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.-

Table of first highly melodic EDF-EDO correspondences

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

Possible usage in Georgian (Kartvelian) music

Since Kartvelian scales are created by dividing the perfect fifth into an arbitrary number of steps, and complementing that with dividing 4/3 into an arbitrary number of steps, EDOs which correspond to highly melodic EDFs have a high density of such scales per their size.