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Cardinality | 6 (hexatonic) |
---|---|
Pitch Class Set | {0,1,2,6,10,11} |
Forte Number | 6-Z37 |
Rotational Symmetry | none |
Reflection Axes | 0 |
Palindromic | yes |
Chirality | no |
Hemitonia | 4 (multihemitonic) |
Cohemitonia | 3 (tricohemitonic) |
Imperfections | 4 |
Modes | 5 |
Prime? | no prime: 287 |
Deep Scale | no |
Interval Vector | 432321 |
Interval Spectrum | p2m3n2s3d4t |
Distribution Spectra | <1> = {1,4} <2> = {2,5,8} <3> = {3,6,9} <4> = {4,7,10} <5> = {8,11} |
Spectra Variation | 4 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 1.866 |
Myhill Property | no |
Balanced | no |
Ridge Tones | [0] |
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 | F♯ | {6,10,1} | 1 | 2 | 1 |
Minor Triads | bm | {11,2,6} | 1 | 2 | 1 |
Augmented Triads | D+ | {2,6,10} | 2 | 1 | 0.67 |
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 | 1 |
Self-Centered | no |
Central Vertices | D+ |
Peripheral Vertices | F♯, bm |
Modes are the rotational transformation of this scale. Scale 3143 can be rotated to make 5 other scales. The 1st mode is itself.
2nd mode: Scale 3619 | ![]() | Thanimic | |||
3rd mode: Scale 3857 | ![]() | Ponimic | |||
4th mode: Scale 497 | ![]() | Kadimic | |||
5th mode: Scale 287 | ![]() | Gynimic | This is the prime mode | ||
6th mode: Scale 2191 | ![]() | Thydimic |
The prime form of this scale is Scale 287
Scale 287 | ![]() | Gynimic |
The hexatonic modal family [3143, 3619, 3857, 497, 287, 2191] (Forte: 6-Z37) is the complement of the hexatonic modal family [119, 1799, 2107, 2947, 3101, 3521] (Forte: 6-Z4)
The inverse of a scale is a reflection using the root as its axis. The inverse of 3143 is itself, because it is a palindromic scale!
Scale 3143 | ![]() | Polimic |
T0 | 3143 | T0I | 3143 | |||||
T1 | 2191 | T1I | 2191 | |||||
T2 | 287 | T2I | 287 | |||||
T3 | 574 | T3I | 574 | |||||
T4 | 1148 | T4I | 1148 | |||||
T5 | 2296 | T5I | 2296 | |||||
T6 | 497 | T6I | 497 | |||||
T7 | 994 | T7I | 994 | |||||
T8 | 1988 | T8I | 1988 | |||||
T9 | 3976 | T9I | 3976 | |||||
T10 | 3857 | T10I | 3857 | |||||
T11 | 3619 | T11I | 3619 |
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 3141 | ![]() | Kanitonic | ||
Scale 3139 | ![]() | |||
Scale 3147 | ![]() | Ryrimic | ||
Scale 3151 | ![]() | Pacrian | ||
Scale 3159 | ![]() | Stocrian | ||
Scale 3175 | ![]() | Eponian | ||
Scale 3079 | ![]() | |||
Scale 3111 | ![]() | |||
Scale 3207 | ![]() | |||
Scale 3271 | ![]() | Mela Raghupriya | ||
Scale 3399 | ![]() | Zonian | ||
Scale 3655 | ![]() | Mathian | ||
Scale 2119 | ![]() | |||
Scale 2631 | ![]() | Macrimic | ||
Scale 1095 | ![]() | Phrythitonic |
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.