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Cardinality | 8 (octatonic) |
---|---|
Pitch Class Set | {0,1,3,4,5,6,8,9} |
Forte Number | 8-17 |
Rotational Symmetry | none |
Reflection Axes | 4.5 |
Palindromic | no |
Chirality | no |
Hemitonia | 5 (multihemitonic) |
Cohemitonia | 2 (dicohemitonic) |
Imperfections | 3 |
Modes | 7 |
Prime? | yes |
Deep Scale | no |
Interval Vector | 546652 |
Interval Spectrum | p5m6n6s4d5t2 |
Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4} <3> = {3,4,5,6} <4> = {5,7} <5> = {6,7,8,9} <6> = {8,9,10} <7> = {9,10,11} |
Spectra Variation | 2 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.616 |
Myhill Property | no |
Balanced | no |
Ridge Tones | [9] |
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 | 2.21 |
F | {5,9,0} | 4 | 4 | 1.93 | |
G♯ | {8,0,3} | 3 | 4 | 2.21 | |
A | {9,1,4} | 3 | 4 | 2.07 | |
Minor Triads | c♯m | {1,4,8} | 3 | 4 | 2.21 |
fm | {5,8,0} | 3 | 4 | 2.07 | |
f♯m | {6,9,1} | 3 | 4 | 2.21 | |
am | {9,0,4} | 4 | 4 | 1.93 | |
Augmented Triads | C+ | {0,4,8} | 4 | 4 | 1.93 |
C♯+ | {1,5,9} | 4 | 4 | 1.93 | |
Diminished Triads | c° | {0,3,6} | 2 | 4 | 2.5 |
d♯° | {3,6,9} | 2 | 4 | 2.5 | |
f♯° | {6,9,0} | 2 | 4 | 2.36 | |
a° | {9,0,3} | 2 | 4 | 2.36 |
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 891 can be rotated to make 7 other scales. The 1st mode is itself.
2nd mode: Scale 2493 | ![]() | Manyllic | |||
3rd mode: Scale 1647 | ![]() | Polyllic | |||
4th mode: Scale 2871 | ![]() | Stanyllic | |||
5th mode: Scale 3483 | ![]() | Mixotharyllic | |||
6th mode: Scale 3789 | ![]() | Eporyllic | |||
7th mode: Scale 1971 | ![]() | Aerynyllic | |||
8th mode: Scale 3033 | ![]() | Doptyllic |
This is the prime form of this scale.
The octatonic modal family [891, 2493, 1647, 2871, 3483, 3789, 1971, 3033] (Forte: 8-17) is the complement of the tetratonic modal family [153, 531, 801, 2313] (Forte: 4-17)
The inverse of a scale is a reflection using the root as its axis. The inverse of 891 is 3033
Scale 3033 | ![]() | Doptyllic |
T0 | 891 | T0I | 3033 | |||||
T1 | 1782 | T1I | 1971 | |||||
T2 | 3564 | T2I | 3942 | |||||
T3 | 3033 | T3I | 3789 | |||||
T4 | 1971 | T4I | 3483 | |||||
T5 | 3942 | T5I | 2871 | |||||
T6 | 3789 | T6I | 1647 | |||||
T7 | 3483 | T7I | 3294 | |||||
T8 | 2871 | T8I | 2493 | |||||
T9 | 1647 | T9I | 891 | |||||
T10 | 3294 | T10I | 1782 | |||||
T11 | 2493 | T11I | 3564 |
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 889 | ![]() | Borian | ||
Scale 893 | ![]() | Dadyllic | ||
Scale 895 | ![]() | Aeolathygic | ||
Scale 883 | ![]() | Ralian | ||
Scale 887 | ![]() | Sathyllic | ||
Scale 875 | ![]() | Locrian Double-flat 7 | ||
Scale 859 | ![]() | Ultralocrian | ||
Scale 827 | ![]() | Mixolocrian | ||
Scale 955 | ![]() | Ionogyllic | ||
Scale 1019 | ![]() | Aeranygic | ||
Scale 635 | ![]() | Epolian | ||
Scale 763 | ![]() | Doryllic | ||
Scale 379 | ![]() | Aeragian | ||
Scale 1403 | ![]() | Espla's Scale | ||
Scale 1915 | ![]() | Thydygic | ||
Scale 2939 | ![]() | Goptygic |
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.