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Cardinality | 8 (octatonic) |
---|---|
Pitch Class Set | {0,1,2,3,5,8,9,11} |
Forte Number | 8-12 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 3739 |
Hemitonia | 5 (multihemitonic) |
Cohemitonia | 3 (tricohemitonic) |
Imperfections | 4 |
Modes | 7 |
Prime? | no prime: 763 |
Deep Scale | no |
Interval Vector | 556543 |
Interval Spectrum | p4m5n6s5d5t3 |
Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4,5} <3> = {3,4,6} <4> = {4,5,7,8} <5> = {6,8,9} <6> = {7,8,9,10} <7> = {9,10,11} |
Spectra Variation | 2.5 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.616 |
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} | 3 | 4 | 2 |
F | {5,9,0} | 3 | 4 | 2 | |
G♯ | {8,0,3} | 3 | 4 | 2 | |
Minor Triads | dm | {2,5,9} | 3 | 4 | 2.17 |
fm | {5,8,0} | 4 | 4 | 1.83 | |
g♯m | {8,11,3} | 3 | 4 | 2.17 | |
Augmented Triads | C♯+ | {1,5,9} | 3 | 4 | 2 |
Diminished Triads | d° | {2,5,8} | 2 | 4 | 2.33 |
f° | {5,8,11} | 2 | 4 | 2.17 | |
g♯° | {8,11,2} | 2 | 4 | 2.33 | |
a° | {9,0,3} | 2 | 4 | 2.33 | |
b° | {11,2,5} | 2 | 4 | 2.33 |
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 2863 can be rotated to make 7 other scales. The 1st mode is itself.
2nd mode: Scale 3479 | ![]() | Rothyllic | |||
3rd mode: Scale 3787 | ![]() | Kagyllic | |||
4th mode: Scale 3941 | ![]() | Stathyllic | |||
5th mode: Scale 2009 | ![]() | Stacryllic | |||
6th mode: Scale 763 | ![]() | Doryllic | This is the prime mode | ||
7th mode: Scale 2429 | ![]() | Kadyllic | |||
8th mode: Scale 1631 | ![]() | Rynyllic |
The prime form of this scale is Scale 763
Scale 763 | ![]() | Doryllic |
The octatonic modal family [2863, 3479, 3787, 3941, 2009, 763, 2429, 1631] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)
The inverse of a scale is a reflection using the root as its axis. The inverse of 2863 is 3739
Scale 3739 | ![]() | Epanyllic |
Only scales that are chiral will have an enantiomorph. Scale 2863 is chiral, and its enantiomorph is scale 3739
Scale 3739 | ![]() | Epanyllic |
T0 | 2863 | T0I | 3739 | |||||
T1 | 1631 | T1I | 3383 | |||||
T2 | 3262 | T2I | 2671 | |||||
T3 | 2429 | T3I | 1247 | |||||
T4 | 763 | T4I | 2494 | |||||
T5 | 1526 | T5I | 893 | |||||
T6 | 3052 | T6I | 1786 | |||||
T7 | 2009 | T7I | 3572 | |||||
T8 | 4018 | T8I | 3049 | |||||
T9 | 3941 | T9I | 2003 | |||||
T10 | 3787 | T10I | 4006 | |||||
T11 | 3479 | T11I | 3917 |
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 2861 | ![]() | Katothian | ||
Scale 2859 | ![]() | Phrycrian | ||
Scale 2855 | ![]() | Epocrain | ||
Scale 2871 | ![]() | Stanyllic | ||
Scale 2879 | ![]() | Stadygic | ||
Scale 2831 | ![]() | |||
Scale 2847 | ![]() | Phracryllic | ||
Scale 2895 | ![]() | Aeoryllic | ||
Scale 2927 | ![]() | Rodygic | ||
Scale 2991 | ![]() | Zanygic | ||
Scale 2607 | ![]() | Aerolian | ||
Scale 2735 | ![]() | Gynyllic | ||
Scale 2351 | ![]() | Gynian | ||
Scale 3375 | ![]() | |||
Scale 3887 | ![]() | Phrathygic | ||
Scale 815 | ![]() | Bolian | ||
Scale 1839 | ![]() | Zogyllic |
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.