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Cardinality | 8 (octatonic) |
---|---|
Pitch Class Set | {0,1,5,7,8,9,10,11} |
Forte Number | 8-2 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 2239 |
Hemitonia | 6 (multihemitonic) |
Cohemitonia | 5 (multicohemitonic) |
Imperfections | 4 |
Modes | 7 |
Prime? | no prime: 383 |
Deep Scale | no |
Interval Vector | 665542 |
Interval Spectrum | p4m5n5s6d6t2 |
Distribution Spectra | <1> = {1,2,4} <2> = {2,3,5,6} <3> = {3,4,6,7} <4> = {4,5,7,8} <5> = {5,6,8,9} <6> = {6,7,9,10} <7> = {8,10,11} |
Spectra Variation | 3.25 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.366 |
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♯ | {1,5,8} | 2 | 3 | 1.57 |
F | {5,9,0} | 2 | 3 | 1.57 | |
Minor Triads | fm | {5,8,0} | 3 | 4 | 1.71 |
a♯m | {10,1,5} | 2 | 4 | 1.86 | |
Augmented Triads | C♯+ | {1,5,9} | 3 | 3 | 1.43 |
Diminished Triads | f° | {5,8,11} | 1 | 5 | 2.43 |
g° | {7,10,1} | 1 | 5 | 2.57 |
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 | 5 |
---|---|
Radius | 3 |
Self-Centered | no |
Central Vertices | C♯, C♯+, F |
Peripheral Vertices | f°, g° |
Modes are the rotational transformation of this scale. Scale 4003 can be rotated to make 7 other scales. The 1st mode is itself.
2nd mode: Scale 4049 | ![]() | Stycryllic | |||
3rd mode: Scale 509 | ![]() | Ionothyllic | |||
4th mode: Scale 1151 | ![]() | Mythyllic | |||
5th mode: Scale 2623 | ![]() | Aerylyllic | |||
6th mode: Scale 3359 | ![]() | Bonyllic | |||
7th mode: Scale 3727 | ![]() | Tholyllic | |||
8th mode: Scale 3911 | ![]() | Katyryllic |
The prime form of this scale is Scale 383
Scale 383 | ![]() | Logyllic |
The octatonic modal family [4003, 4049, 509, 1151, 2623, 3359, 3727, 3911] (Forte: 8-2) is the complement of the tetratonic modal family [23, 1793, 2059, 3077] (Forte: 4-2)
The inverse of a scale is a reflection using the root as its axis. The inverse of 4003 is 2239
Scale 2239 | ![]() | Dacryllic |
Only scales that are chiral will have an enantiomorph. Scale 4003 is chiral, and its enantiomorph is scale 2239
Scale 2239 | ![]() | Dacryllic |
T0 | 4003 | T0I | 2239 | |||||
T1 | 3911 | T1I | 383 | |||||
T2 | 3727 | T2I | 766 | |||||
T3 | 3359 | T3I | 1532 | |||||
T4 | 2623 | T4I | 3064 | |||||
T5 | 1151 | T5I | 2033 | |||||
T6 | 2302 | T6I | 4066 | |||||
T7 | 509 | T7I | 4037 | |||||
T8 | 1018 | T8I | 3979 | |||||
T9 | 2036 | T9I | 3863 | |||||
T10 | 4072 | T10I | 3631 | |||||
T11 | 4049 | T11I | 3167 |
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 4001 | ![]() | |||
Scale 4005 | ![]() | |||
Scale 4007 | ![]() | Doptygic | ||
Scale 4011 | ![]() | Styrygic | ||
Scale 4019 | ![]() | Lonygic | ||
Scale 3971 | ![]() | |||
Scale 3987 | ![]() | Loryllic | ||
Scale 4035 | ![]() | |||
Scale 4067 | ![]() | Aeolarygic | ||
Scale 3875 | ![]() | Aeryptian | ||
Scale 3939 | ![]() | Dogyllic | ||
Scale 3747 | ![]() | Myrian | ||
Scale 3491 | ![]() | Tharian | ||
Scale 2979 | ![]() | Gyptian | ||
Scale 1955 | ![]() | Sonian |
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.