kHierarchizabilityBreakdown PatternDiagram11(110001)(110001)2275k = 1h = 121(110001)(110001)2275k = 2h = 131(110001)(110001)2275k = 3h = 141(110001)(110001)2275k = 4h = 151(110001)(110001)2275k = 5h = 1
Center of Gravity
If tones of the scale are imagined as identical physical objects spaced around a unit circle, the center of gravity is the point where the scale is balanced.
Transformations:
In the abbreviation, the subscript number after “T” is the number of semitones of tranposition, “M” means the pitch class is multiplied by 5, and “I” means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b. A note about the multipliers: multiplying by 1 changes nothing, multiplying by 11 produces the same result as inversion. 5 is the only non-degenerate multiplier, with the multiplier 7 producing the inverse of 5.
Abbrev Operation Result Abbrev Operation Result T0 <1,0> 2275 T0I <11,0> 2275 T1 <1,1> 455 T1I <11,1> 455T2 <1,2> 910 T2I <11,2> 910T3 <1,3> 1820 T3I <11,3> 1820T4 <1,4> 3640 T4I <11,4> 3640T5 <1,5> 3185 T5I <11,5> 3185T6 <1,6> 2275 T6I <11,6> 2275 T7 <1,7> 455 T7I <11,7> 455T8 <1,8> 910 T8I <11,8> 910T9 <1,9> 1820 T9I <11,9> 1820T10 <1,10> 3640 T10I <11,10> 3640T11 <1,11> 3185 T11I <11,11> 3185 Abbrev Operation Result Abbrev Operation Result T0M <5,0> 2275 T0MI <7,0> 2275 T1M <5,1> 455 T1MI <7,1> 455T2M <5,2> 910 T2MI <7,2> 910T3M <5,3> 1820 T3MI <7,3> 1820T4M <5,4> 3640 T4MI <7,4> 3640T5M <5,5> 3185 T5MI <7,5> 3185T6M <5,6> 2275 T6MI <7,6> 2275 T7M <5,7> 455 T7MI <7,7> 455T8M <5,8> 910 T8MI <7,8> 910T9M <5,9> 1820 T9MI <7,9> 1820T10M <5,10> 3640 T10MI <7,10> 3640T11M <5,11> 3185 T11MI <7,11> 3185
The transformations that map this set to itself are: T0, T6, T0I, T6I, T0M, T6M, T0MI, T6MI
Nearby Scales:
These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.
This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by Lilypond, graph visualization by Graphviz, audio by TiMIDIty and FFMPEG. All other diagrams and visualizations are © Ian Ring. Some scale names used on this and other pages were invented by living persons, and used here with permission where required: notably collections of names by William Zeitler, Justin Pecot, Rich Cochrane, and Robert Bedwell.
Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (DOI, Patent owner: Dokuz Eylül University, Used with Permission.
Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy, and George Howlett for assistance with naming the Carnatic ragas. Thanks to Niels Verosky for collaborating on the Hierarchizability diagrams. Gratitudes to Qid Love for the Xenomes. Thanks to B P Leonard for the Brightness metrics. Thanks to u/howaboot for inventing the Center of Gravity metrics.
