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Cardinality | 6 (hexatonic) |
---|---|
Pitch Class Set | {0,1,3,4,6,10} |
Forte Number | 6-Z23 |
Rotational Symmetry | none |
Reflection Axes | 2 |
Palindromic | no |
Chirality | no |
Hemitonia | 2 (dihemitonic) |
Cohemitonia | 0 (ancohemitonic) |
Imperfections | 4 |
Modes | 5 |
Prime? | no prime: 365 |
Deep Scale | no |
Interval Vector | 234222 |
Interval Spectrum | p2m2n4s3d2t2 |
Distribution Spectra | <1> = {1,2,4} <2> = {3,6} <3> = {4,5,7,8} <4> = {6,9} <5> = {8,10,11} |
Spectra Variation | 2.667 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.232 |
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 | F♯ | {6,10,1} | 2 | 2 | 1 |
Minor Triads | d♯m | {3,6,10} | 2 | 2 | 1 |
Diminished Triads | c° | {0,3,6} | 1 | 3 | 1.5 |
a♯° | {10,1,4} | 1 | 3 | 1.5 |
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 | 3 |
---|---|
Radius | 2 |
Self-Centered | no |
Central Vertices | d♯m, F♯ |
Peripheral Vertices | c°, a♯° |
Modes are the rotational transformation of this scale. Scale 1115 can be rotated to make 5 other scales. The 1st mode is itself.
2nd mode: Scale 2605 | ![]() | Rylimic | |||
3rd mode: Scale 1675 | ![]() | Raga Salagavarali | |||
4th mode: Scale 2885 | ![]() | Byrimic | |||
5th mode: Scale 1745 | ![]() | Raga Vutari | |||
6th mode: Scale 365 | ![]() | Marimic | This is the prime mode |
The prime form of this scale is Scale 365
Scale 365 | ![]() | Marimic |
The hexatonic modal family [1115, 2605, 1675, 2885, 1745, 365] (Forte: 6-Z23) is the complement of the hexatonic modal family [605, 745, 1175, 1865, 2635, 3365] (Forte: 6-Z45)
The inverse of a scale is a reflection using the root as its axis. The inverse of 1115 is 2885
Scale 2885 | ![]() | Byrimic |
T0 | 1115 | T0I | 2885 | |||||
T1 | 2230 | T1I | 1675 | |||||
T2 | 365 | T2I | 3350 | |||||
T3 | 730 | T3I | 2605 | |||||
T4 | 1460 | T4I | 1115 | |||||
T5 | 2920 | T5I | 2230 | |||||
T6 | 1745 | T6I | 365 | |||||
T7 | 3490 | T7I | 730 | |||||
T8 | 2885 | T8I | 1460 | |||||
T9 | 1675 | T9I | 2920 | |||||
T10 | 3350 | T10I | 1745 | |||||
T11 | 2605 | T11I | 3490 |
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 1113 | ![]() | Locrian Pentatonic 2 | ||
Scale 1117 | ![]() | Raptimic | ||
Scale 1119 | ![]() | Rarian | ||
Scale 1107 | ![]() | Mogitonic | ||
Scale 1111 | ![]() | Sycrimic | ||
Scale 1099 | ![]() | Dyritonic | ||
Scale 1131 | ![]() | Honchoshi Plagal Form | ||
Scale 1147 | ![]() | Epynian | ||
Scale 1051 | ![]() | |||
Scale 1083 | ![]() | |||
Scale 1179 | ![]() | Sonimic | ||
Scale 1243 | ![]() | Epylian | ||
Scale 1371 | ![]() | Superlocrian | ||
Scale 1627 | ![]() | Zyptian | ||
Scale 91 | ![]() | |||
Scale 603 | ![]() | Aeolygimic | ||
Scale 2139 | ![]() | |||
Scale 3163 | ![]() | Rogian |
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.