EDF: Difference between revisions
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=Individual pages for EDFs= | =Individual pages for EDFs= | ||
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*[[2edf]] | |||
*[[3edf]] | |||
*[[4edf]] | *[[4edf]] | ||
*[[5edf]] | *[[5edf]] | ||
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*[[58edf]] | *[[58edf]] | ||
*[[59edf]] | *[[59edf]] | ||
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*[[60edf]] | *[[60edf]] | ||
*[[61edf]] | *[[61edf]] | ||
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*[[99edf]] | *[[99edf]] | ||
*[[100edf]] | *[[100edf]] | ||
*[[101edf]] | |||
*[[102edf]] | |||
*[[103edf]] | |||
*[[104edf]] | |||
*[[105edf]] | |||
*[[106edf]] | |||
*[[107edf]] | |||
*[[108edf]] | |||
*[[109edf]] | |||
*[[110edf]] | |||
*[[111edf]] | |||
*[[112edf]] | |||
*[[113edf]] | |||
*[[114edf]] | |||
*[[115edf]] | |||
*[[116edf]] | |||
*[[117edf]] | |||
</div><div style="float:left; vertical-align:top"> | |||
*[[118edf]] | |||
*[[119edf]] | |||
*[[120edf]] | |||
*[[121edf]] | |||
*[[122edf]] | |||
*[[123edf]] | |||
*[[124edf]] | |||
*[[125edf]] | |||
*[[126edf]] | |||
*[[127edf]] | |||
*[[128edf]] | |||
*[[129edf]] | |||
*[[130edf]] | |||
*[[131edf]] | |||
*[[132edf]] | |||
*[[133edf]] | |||
*[[134edf]] | |||
*[[135edf]] | |||
*[[136edf]] | |||
*[[137edf]] | |||
*[[138edf]] | |||
*[[139edf]] | |||
*[[140edf]] | |||
*[[141edf]] | |||
*[[142edf]] | |||
*[[143edf]] | |||
*[[144edf]] | |||
*[[145edf]] | |||
*[[146edf]] | |||
*[[147edf]] | |||
*[[148edf]] | |||
*[[149edf]] | |||
*[[150edf]] | |||
*[[151edf]] | |||
*[[152edf]] | |||
*[[153edf]] | |||
*[[154edf]] | |||
*[[155edf]] | |||
*[[156edf]] | |||
*[[157edf]] | |||
*[[158edf]] | |||
*[[159edf]] | |||
*[[160edf]] | |||
*[[161edf]] | |||
*[[162edf]] | |||
*[[163edf]] | |||
*[[164edf]] | |||
*[[165edf]] | |||
*[[166edf]] | |||
*[[167edf]] | |||
*[[168edf]] | |||
*[[169edf]] | |||
*[[170edf]] | |||
*[[171edf]] | |||
*[[172edf]] | |||
*[[173edf]] | |||
*[[174edf]] | |||
*[[175edf]] | |||
</div> | |||
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=EDF-EDO correspondence= | =EDF-EDO correspondence= | ||
Revision as of 16:43, 5 February 2019
EDF or Ed3/2 means Division of the Perfect Fifth (3/2) into n equal parts.
Division of the perfect fifth (3/2) into n equal parts
Division of the 3:2 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 3:2 as a base though, is apparent by being one of the strongest consonances after the octave. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
Perhaps the first to divide the perfect fifth was Wendy Carlos ( http://www.wendycarlos.com/resources/pitch.html). Carlo Serafini has also made much use of the alpha, beta and gamma scales.
Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it if it hasn't been named yet, but in any case here is an example of it.
Individual pages for EDFs
- 2edf
- 3edf
- 4edf
- 5edf
- 6edf
- 7edf
- 8edf
- 9edf (Carlos Alpha)
- 10edf
- 11edf (Carlos Beta)
- 12edf
- 13edf
- 14edf
- 15edf
- 16edf
- 17edf
- 18edf
- 19edf
- 20edf (Carlos Gamma)
- 21edf
- 22edf
- 23edf
- 24edf
- 25edf
- 26edf
- 27edf
- 28edf
- 29edf
- 30edf
- 31edf
- 32edf
- 33edf
- 34edf
- 35edf
- 36edf
- 37edf
- 38edf
- 39edf
- 40edf
- 41edf
- 42edf
- 43edf
- 44edf
- 45edf
- 46edf
- 47edf
- 48edf
- 49edf
- 50edf
- 51edf
- 52edf
- 53edf
- 54edf
- 55edf
- 56edf
- 57edf
- 58edf
- 59edf
- 60edf
- 61edf
- 62edf
- 63edf
- 64edf
- 65edf
- 66edf
- 67edf
- 68edf
- 69edf
- 70edf
- 71edf
- 72edf
- 73edf
- 74edf
- 75edf
- 76edf
- 77edf
- 78edf
- 79edf
- 80edf
- 81edf
- 82edf
- 83edf
- 84edf
- 85edf
- 86edf
- 87edf
- 88edf
- 89edf
- 90edf
- 91edf
- 92edf
- 93edf
- 94edf
- 95edf
- 96edf
- 97edf
- 98edf
- 99edf
- 100edf
- 101edf
- 102edf
- 103edf
- 104edf
- 105edf
- 106edf
- 107edf
- 108edf
- 109edf
- 110edf
- 111edf
- 112edf
- 113edf
- 114edf
- 115edf
- 116edf
- 117edf
- 118edf
- 119edf
- 120edf
- 121edf
- 122edf
- 123edf
- 124edf
- 125edf
- 126edf
- 127edf
- 128edf
- 129edf
- 130edf
- 131edf
- 132edf
- 133edf
- 134edf
- 135edf
- 136edf
- 137edf
- 138edf
- 139edf
- 140edf
- 141edf
- 142edf
- 143edf
- 144edf
- 145edf
- 146edf
- 147edf
- 148edf
- 149edf
- 150edf
- 151edf
- 152edf
- 153edf
- 154edf
- 155edf
- 156edf
- 157edf
- 158edf
- 159edf
- 160edf
- 161edf
- 162edf
- 163edf
- 164edf
- 165edf
- 166edf
- 167edf
- 168edf
- 169edf
- 170edf
- 171edf
- 172edf
- 173edf
- 174edf
