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Cardinality | 6 (hexatonic) |
---|---|
Pitch Class Set | {0,2,5,8,9,10} |
Forte Number | 6-Z46 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 1181 |
Hemitonia | 2 (dihemitonic) |
Cohemitonia | 1 (uncohemitonic) |
Imperfections | 3 |
Modes | 5 |
Prime? | no prime: 599 |
Deep Scale | no |
Interval Vector | 233331 |
Interval Spectrum | p3m3n3s3d2t |
Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4,5,6} <3> = {4,5,7,8} <4> = {6,7,8,9,10} <5> = {9,10,11} |
Spectra Variation | 2.667 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.366 |
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 | F | {5,9,0} | 2 | 2 | 1.2 |
A♯ | {10,2,5} | 1 | 3 | 1.6 | |
Minor Triads | dm | {2,5,9} | 3 | 2 | 1 |
fm | {5,8,0} | 2 | 3 | 1.4 | |
Diminished Triads | d° | {2,5,8} | 2 | 2 | 1.2 |
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°, dm, F |
Peripheral Vertices | fm, A♯ |
Modes are the rotational transformation of this scale. Scale 1829 can be rotated to make 5 other scales. The 1st mode is itself.
2nd mode: Scale 1481 | ![]() | Zagimic | |||
3rd mode: Scale 697 | ![]() | Lagimic | |||
4th mode: Scale 599 | ![]() | Thyrimic | This is the prime mode | ||
5th mode: Scale 2347 | ![]() | Raga Viyogavarali | |||
6th mode: Scale 3221 | ![]() | Bycrimic |
The prime form of this scale is Scale 599
Scale 599 | ![]() | Thyrimic |
The hexatonic modal family [1829, 1481, 697, 599, 2347, 3221] (Forte: 6-Z46) is the complement of the hexatonic modal family [347, 1457, 1579, 1733, 2221, 2837] (Forte: 6-Z24)
The inverse of a scale is a reflection using the root as its axis. The inverse of 1829 is 1181
Scale 1181 | ![]() | Katagimic |
Only scales that are chiral will have an enantiomorph. Scale 1829 is chiral, and its enantiomorph is scale 1181
Scale 1181 | ![]() | Katagimic |
T0 | 1829 | T0I | 1181 | |||||
T1 | 3658 | T1I | 2362 | |||||
T2 | 3221 | T2I | 629 | |||||
T3 | 2347 | T3I | 1258 | |||||
T4 | 599 | T4I | 2516 | |||||
T5 | 1198 | T5I | 937 | |||||
T6 | 2396 | T6I | 1874 | |||||
T7 | 697 | T7I | 3748 | |||||
T8 | 1394 | T8I | 3401 | |||||
T9 | 2788 | T9I | 2707 | |||||
T10 | 1481 | T10I | 1319 | |||||
T11 | 2962 | T11I | 2638 |
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 1831 | ![]() | Pothian | ||
Scale 1825 | ![]() | |||
Scale 1827 | ![]() | Katygimic | ||
Scale 1833 | ![]() | Ionacrimic | ||
Scale 1837 | ![]() | Dalian | ||
Scale 1845 | ![]() | Lagian | ||
Scale 1797 | ![]() | |||
Scale 1813 | ![]() | Katothimic | ||
Scale 1861 | ![]() | Phrygimic | ||
Scale 1893 | ![]() | Ionylian | ||
Scale 1957 | ![]() | Pyrian | ||
Scale 1573 | ![]() | Raga Guhamanohari | ||
Scale 1701 | ![]() | Dominant Seventh | ||
Scale 1317 | ![]() | Chaio | ||
Scale 805 | ![]() | Rothitonic | ||
Scale 2853 | ![]() | Baptimic | ||
Scale 3877 | ![]() | Thanian |
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.