Highly melodic EDF
Highly Melodic EDFs are equal division scales with a superabundant or a highly composite number of pitches in a perfect fifth (3/2).
Unlike highly melodic EDOs, whose harmonic content tends to be random and usually contorted, highly melodic EDFs often correspond to a useful EDO.
Highly melodic EDF-EDO correspondence
The following is a table of first 19 highly melodic EDFs and their corresponding EDOs, since first 19 superabundant and highly composite numbers are the same.-
| EDF | EDO | log2/log1.5*EDF
(exact EDO) |
Comments |
|---|---|---|---|
| 1 | 2 | 1.7095112 | Trivial |
| 2 | 3 | 3.4190226 | Completely misses the octave. |
| 4 | 7 | 6.8380452 | |
| 6 | 10 | 10.257068 | 10edo, but with a heavy stretch |
| 12 | - | 20.514135 | Completely misses the octave |
| 24 | 41 | 41.028271 | 24edf is equivalent to 41edo. Patent vals match through the 19-limit. |
| 36 | - | 61.542406 | |
| 48 | 82 | 82.056542 | 48edf is equivalent to 82edo. |
| 60 | 103 | 102.57067 | Surprisingly, it's a match to 103edo despite 60edf falling halfway between 102 and 103. |
| 120 | 205 | 205.14135 | |
| 180 | 308 | 307.71203 | Corresponds to 308edo, but with quite a stretch. |
| 240 | 410 | 410.28271 | |
| 360 | - | 615.42406 | Falls halfway between 615 and 616edo. Also, one step is quite close to the schisma. |
| 720 | 1231 | 1230.8481 | |
| 840 | 1436 | 1435.9895 | |
| 1260 | 2154 | 2153.9842 | |
| 1680 | 2872 | 2871.9789 | |
| 2520 | 4308 | 4397.9685 | |
| 5040 | 8616 | 8615.9369 |