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Cardinality | 8 (octatonic) |
---|---|
Pitch Class Set | {0,1,4,5,6,8,9,10} |
Forte Number | 8-19 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 2525 |
Hemitonia | 5 (multihemitonic) |
Cohemitonia | 2 (dicohemitonic) |
Imperfections | 3 |
Modes | 7 |
Prime? | no prime: 887 |
Deep Scale | no |
Interval Vector | 545752 |
Interval Spectrum | p5m7n5s4d5t2 |
Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4} <3> = {4,5,6} <4> = {5,6,7} <5> = {6,7,8} <6> = {8,9,10} <7> = {9,10,11} |
Spectra Variation | 1.75 |
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 | 3 | 1.92 |
F | {5,9,0} | 4 | 3 | 1.77 | |
F♯ | {6,10,1} | 2 | 5 | 2.62 | |
A | {9,1,4} | 4 | 3 | 1.77 | |
Minor Triads | c♯m | {1,4,8} | 3 | 4 | 2.15 |
fm | {5,8,0} | 3 | 4 | 2.15 | |
f♯m | {6,9,1} | 3 | 4 | 2.08 | |
am | {9,0,4} | 3 | 4 | 2 | |
a♯m | {10,1,5} | 3 | 4 | 2.08 | |
Augmented Triads | C+ | {0,4,8} | 3 | 5 | 2.38 |
C♯+ | {1,5,9} | 5 | 3 | 1.54 | |
Diminished Triads | f♯° | {6,9,0} | 2 | 4 | 2.31 |
a♯° | {10,1,4} | 2 | 4 | 2.31 |
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, A |
Peripheral Vertices | C+, F♯ |
Modes are the rotational transformation of this scale. Scale 1907 can be rotated to make 7 other scales. The 1st mode is itself.
2nd mode: Scale 3001 | ![]() | Lonyllic | |||
3rd mode: Scale 887 | ![]() | Sathyllic | This is the prime mode | ||
4th mode: Scale 2491 | ![]() | Layllic | |||
5th mode: Scale 3293 | ![]() | Saryllic | |||
6th mode: Scale 1847 | ![]() | Thacryllic | |||
7th mode: Scale 2971 | ![]() | Aeolynyllic | |||
8th mode: Scale 3533 | ![]() | Thadyllic |
The prime form of this scale is Scale 887
Scale 887 | ![]() | Sathyllic |
The octatonic modal family [1907, 3001, 887, 2491, 3293, 1847, 2971, 3533] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)
The inverse of a scale is a reflection using the root as its axis. The inverse of 1907 is 2525
Scale 2525 | ![]() | Aeolaryllic |
Only scales that are chiral will have an enantiomorph. Scale 1907 is chiral, and its enantiomorph is scale 2525
Scale 2525 | ![]() | Aeolaryllic |
T0 | 1907 | T0I | 2525 | |||||
T1 | 3814 | T1I | 955 | |||||
T2 | 3533 | T2I | 1910 | |||||
T3 | 2971 | T3I | 3820 | |||||
T4 | 1847 | T4I | 3545 | |||||
T5 | 3694 | T5I | 2995 | |||||
T6 | 3293 | T6I | 1895 | |||||
T7 | 2491 | T7I | 3790 | |||||
T8 | 887 | T8I | 3485 | |||||
T9 | 1774 | T9I | 2875 | |||||
T10 | 3548 | T10I | 1655 | |||||
T11 | 3001 | T11I | 3310 |
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 1905 | ![]() | Katacrian | ||
Scale 1909 | ![]() | Epicryllic | ||
Scale 1911 | ![]() | Messiaen Mode 3 | ||
Scale 1915 | ![]() | Thydygic | ||
Scale 1891 | ![]() | Thalian | ||
Scale 1899 | ![]() | Moptyllic | ||
Scale 1875 | ![]() | Persichetti Scale | ||
Scale 1843 | ![]() | Ionygian | ||
Scale 1971 | ![]() | Aerynyllic | ||
Scale 2035 | ![]() | Aerythygic | ||
Scale 1651 | ![]() | Asian | ||
Scale 1779 | ![]() | Zynyllic | ||
Scale 1395 | ![]() | Locrian Dominant | ||
Scale 883 | ![]() | Ralian | ||
Scale 2931 | ![]() | Zathyllic | ||
Scale 3955 | ![]() | Pothygic |
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.