more than you ever wanted to know about...
Cardinality | 8 (octatonic) |
---|---|
Pitch Class Set | {0,3,4,6,7,8,9,10} |
Forte Number | 8-12 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 893 |
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 | {0,4,7} | 3 | 4 | 2 |
D♯ | {3,7,10} | 3 | 4 | 2 | |
G♯ | {8,0,3} | 3 | 4 | 2 | |
Minor Triads | cm | {0,3,7} | 4 | 4 | 1.83 |
d♯m | {3,6,10} | 3 | 4 | 2.17 | |
am | {9,0,4} | 3 | 4 | 2.17 | |
Augmented Triads | C+ | {0,4,8} | 3 | 4 | 2 |
Diminished Triads | c° | {0,3,6} | 2 | 4 | 2.17 |
d♯° | {3,6,9} | 2 | 4 | 2.33 | |
e° | {4,7,10} | 2 | 4 | 2.33 | |
f♯° | {6,9,0} | 2 | 4 | 2.33 | |
a° | {9,0,3} | 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 2009 can be rotated to make 7 other scales. The 1st mode is itself.
2nd mode: Scale 763 | ![]() | Doryllic | This is the prime mode | ||
3rd mode: Scale 2429 | ![]() | Kadyllic | |||
4th mode: Scale 1631 | ![]() | Rynyllic | |||
5th mode: Scale 2863 | ![]() | Aerogyllic | |||
6th mode: Scale 3479 | ![]() | Rothyllic | |||
7th mode: Scale 3787 | ![]() | Kagyllic | |||
8th mode: Scale 3941 | ![]() | Stathyllic |
The prime form of this scale is Scale 763
Scale 763 | ![]() | Doryllic |
The octatonic modal family [2009, 763, 2429, 1631, 2863, 3479, 3787, 3941] (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 2009 is 893
Scale 893 | ![]() | Dadyllic |
Only scales that are chiral will have an enantiomorph. Scale 2009 is chiral, and its enantiomorph is scale 893
Scale 893 | ![]() | Dadyllic |
T0 | 2009 | T0I | 893 | |||||
T1 | 4018 | T1I | 1786 | |||||
T2 | 3941 | T2I | 3572 | |||||
T3 | 3787 | T3I | 3049 | |||||
T4 | 3479 | T4I | 2003 | |||||
T5 | 2863 | T5I | 4006 | |||||
T6 | 1631 | T6I | 3917 | |||||
T7 | 3262 | T7I | 3739 | |||||
T8 | 2429 | T8I | 3383 | |||||
T9 | 763 | T9I | 2671 | |||||
T10 | 1526 | T10I | 1247 | |||||
T11 | 3052 | T11I | 2494 |
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 2011 | ![]() | Raphygic | ||
Scale 2013 | ![]() | Mocrygic | ||
Scale 2001 | ![]() | Gydian | ||
Scale 2005 | ![]() | Gygyllic | ||
Scale 1993 | ![]() | Katoptian | ||
Scale 2025 | ![]() | |||
Scale 2041 | ![]() | Aeolacrygic | ||
Scale 1945 | ![]() | Zarian | ||
Scale 1977 | ![]() | Dagyllic | ||
Scale 1881 | ![]() | Katorian | ||
Scale 1753 | ![]() | Hungarian Major | ||
Scale 1497 | ![]() | Mela Jyotisvarupini | ||
Scale 985 | ![]() | Mela Sucaritra | ||
Scale 3033 | ![]() | Doptyllic | ||
Scale 4057 | ![]() | Phrygic |
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.