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Cardinality | 8 (octatonic) |
---|---|
Pitch Class Set | {0,1,3,4,5,6,8,11} |
Forte Number | 8-14 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 3027 |
Hemitonia | 5 (multihemitonic) |
Cohemitonia | 3 (tricohemitonic) |
Imperfections | 2 |
Modes | 7 |
Prime? | no prime: 759 |
Deep Scale | no |
Interval Vector | 555562 |
Interval Spectrum | p6m5n5s5d5t2 |
Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4,5} <3> = {3,4,5,6} <4> = {5,7} <5> = {6,7,8,9} <6> = {7,8,9,10} <7> = {9,10,11} |
Spectra Variation | 2.25 |
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} | 2 | 5 | 2.5 |
E | {4,8,11} | 3 | 3 | 1.7 | |
G♯ | {8,0,3} | 3 | 3 | 1.7 | |
B | {11,3,6} | 2 | 5 | 2.5 | |
Minor Triads | c♯m | {1,4,8} | 2 | 4 | 2.1 |
fm | {5,8,0} | 3 | 4 | 1.9 | |
g♯m | {8,11,3} | 3 | 4 | 1.9 | |
Augmented Triads | C+ | {0,4,8} | 4 | 3 | 1.5 |
Diminished Triads | c° | {0,3,6} | 2 | 4 | 2.3 |
f° | {5,8,11} | 2 | 4 | 2.1 |
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+, E, G♯ |
Peripheral Vertices | C♯, B |
Modes are the rotational transformation of this scale. Scale 2427 can be rotated to make 7 other scales. The 1st mode is itself.
2nd mode: Scale 3261 | ![]() | Dodyllic | |||
3rd mode: Scale 1839 | ![]() | Zogyllic | |||
4th mode: Scale 2967 | ![]() | Madyllic | |||
5th mode: Scale 3531 | ![]() | Neveseri | |||
6th mode: Scale 3813 | ![]() | Aeologyllic | |||
7th mode: Scale 1977 | ![]() | Dagyllic | |||
8th mode: Scale 759 | ![]() | Katalyllic | This is the prime mode |
The prime form of this scale is Scale 759
Scale 759 | ![]() | Katalyllic |
The octatonic modal family [2427, 3261, 1839, 2967, 3531, 3813, 1977, 759] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)
The inverse of a scale is a reflection using the root as its axis. The inverse of 2427 is 3027
Scale 3027 | ![]() | Rythyllic |
Only scales that are chiral will have an enantiomorph. Scale 2427 is chiral, and its enantiomorph is scale 3027
Scale 3027 | ![]() | Rythyllic |
T0 | 2427 | T0I | 3027 | |||||
T1 | 759 | T1I | 1959 | |||||
T2 | 1518 | T2I | 3918 | |||||
T3 | 3036 | T3I | 3741 | |||||
T4 | 1977 | T4I | 3387 | |||||
T5 | 3954 | T5I | 2679 | |||||
T6 | 3813 | T6I | 1263 | |||||
T7 | 3531 | T7I | 2526 | |||||
T8 | 2967 | T8I | 957 | |||||
T9 | 1839 | T9I | 1914 | |||||
T10 | 3678 | T10I | 3828 | |||||
T11 | 3261 | T11I | 3561 |
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 2425 | ![]() | Rorian | ||
Scale 2429 | ![]() | Kadyllic | ||
Scale 2431 | ![]() | Gythygic | ||
Scale 2419 | ![]() | Raga Lalita | ||
Scale 2423 | ![]() | |||
Scale 2411 | ![]() | Aeolorian | ||
Scale 2395 | ![]() | Zoptian | ||
Scale 2363 | ![]() | Kataptian | ||
Scale 2491 | ![]() | Layllic | ||
Scale 2555 | ![]() | Bythygic | ||
Scale 2171 | ![]() | |||
Scale 2299 | ![]() | Phraptyllic | ||
Scale 2683 | ![]() | Thodyllic | ||
Scale 2939 | ![]() | Goptygic | ||
Scale 3451 | ![]() | Garygic | ||
Scale 379 | ![]() | Aeragian | ||
Scale 1403 | ![]() | Espla's Scale |
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.