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Cardinality | 7 (heptatonic) |
---|---|
Pitch Class Set | {0,1,2,4,5,7,11} |
Forte Number | 7-Z36 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 3491 |
Hemitonia | 4 (multihemitonic) |
Cohemitonia | 2 (dicohemitonic) |
Imperfections | 3 |
Modes | 6 |
Prime? | no prime: 367 |
Deep Scale | no |
Interval Vector | 444342 |
Interval Spectrum | p4m3n4s4d4t2 |
Distribution Spectra | <1> = {1,2,4} <2> = {2,3,5,6} <3> = {3,4,5,6,7} <4> = {5,6,7,8,9} <5> = {6,7,9,10} <6> = {8,10,11} |
Spectra Variation | 3.143 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.299 |
Myhill Property | no |
Balanced | no |
Ridge Tones | none |
Propriety | Improper |
Heliotonic | yes |
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 | C | {0,4,7} | 2 | 3 | 1.4 |
G | {7,11,2} | 2 | 3 | 1.4 | |
Minor Triads | em | {4,7,11} | 2 | 2 | 1.2 |
Diminished Triads | c♯° | {1,4,7} | 1 | 4 | 2 |
b° | {11,2,5} | 1 | 4 | 2 |
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 | 4 |
---|---|
Radius | 2 |
Self-Centered | no |
Central Vertices | em |
Peripheral Vertices | c♯°, b° |
Modes are the rotational transformation of this scale. Scale 2231 can be rotated to make 6 other scales. The 1st mode is itself.
2nd mode: Scale 3163 | ![]() | Rogian | |||
3rd mode: Scale 3629 | ![]() | Boptian | |||
4th mode: Scale 1931 | ![]() | Stogian | |||
5th mode: Scale 3013 | ![]() | Thynian | |||
6th mode: Scale 1777 | ![]() | Saptian | |||
7th mode: Scale 367 | ![]() | Aerodian | This is the prime mode |
The prime form of this scale is Scale 367
Scale 367 | ![]() | Aerodian |
The heptatonic modal family [2231, 3163, 3629, 1931, 3013, 1777, 367] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)
The inverse of a scale is a reflection using the root as its axis. The inverse of 2231 is 3491
Scale 3491 | ![]() | Tharian |
Only scales that are chiral will have an enantiomorph. Scale 2231 is chiral, and its enantiomorph is scale 3491
Scale 3491 | ![]() | Tharian |
T0 | 2231 | T0I | 3491 | |||||
T1 | 367 | T1I | 2887 | |||||
T2 | 734 | T2I | 1679 | |||||
T3 | 1468 | T3I | 3358 | |||||
T4 | 2936 | T4I | 2621 | |||||
T5 | 1777 | T5I | 1147 | |||||
T6 | 3554 | T6I | 2294 | |||||
T7 | 3013 | T7I | 493 | |||||
T8 | 1931 | T8I | 986 | |||||
T9 | 3862 | T9I | 1972 | |||||
T10 | 3629 | T10I | 3944 | |||||
T11 | 3163 | T11I | 3793 |
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 2229 | ![]() | Raga Nalinakanti | ||
Scale 2227 | ![]() | Raga Gaula | ||
Scale 2235 | ![]() | Bathian | ||
Scale 2239 | ![]() | Dacryllic | ||
Scale 2215 | ![]() | Ranimic | ||
Scale 2223 | ![]() | Konian | ||
Scale 2199 | ![]() | Dyptimic | ||
Scale 2263 | ![]() | Lycrian | ||
Scale 2295 | ![]() | Kogyllic | ||
Scale 2103 | ![]() | |||
Scale 2167 | ![]() | |||
Scale 2359 | ![]() | Gadian | ||
Scale 2487 | ![]() | Dothyllic | ||
Scale 2743 | ![]() | Staptyllic | ||
Scale 3255 | ![]() | Daryllic | ||
Scale 183 | ![]() | |||
Scale 1207 | ![]() | Aeoloptian |
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.