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Cardinality | 6 (hexatonic) |
---|---|
Pitch Class Set | {0,2,3,5,10,11} |
Forte Number | 6-Z11 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 1671 |
Hemitonia | 3 (trihemitonic) |
Cohemitonia | 1 (uncohemitonic) |
Imperfections | 3 |
Modes | 5 |
Prime? | no prime: 183 |
Deep Scale | no |
Interval Vector | 333231 |
Interval Spectrum | p3m2n3s3d3t |
Distribution Spectra | <1> = {1,2,5} <2> = {2,3,6,7} <3> = {4,5,7,8} <4> = {5,6,9,10} <5> = {7,10,11} |
Spectra Variation | 3.667 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 1.866 |
Myhill Property | no |
Balanced | no |
Ridge Tones | none |
Propriety | Improper |
Heliotonic | no |
These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.
* Pitches are shown with C as the root
Triad Type | Triad* | Pitch Classes | Degree | Eccentricity | Closeness Centrality |
---|---|---|---|---|---|
Major Triads | A♯ | {10,2,5} | 1 | 1 | 0.5 |
Diminished Triads | b° | {11,2,5} | 1 | 1 | 0.5 |
Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.
Diameter | 1 |
---|---|
Radius | 1 |
Self-Centered | yes |
Modes are the rotational transformation of this scale. Scale 3117 can be rotated to make 5 other scales. The 1st mode is itself.
2nd mode: Scale 1803 | ![]() | ||||
3rd mode: Scale 2949 | ![]() | ||||
4th mode: Scale 1761 | ![]() | ||||
5th mode: Scale 183 | ![]() | This is the prime mode | |||
6th mode: Scale 2139 | ![]() |
The prime form of this scale is Scale 183
Scale 183 | ![]() |
The hexatonic modal family [3117, 1803, 2949, 1761, 183, 2139] (Forte: 6-Z11) is the complement of the hexatonic modal family [303, 753, 1929, 2199, 3147, 3621] (Forte: 6-Z40)
The inverse of a scale is a reflection using the root as its axis. The inverse of 3117 is 1671
Scale 1671 | ![]() |
Only scales that are chiral will have an enantiomorph. Scale 3117 is chiral, and its enantiomorph is scale 1671
Scale 1671 | ![]() |
T0 | 3117 | T0I | 1671 | |||||
T1 | 2139 | T1I | 3342 | |||||
T2 | 183 | T2I | 2589 | |||||
T3 | 366 | T3I | 1083 | |||||
T4 | 732 | T4I | 2166 | |||||
T5 | 1464 | T5I | 237 | |||||
T6 | 2928 | T6I | 474 | |||||
T7 | 1761 | T7I | 948 | |||||
T8 | 3522 | T8I | 1896 | |||||
T9 | 2949 | T9I | 3792 | |||||
T10 | 1803 | T10I | 3489 | |||||
T11 | 3606 | T11I | 2883 |
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.
Scale 3119 | ![]() | |||
Scale 3113 | ![]() | |||
Scale 3115 | ![]() | |||
Scale 3109 | ![]() | |||
Scale 3125 | ![]() | |||
Scale 3133 | ![]() | |||
Scale 3085 | ![]() | |||
Scale 3101 | ![]() | |||
Scale 3149 | ![]() | Phrycrimic | ||
Scale 3181 | ![]() | Rolian | ||
Scale 3245 | ![]() | Mela Varunapriya | ||
Scale 3373 | ![]() | Lodian | ||
Scale 3629 | ![]() | Boptian | ||
Scale 2093 | ![]() | |||
Scale 2605 | ![]() | Rylimic | ||
Scale 1069 | ![]() |
This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.
Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO
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.