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Cardinality | 8 (octatonic) |
---|---|
Pitch Class Set | {0,4,5,6,7,9,10,11} |
Forte Number | 8-6 |
Rotational Symmetry | none |
Reflection Axes | 2 |
Palindromic | no |
Chirality | no |
Hemitonia | 6 (multihemitonic) |
Cohemitonia | 4 (multicohemitonic) |
Imperfections | 2 |
Modes | 7 |
Prime? | no prime: 495 |
Deep Scale | no |
Interval Vector | 654463 |
Interval Spectrum | p6m4n4s5d6t3 |
Distribution Spectra | <1> = {1,2,4} <2> = {2,3,5} <3> = {3,4,6} <4> = {5,7} <5> = {6,8,9} <6> = {7,9,10} <7> = {8,10,11} |
Spectra Variation | 2.5 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.366 |
Myhill Property | no |
Balanced | no |
Ridge Tones | [4] |
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} | 2 | 3 | 1.5 |
F | {5,9,0} | 2 | 4 | 1.83 | |
Minor Triads | em | {4,7,11} | 2 | 4 | 1.83 |
am | {9,0,4} | 2 | 3 | 1.5 | |
Diminished Triads | e° | {4,7,10} | 1 | 5 | 2.5 |
f♯° | {6,9,0} | 1 | 5 | 2.5 |
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, am |
Peripheral Vertices | e°, f♯° |
Modes are the rotational transformation of this scale. Scale 3825 can be rotated to make 7 other scales. The 1st mode is itself.
2nd mode: Scale 495 | ![]() | Bocryllic | This is the prime mode | ||
3rd mode: Scale 2295 | ![]() | Kogyllic | |||
4th mode: Scale 3195 | ![]() | Raryllic | |||
5th mode: Scale 3645 | ![]() | Zycryllic | |||
6th mode: Scale 1935 | ![]() | Mycryllic | |||
7th mode: Scale 3015 | ![]() | Laptyllic | |||
8th mode: Scale 3555 | ![]() | Pylyllic |
The prime form of this scale is Scale 495
Scale 495 | ![]() | Bocryllic |
The octatonic modal family [3825, 495, 2295, 3195, 3645, 1935, 3015, 3555] (Forte: 8-6) is the complement of the tetratonic modal family [135, 225, 2115, 3105] (Forte: 4-6)
The inverse of a scale is a reflection using the root as its axis. The inverse of 3825 is 495
Scale 495 | ![]() | Bocryllic |
T0 | 3825 | T0I | 495 | |||||
T1 | 3555 | T1I | 990 | |||||
T2 | 3015 | T2I | 1980 | |||||
T3 | 1935 | T3I | 3960 | |||||
T4 | 3870 | T4I | 3825 | |||||
T5 | 3645 | T5I | 3555 | |||||
T6 | 3195 | T6I | 3015 | |||||
T7 | 2295 | T7I | 1935 | |||||
T8 | 495 | T8I | 3870 | |||||
T9 | 990 | T9I | 3645 | |||||
T10 | 1980 | T10I | 3195 | |||||
T11 | 3960 | T11I | 2295 |
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 3827 | ![]() | Bodygic | ||
Scale 3829 | ![]() | Taishikicho | ||
Scale 3833 | ![]() | Dycrygic | ||
Scale 3809 | ![]() | |||
Scale 3817 | ![]() | Zoryllic | ||
Scale 3793 | ![]() | Aeopian | ||
Scale 3761 | ![]() | Raga Madhuri | ||
Scale 3697 | ![]() | Ionarian | ||
Scale 3953 | ![]() | Thagyllic | ||
Scale 4081 | ![]() | Manygic | ||
Scale 3313 | ![]() | Aeolacrian | ||
Scale 3569 | ![]() | Aeoladyllic | ||
Scale 2801 | ![]() | Zogian | ||
Scale 1777 | ![]() | Saptian |
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.