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Cardinality | 9 (nonatonic) |
---|---|
Pitch Class Set | {0,1,4,6,7,8,9,10,11} |
Forte Number | 9-2 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 2431 |
Hemitonia | 7 (multihemitonic) |
Cohemitonia | 6 (multicohemitonic) |
Imperfections | 3 |
Modes | 8 |
Prime? | no prime: 767 |
Deep Scale | no |
Interval Vector | 777663 |
Interval Spectrum | p6m6n7s7d7t3 |
Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4,5} <3> = {3,4,5,6} <4> = {4,5,6,7} <5> = {5,6,7,8} <6> = {6,7,8,9} <7> = {7,8,9,10} <8> = {9,10,11} |
Spectra Variation | 2.444 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.683 |
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 | C | {0,4,7} | 3 | 4 | 2.29 |
E | {4,8,11} | 2 | 4 | 2.43 | |
F♯ | {6,10,1} | 3 | 4 | 2.43 | |
A | {9,1,4} | 4 | 4 | 2.07 | |
Minor Triads | c♯m | {1,4,8} | 3 | 4 | 2.14 |
em | {4,7,11} | 3 | 4 | 2.43 | |
f♯m | {6,9,1} | 3 | 4 | 2.29 | |
am | {9,0,4} | 3 | 4 | 2.14 | |
Augmented Triads | C+ | {0,4,8} | 4 | 4 | 2.07 |
Diminished Triads | c♯° | {1,4,7} | 2 | 4 | 2.5 |
e° | {4,7,10} | 2 | 4 | 2.57 | |
f♯° | {6,9,0} | 2 | 4 | 2.5 | |
g° | {7,10,1} | 2 | 4 | 2.57 | |
a♯° | {10,1,4} | 2 | 4 | 2.43 |
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 4051 can be rotated to make 8 other scales. The 1st mode is itself.
2nd mode: Scale 4073 | ![]() | Sathygic | |||
3rd mode: Scale 1021 | ![]() | Ladygic | |||
4th mode: Scale 1279 | ![]() | Sarygic | |||
5th mode: Scale 2687 | ![]() | Thacrygic | |||
6th mode: Scale 3391 | ![]() | Aeolynygic | |||
7th mode: Scale 3743 | ![]() | Thadygic | |||
8th mode: Scale 3919 | ![]() | Lynygic | |||
9th mode: Scale 4007 | ![]() | Doptygic |
The prime form of this scale is Scale 767
Scale 767 | ![]() | Raptygic |
The nonatonic modal family [4051, 4073, 1021, 1279, 2687, 3391, 3743, 3919, 4007] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)
The inverse of a scale is a reflection using the root as its axis. The inverse of 4051 is 2431
Scale 2431 | ![]() | Gythygic |
Only scales that are chiral will have an enantiomorph. Scale 4051 is chiral, and its enantiomorph is scale 2431
Scale 2431 | ![]() | Gythygic |
T0 | 4051 | T0I | 2431 | |||||
T1 | 4007 | T1I | 767 | |||||
T2 | 3919 | T2I | 1534 | |||||
T3 | 3743 | T3I | 3068 | |||||
T4 | 3391 | T4I | 2041 | |||||
T5 | 2687 | T5I | 4082 | |||||
T6 | 1279 | T6I | 4069 | |||||
T7 | 2558 | T7I | 4043 | |||||
T8 | 1021 | T8I | 3991 | |||||
T9 | 2042 | T9I | 3887 | |||||
T10 | 4084 | T10I | 3679 | |||||
T11 | 4073 | T11I | 3263 |
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 4049 | ![]() | Stycryllic | ||
Scale 4053 | ![]() | Kyrygic | ||
Scale 4055 | ![]() | Dagyllian | ||
Scale 4059 | ![]() | Zolyllian | ||
Scale 4035 | ![]() | |||
Scale 4043 | ![]() | Phrocrygic | ||
Scale 4067 | ![]() | Aeolarygic | ||
Scale 4083 | ![]() | Bathyllian | ||
Scale 3987 | ![]() | Loryllic | ||
Scale 4019 | ![]() | Lonygic | ||
Scale 3923 | ![]() | Stoptyllic | ||
Scale 3795 | ![]() | Epothyllic | ||
Scale 3539 | ![]() | Aeoryllic | ||
Scale 3027 | ![]() | Rythyllic | ||
Scale 2003 | ![]() | Podyllic |
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.