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Cardinality | 6 (hexatonic) |
---|---|
Pitch Class Set | {0,2,3,4,8,9} |
Forte Number | 6-Z17 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 1817 |
Hemitonia | 3 (trihemitonic) |
Cohemitonia | 1 (uncohemitonic) |
Imperfections | 3 |
Modes | 5 |
Prime? | no prime: 407 |
Deep Scale | no |
Interval Vector | 322332 |
Interval Spectrum | p3m3n2s2d3t2 |
Distribution Spectra | <1> = {1,2,3,4} <2> = {2,3,4,5} <3> = {4,6,8} <4> = {7,8,9,10} <5> = {8,9,10,11} |
Spectra Variation | 2.667 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.116 |
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 | G♯ | {8,0,3} | 2 | 2 | 1 |
Minor Triads | am | {9,0,4} | 2 | 2 | 1 |
Augmented Triads | C+ | {0,4,8} | 2 | 2 | 1 |
Diminished Triads | a° | {9,0,3} | 2 | 2 | 1 |
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 | 2 |
---|---|
Radius | 2 |
Self-Centered | yes |
Modes are the rotational transformation of this scale. Scale 797 can be rotated to make 5 other scales. The 1st mode is itself.
2nd mode: Scale 1223 | ![]() | Phryptimic | |||
3rd mode: Scale 2659 | ![]() | Katynimic | |||
4th mode: Scale 3377 | ![]() | Phralimic | |||
5th mode: Scale 467 | ![]() | Raga Dhavalangam | |||
6th mode: Scale 2281 | ![]() | Rathimic |
The prime form of this scale is Scale 407
Scale 407 | ![]() | Zylimic |
The hexatonic modal family [797, 1223, 2659, 3377, 467, 2281] (Forte: 6-Z17) is the complement of the hexatonic modal family [359, 907, 1649, 2227, 2501, 3161] (Forte: 6-Z43)
The inverse of a scale is a reflection using the root as its axis. The inverse of 797 is 1817
Scale 1817 | ![]() | Phrythimic |
Only scales that are chiral will have an enantiomorph. Scale 797 is chiral, and its enantiomorph is scale 1817
Scale 1817 | ![]() | Phrythimic |
T0 | 797 | T0I | 1817 | |||||
T1 | 1594 | T1I | 3634 | |||||
T2 | 3188 | T2I | 3173 | |||||
T3 | 2281 | T3I | 2251 | |||||
T4 | 467 | T4I | 407 | |||||
T5 | 934 | T5I | 814 | |||||
T6 | 1868 | T6I | 1628 | |||||
T7 | 3736 | T7I | 3256 | |||||
T8 | 3377 | T8I | 2417 | |||||
T9 | 2659 | T9I | 739 | |||||
T10 | 1223 | T10I | 1478 | |||||
T11 | 2446 | T11I | 2956 |
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 799 | ![]() | Lolian | ||
Scale 793 | ![]() | Mocritonic | ||
Scale 795 | ![]() | Aeologimic | ||
Scale 789 | ![]() | Zogitonic | ||
Scale 781 | ![]() | |||
Scale 813 | ![]() | Larimic | ||
Scale 829 | ![]() | Lygian | ||
Scale 861 | ![]() | Rylian | ||
Scale 925 | ![]() | Chromatic Hypodorian | ||
Scale 541 | ![]() | |||
Scale 669 | ![]() | Gycrimic | ||
Scale 285 | ![]() | Zaritonic | ||
Scale 1309 | ![]() | Pogimic | ||
Scale 1821 | ![]() | Aeradian | ||
Scale 2845 | ![]() | Baptian |
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.