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