- 175edf
EDF-EDO correspondence
| EDF | EDO | Comments |
|---|---|---|
| 4edf | 7edo | 4edf is 7edo with 28.5 cent stretched octaves. Equivalently, 7edo is 4edf with 3/2s compressed by ~16 cents. Patent vals match through the 5 limit. Only a rough correspondence. |
| 5edf | 9edo | Very rough correspondence - patent vals disagree in the 5 limit. |
| 6edf | 10edo | Also very rough. |
| 7edf | 12edo | 7edf is 12edo with 3.4 cent stretched octaves. Equivalently, 12edo is 7edf with 2.0 cent compressed 3/2s. With the exception of 11 (which falls almost exactly halfway between steps in both cases), the patent vals match through the 31 limit, so the agreement is excellent. |
| 8edf | Since 88cET/octacot is well known to approximate some intervals quite accurately, it would be wrong to lump this in with 14edo. | |
| 9edf | The Carlos alpha scale is neither 15edo nor 16edo. | |
| 10edf | 17edo | 10edf is 17edo with 6.6 cent compressed octaves. Patent vals match through the 13 limit, with the exception of 5 (as expected). |
| 11edf | 19edo | 11edf is 19edo with 12.5 cent stretched octaves. Patent vals match through the 7 limit. If you don't think Carlos beta is accurately represented by 19edo then ignore this correspondence. |
| 12edf | 12edf entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\41 of an octave. | |
| 13edf | Perhaps surprisingly, this is not very similar to 22edo. Patent vals differ in the 5 limit. | |
| 14edf | 24edo | Same 3.4 cent octave stretch as 7edf~12edo. Patent vals agree through the 19 limit. |
| 15edf | 26edo | Fairly rough correspondence. 15edf is 26edo with ~17 cent stretched octaves. Patent vals agree through the 5 limit, but not through the 7 limit. |
| 16edf | ||
| 17edf | 29edo | 17edf is 29edo with 2.5 cent compressed octaves. Patent vals disagree in the 7 limit. |
| 18edf | Perhaps surprisingly, this is not very similar to 31edo. Patent vals differ in the 5 limit. | |
| 19edf | ||
| 20edf | 34edo | Same 6.6 cent octave compression as 10edf~17edo. Patent vals match through the 5 limit, but not the 7 limit. If you don't think Carlos gamma is accurately represented by 34edo then ignore this correspondence. |
| 21edf | 36edo | Same 3.4 cent octave stretch as 7edf~12edo. Patent vals differ in the 5 limit. |
| 22edf | 38edo | Only rough correspondence. Patent vals differ in the 5 limit. |
| 23edf | 39edo | Only rough correspondence. 23edf is 39edo with ~9.7 cent compressed octaves. Patent vals differ in the 7-limit. |
| 24edf | 41edo | 24edf is 41edo with 0.83 cent compressed octaves. Patent vals match through the 19 limit. |
| 25edf | 43edo | 25edf is 43edo with 7.4 cent stretched octaves, but a rough correspondence. Patent vals differ in the 5 limit. |
| 27edf | 46edo | 27edf is 46edo with 4.1 cent compressed octaves. Patent vals match through the 5 limit, but not the 7 limit. |
| 28edf | 48edo | Same 3.4 cent octave stretch as 7edf~12edo. Patent vals match through the 5 limit, but not the 7 limit. |
| 31edf | 53edo | 31edf is 53edo with 0.12 cent stretched octaves. Patent vals match through the 61 limit. |
| 34edf | 58edo | Same 2.5 cent octave compression as 17edf~29edo. Patent vals match through the 13 limit. |
| 35edf | 60edo | Same 3.4 cent octave stretch as 7edf~12edo. Patent vals match through the 7 limit. |
| 38edf | 65edo | 38edf is 65edo with 0.71 cent stretched octaves. Patent vals match through the 11 limit. |
| 41edf | 70edo | 41edf is 70edo with 1.5 cent compressed octaves. Patent vals match through the 17 limit. |
| 42edf | 72edo | This is a rough correspondence, as the (7n)edf ~ (12n)edo sequence begins to break down. Patent vals match through the 7 limit. |
| 45edf | 77edo | 45edf is 77edo with 1.1 cent stretched octaves. Patent vals match through the 13 limit. |
| 48edf | 82edo | Same 0.83 cent octave compression as 24edf~41edo. Patent vals match through the 11 limit, with the exception of 5. |
| 51edf | 87edo | Same 2.5 cent octave compression as 17edf~29edo. Patent vals match through the 5 limit, but not the 7 limit. |
| 52edf | 89edo | 52edf is 89edo with 1.4 cent stretched octaves. Patent vals match through the 13 limit, with the exception of 5. |
| 55edf | 94edo | 55edf is 94edo with 0.3 cent compressed octaves. Patent vals match through the 47 limit. |
| 58edf | 99edo | 58edf is 99edo with 1.8 cent compressed octaves. Patent vals match through the 7 limit. |