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Cardinality | 9 (nonatonic) |
---|---|
Pitch Class Set | {0,2,4,5,6,8,9,10,11} |
Forte Number | 9-8 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 1503 |
Hemitonia | 6 (multihemitonic) |
Cohemitonia | 4 (multicohemitonic) |
Imperfections | 3 |
Modes | 8 |
Prime? | no prime: 1503 |
Deep Scale | no |
Interval Vector | 676764 |
Interval Spectrum | p6m7n6s7d6t4 |
Distribution Spectra | <1> = {1,2} <2> = {2,3,4} <3> = {3,4,5} <4> = {4,5,6} <5> = {6,7,8} <6> = {7,8,9} <7> = {8,9,10} <8> = {10,11} |
Spectra Variation | 1.556 |
Maximally Even | no |
Maximal Area Set | yes |
Interior Area | 2.799 |
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 | D | {2,6,9} | 3 | 4 | 2.33 |
E | {4,8,11} | 3 | 4 | 2.47 | |
F | {5,9,0} | 4 | 4 | 2.07 | |
A♯ | {10,2,5} | 3 | 4 | 2.33 | |
Minor Triads | dm | {2,5,9} | 4 | 4 | 2.07 |
fm | {5,8,0} | 4 | 4 | 2.2 | |
am | {9,0,4} | 2 | 4 | 2.47 | |
bm | {11,2,6} | 3 | 4 | 2.47 | |
Augmented Triads | C+ | {0,4,8} | 3 | 4 | 2.4 |
D+ | {2,6,10} | 3 | 4 | 2.4 | |
Diminished Triads | d° | {2,5,8} | 2 | 4 | 2.33 |
f° | {5,8,11} | 2 | 4 | 2.53 | |
f♯° | {6,9,0} | 2 | 4 | 2.47 | |
g♯° | {8,11,2} | 2 | 4 | 2.53 | |
b° | {11,2,5} | 2 | 4 | 2.67 |
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 | 4 |
---|---|
Radius | 4 |
Self-Centered | yes |
Modes are the rotational transformation of this scale. Scale 3957 can be rotated to make 8 other scales. The 1st mode is itself.
2nd mode: Scale 2013 | ![]() | Mocrygic | |||
3rd mode: Scale 1527 | ![]() | Aeolyrigic | |||
4th mode: Scale 2811 | ![]() | Barygic | |||
5th mode: Scale 3453 | ![]() | Katarygic | |||
6th mode: Scale 1887 | ![]() | Aerocrygic | |||
7th mode: Scale 2991 | ![]() | Zanygic | |||
8th mode: Scale 3543 | ![]() | Aeolonygic | |||
9th mode: Scale 3819 | ![]() | Aeolanygic |
The prime form of this scale is Scale 1503
Scale 1503 | ![]() | Padygic |
The nonatonic modal family [3957, 2013, 1527, 2811, 3453, 1887, 2991, 3543, 3819] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)
The inverse of a scale is a reflection using the root as its axis. The inverse of 3957 is 1503
Scale 1503 | ![]() | Padygic |
Only scales that are chiral will have an enantiomorph. Scale 3957 is chiral, and its enantiomorph is scale 1503
Scale 1503 | ![]() | Padygic |
T0 | 3957 | T0I | 1503 | |||||
T1 | 3819 | T1I | 3006 | |||||
T2 | 3543 | T2I | 1917 | |||||
T3 | 2991 | T3I | 3834 | |||||
T4 | 1887 | T4I | 3573 | |||||
T5 | 3774 | T5I | 3051 | |||||
T6 | 3453 | T6I | 2007 | |||||
T7 | 2811 | T7I | 4014 | |||||
T8 | 1527 | T8I | 3933 | |||||
T9 | 3054 | T9I | 3771 | |||||
T10 | 2013 | T10I | 3447 | |||||
T11 | 4026 | T11I | 2799 |
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 3959 | ![]() | Katagyllian | ||
Scale 3953 | ![]() | Thagyllic | ||
Scale 3955 | ![]() | Pothygic | ||
Scale 3961 | ![]() | Zathygic | ||
Scale 3965 | ![]() | Messiaen Mode 7 Inverse | ||
Scale 3941 | ![]() | Stathyllic | ||
Scale 3949 | ![]() | Koptygic | ||
Scale 3925 | ![]() | Thyryllic | ||
Scale 3893 | ![]() | Phrocryllic | ||
Scale 4021 | ![]() | Raga Pahadi | ||
Scale 4085 | ![]() | Sydyllian | ||
Scale 3701 | ![]() | Bagyllic | ||
Scale 3829 | ![]() | Taishikicho | ||
Scale 3445 | ![]() | Messiaen Mode 6 Inverse | ||
Scale 2933 | ![]() | |||
Scale 1909 | ![]() | Epicryllic |
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.