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Cardinality | 6 (hexatonic) |
---|---|
Pitch Class Set | {0,1,2,4,6,11} |
Forte Number | 6-9 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 3395 |
Hemitonia | 3 (trihemitonic) |
Cohemitonia | 2 (dicohemitonic) |
Imperfections | 3 |
Modes | 5 |
Prime? | no prime: 175 |
Deep Scale | no |
Interval Vector | 342231 |
Interval Spectrum | p3m2n2s4d3t |
Distribution Spectra | <1> = {1,2,5} <2> = {2,3,4,6,7} <3> = {3,4,5,7,8,9} <4> = {5,6,8,9,10} <5> = {7,10,11} |
Spectra Variation | 4 |
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 |
---|---|---|---|---|---|
Minor Triads | bm | {11,2,6} | 0 | 0 | 0 |
Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.
Modes are the rotational transformation of this scale. Scale 2135 can be rotated to make 5 other scales. The 1st mode is itself.
2nd mode: Scale 3115 | ![]() | ||||
3rd mode: Scale 3605 | ![]() | ||||
4th mode: Scale 1925 | ![]() | ||||
5th mode: Scale 1505 | ![]() | ||||
6th mode: Scale 175 | ![]() | This is the prime mode |
The prime form of this scale is Scale 175
Scale 175 | ![]() |
The hexatonic modal family [2135, 3115, 3605, 1925, 1505, 175] (Forte: 6-9) is the complement of the hexatonic modal family [175, 1505, 1925, 2135, 3115, 3605] (Forte: 6-9)
The inverse of a scale is a reflection using the root as its axis. The inverse of 2135 is 3395
Scale 3395 | ![]() |
Only scales that are chiral will have an enantiomorph. Scale 2135 is chiral, and its enantiomorph is scale 3395
Scale 3395 | ![]() |
T0 | 2135 | T0I | 3395 | |||||
T1 | 175 | T1I | 2695 | |||||
T2 | 350 | T2I | 1295 | |||||
T3 | 700 | T3I | 2590 | |||||
T4 | 1400 | T4I | 1085 | |||||
T5 | 2800 | T5I | 2170 | |||||
T6 | 1505 | T6I | 245 | |||||
T7 | 3010 | T7I | 490 | |||||
T8 | 1925 | T8I | 980 | |||||
T9 | 3850 | T9I | 1960 | |||||
T10 | 3605 | T10I | 3920 | |||||
T11 | 3115 | T11I | 3745 |
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 2133 | ![]() | Raga Kumurdaki | ||
Scale 2131 | ![]() | |||
Scale 2139 | ![]() | |||
Scale 2143 | ![]() | |||
Scale 2119 | ![]() | |||
Scale 2127 | ![]() | |||
Scale 2151 | ![]() | |||
Scale 2167 | ![]() | |||
Scale 2071 | ![]() | |||
Scale 2103 | ![]() | |||
Scale 2199 | ![]() | Dyptimic | ||
Scale 2263 | ![]() | Lycrian | ||
Scale 2391 | ![]() | Molian | ||
Scale 2647 | ![]() | Dadian | ||
Scale 3159 | ![]() | Stocrian | ||
Scale 87 | ![]() | |||
Scale 1111 | ![]() | Sycrimic |
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.