Volume 2: The Scales 7
Scale 7
Tritonic Chromatic
Also known as: ABOian
Analysis Modes
Cardinality 3 (tritonic) Scale 7: Tritonic Chromatic
Pitch Class Set
Interval Structure
{0,1,2}
[1,1,10]
1.
Forte Number 3-1
Generator 1 Scale 2051: Tritonic Chromatic 2
Rotational Symmetry
Reflection Axes
none
[1]
2.
Ridge Tones [2]
Palindromicity no Scale 3073: Tritonic Chromatic Descending
Chirality no 3.
Hemitonia 2 (dihemitonic)
Cohemitonia 1 (uncohemitonic)
Imperfections 3
Prime Form 7
Tonnetz Diagram
Deep Scale no
Interval Vector <2,1,0,0,0,0>
Distribution Spectra <1> = {1,10}
<2> = {2,11}
Spectra Variation 6
Saturation Vector <1,0.5,0,0,0,0>
Maximal Evenness no
Interior Area 0.067
Polygon Perimeter 2.035
Myhill Property yes
Center of Gravity Distance 0.911
Propriety Improper
Coherence Quotient 0
Sameness Quotient 0.333
Heteromorphic Profile (1,0,4)
Hierarchizability (k = 2) 1
Hierarchizability (k = 4) 2
Maximal Area no
Hierarchizability Diagrams Interval Matrix
The "scale" so sparse and clustered that you would barely call it a scale. And indeed, it would fail many of the common criteria
used to elevate a Scale from being a mere Pitch Class Set. This one has the dubious distinction of being the prime scale with the
smallest non-zero polygonal interior area.
Ian Ring: An Exhausting Yet Necessarily Incomplete Study Of The Properties Of Musical Scales, Volume 2 © 2022
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