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Scale 733: "Donian"

Scale 733: Donian, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Donian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,4,6,7,9}
Forte Number7-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1897
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector345342
Interval Spectrump4m3n5s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Common Triads

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 TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsC{0,4,7}231.75
D{2,6,9}231.88
Minor Triadscm{0,3,7}331.63
am{9,0,4}331.63
Diminished Triads{0,3,6}231.75
d♯°{3,6,9}231.88
f♯°{6,9,0}231.75
{9,0,3}231.75
Parsimonious Voice Leading Between Common Triads of Scale 733. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° C C cm->C cm->a° am am C->am D D D->d#° f#° f#° D->f#° f#°->am a°->am

view full size

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 733 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1207
Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
3rd mode:
Scale 2651
Scale 2651: Panian, Ian Ring Music TheoryPanian
4th mode:
Scale 3373
Scale 3373: Lodian, Ian Ring Music TheoryLodian
5th mode:
Scale 1867
Scale 1867: Solian, Ian Ring Music TheorySolian
6th mode:
Scale 2981
Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
7th mode:
Scale 1769
Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [733, 1207, 2651, 3373, 1867, 2981, 1769] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 733 is 1897

Scale 1897Scale 1897: Ionopian, Ian Ring Music TheoryIonopian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 733 is chiral, and its enantiomorph is scale 1897

Scale 1897Scale 1897: Ionopian, Ian Ring Music TheoryIonopian

Transformations:

T0 733  T0I 1897
T1 1466  T1I 3794
T2 2932  T2I 3493
T3 1769  T3I 2891
T4 3538  T4I 1687
T5 2981  T5I 3374
T6 1867  T6I 2653
T7 3734  T7I 1211
T8 3373  T8I 2422
T9 2651  T9I 749
T10 1207  T10I 1498
T11 2414  T11I 2996

Nearby Scales:

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 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 729Scale 729: Stygimic, Ian Ring Music TheoryStygimic
Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian
Scale 725Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani
Scale 717Scale 717: Raga Vijayanagari, Ian Ring Music TheoryRaga Vijayanagari
Scale 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian
Scale 765Scale 765, Ian Ring Music Theory
Scale 669Scale 669: Gycrimic, Ian Ring Music TheoryGycrimic
Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian
Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic
Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian
Scale 989Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
Scale 221Scale 221, Ian Ring Music Theory
Scale 477Scale 477: Stacrian, Ian Ring Music TheoryStacrian
Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian
Scale 1757Scale 1757, Ian Ring Music Theory
Scale 2781Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic

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.