scale with generator 2\221 of an octave.
|-
|-
| | [[176edt]]
| | [[176edt]]
| | [[111edo]]
| | [[111edo]]
| | 176edt is 111edo with ~0.47 cent compressed octaves.
| | 176edt is 111edo with ~0.47 cent compressed octaves.
|-
|[[177edt]]
|
|177edt is 112edo with a ~3.5 cent compressed octave, but also 223ed4 with a ~3.75 cent compressed 4/1.
|-
|[[178edt]]
|
|Same ~3.3 cent octave stretch as 89edt~56edo, but actually more strongly resembles the scale with generator 2\225 of an octave.
|-
|-
| | [[179edt]]
| | [[179edt]]
| | [[113edo]]
| | [[113edo]]
| | 179edt is 113edo with ~0.68 cent stretched octaves.
| | 179edt is 113edo with ~0.68 cent stretched octaves.
|-
|[[180edt]]
|
|Same ~4.6 cent octave stretch as 30edt~19edo, but actually more strongly resembles the scale with generator 2\227 of an octave.
|-
|[[181edt]]
|[[114edo]]
|181edt is 114edo with ~2.1 cent compressed octaves
|-
|[[182edt]]
|[[115edo]]
|182edt is 115edo with ~1.8 cent stretched octaves
|-
|[[183edt]]
|
|183edt falls exactly halfway between 115 and 116 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\231 of an octave.
|-
|-
| | [[184edt]]
| | [[184edt]]
| | [[116edo]]
| | [[116edo]]
| | Same ~0.94 cent octave compression as 46edt~29edo.
| | Same ~0.94 cent octave compression as 46edt~29edo.
|-
|[[185edt]]
|[[117edo]]
|185edt is 117edo with a ~2.9 cent stretched octave.
|-
|[[186edt]]
|
|Same ~3.6 cent octave compression as 62edt~39edo, but actually more strongly resembles the scale with generator 2\235 of an octave.
|-
|-
| | [[187edt]]
| | [[187edt]]
| | [[118edo]]
| | [[118edo]]
| | 187edt is 118edo with ~0.16 cent stretched octaves.
| | 187edt is 118edo with ~0.16 cent stretched octaves.
|-
|[[188edt]]
|
|188edt is 119edo with ~3.9 cent stretched octaves, but also 237ed4 with an ~2.3 cent compressed 4/1.
|-
|[[189edt]]
|[[119edo]]
|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.
|-
|-
| | [[190edt]]
| | [[190edt]]
| | [[120edo]]
| | [[120edo]]
| | Same ~1.2 cent octave stretch as 19edt~12edo.
| | Same ~1.2 cent octave stretch as 19edt~12edo.
|-
|[[191edt]]
|
|191edt falls exactly halfway between 120 and 121 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\241 of an octave.
|-
|-
| | [[192edt]]
| | [[192edt]]
| | [[121edo]]
| | [[121edo]]
| | 192edt is 121edo with ~1.4 cent compressed octaves.
| | 192edt is 121edo with ~1.4 cent compressed octaves.
|-
|[[193edt]]
|[[122edo]]
|193edt is 122edo with ~2.3 cent stretched octaves.
|-
|[[194edt]]
|
|Same ~3.9 cent octave compression as 97edt~61edo, but actually more strongly resembles the scale with generator 2\245 of an octave.
|-
|-
| | [[195edt]]
| | [[195edt]]
| | [[123edo]]
| | [[123edo]]
| | Same ~0.31 cent octave compression as 65edt~41edo.
| | Same ~0.31 cent octave compression as 65edt~41edo.
|-
|[[196edt]]
|
|Same ~3.3 cent octave compression as 49edt~31edo, but actually more strongly resembles the scale with generator 2\247 of an octave.
|-
|[[197edt]]
|
|197edt is 124edo with a ~2.9 cent compressed octave, but also 249ed4 with a ~4 cent stretched 4/1.
|-
|-
| | [[198edt]]
| | [[198edt]]
| | [[125edo]]
| | [[125edo]]
| | 198edt is 125edo with ~0.73 cent stretched octaves.
| | 198edt is 125edo with ~0.73 cent stretched octaves.
|-
|[[199edt]]
|
|199edt falls exactly halfway between 125 and 126 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\251 of an octave.
|-
|[[200edt]]
|[[126edo]]
|Same ~1.8 cent octave compression as 100edt~63edo.
|-
|[[201edt]]
|[[127edo]]
|201edt is 127edo with ~1.7 cent compressed octave.
|-
|[[202edt]]
|
|202edt falls exactly halfway between 127 and 128 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\255 of an octave.
|-
|-
| | [[203edt]]
| | [[203edt]]
| | [[128edo]]
| | [[128edo]]
| | 203edt is 128edo with ~0.74 cent compressed octaves.
| | 203edt is 128edo with ~0.74 cent compressed octaves.
|-
|[[204edt]]
|
|Same ~2.7 cent octave stretch as 68edt~43edo, but actually more strongly resembles the scale with generator 2\257 of an octave.
|-
|[[205edt]]
|
|205edt is 129edo with a ~3.2 cent compressed octave, but also 259ed4 with a ~3 cent stretched 4/1.
|-
|-
| | [[206edt]]
| | [[206edt]]
| | [[130edo]]
| | [[130edo]]
| | Same ~2.4 cent octave stretch as 103edt~65edo.
| | Same ~2.4 cent octave stretch as 103edt~65edo.
|-
|[[207edt]]
|
|205edt falls exactly halfway between 130 and 131 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\261 of an octave.
|-
|[[208edt]]
|[[131edo]]
|208edt is 131edo with ~2.1 cent compressed octaves.
|-
|-
| | [[209edt]]
| | [[209edt]]
| | [[132edo]]
| | [[132edo]]
| | Same ~1.2 cent octave stretch as 19edt~12edo.
| | Same ~1.2 cent octave stretch as 19edt~12edo.
|-
|[[210edt]]
|
|210edt falls exactly halfway between 132 and 133 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\265 of an octave.
|-
|-
| | [[211edt]]
| | [[211edt]]
| | [[133edo]]
| | [[133edo]]
| | 211edt is 133edo with ~1.1 cent compressed octaves.
| | 211edt is 133edo with ~1.1 cent compressed octaves.
|-
|[[212edt]]
|[[134edo]]
|Same ~2.2 cent octave stretch as 106edt~67edo, but patent vals surprisingly actually match through the 7-limit, though the 7s nevertheless cannot be said to match with a straight face.
|-
|[[213edt]]
|
|213edt falls exactly halfway between 134 and 135 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\269 of an octave.
|-
|-
| | [[214edt]]
| | [[214edt]]
| | [[135edo]]
| | [[135edo]]
| | 214edt is 135edo with ~0.17 cent compressed octaves.
| | 214edt is 135edo with ~0.17 cent compressed octaves.
|-
|[[215edt]]
|
|
|-
|[[216edt]]
|[[136edo]]
|Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 5-limit.
|-
|-
| | [[217edt]]
| | [[217edt]]
Line 1,081: Line 1,237:


=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 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.
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 1,087: Line 1,243:
* [[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 [[Category:Edt| ]] <!-- main article -->
* Heinz Bohlen's work: http://www.huygens-fokker.org/bpsite/otherscales.html   [[Category:Edt| ]] <!-- main article -->
[[Category:3/1]]
[[Category:3/1]]
[[category:nonoctave]]
[[category:nonoctave]]
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