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Scale 2251: "Zodimic"

Scale 2251: Zodimic, 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

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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
Zodimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,6,7,11}
Forte Number6-Z17
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2659
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 407
Deep Scaleno
Interval Vector322332
Interval Spectrump3m3n2s2d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5}
<3> = {4,6,8}
<4> = {7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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 TriadsB{11,3,6}221
Minor Triadscm{0,3,7}221
Augmented TriadsD♯+{3,7,11}221
Diminished Triads{0,3,6}221
Parsimonious Voice Leading Between Common Triads of Scale 2251. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ D#+->B

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.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2251 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3173
Scale 3173: Zarimic, Ian Ring Music TheoryZarimic
3rd mode:
Scale 1817
Scale 1817: Phrythimic, Ian Ring Music TheoryPhrythimic
4th mode:
Scale 739
Scale 739: Rorimic, Ian Ring Music TheoryRorimic
5th mode:
Scale 2417
Scale 2417: Kanimic, Ian Ring Music TheoryKanimic
6th mode:
Scale 407
Scale 407: Zylimic, Ian Ring Music TheoryZylimicThis is the prime mode

Prime

The prime form of this scale is Scale 407

Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic

Complement

The hexatonic modal family [2251, 3173, 1817, 739, 2417, 407] (Forte: 6-Z17) is the complement of the hexatonic modal family [359, 907, 1649, 2227, 2501, 3161] (Forte: 6-Z43)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2251 is 2659

Scale 2659Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2251 is chiral, and its enantiomorph is scale 2659

Scale 2659Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic

Transformations:

T0 2251  T0I 2659
T1 407  T1I 1223
T2 814  T2I 2446
T3 1628  T3I 797
T4 3256  T4I 1594
T5 2417  T5I 3188
T6 739  T6I 2281
T7 1478  T7I 467
T8 2956  T8I 934
T9 1817  T9I 1868
T10 3634  T10I 3736
T11 3173  T11I 3377

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 2249Scale 2249: Raga Multani, Ian Ring Music TheoryRaga Multani
Scale 2253Scale 2253: Raga Amarasenapriya, Ian Ring Music TheoryRaga Amarasenapriya
Scale 2255Scale 2255: Dylian, Ian Ring Music TheoryDylian
Scale 2243Scale 2243, Ian Ring Music Theory
Scale 2247Scale 2247: Raga Vijayasri, Ian Ring Music TheoryRaga Vijayasri
Scale 2259Scale 2259: Raga Mandari, Ian Ring Music TheoryRaga Mandari
Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian
Scale 2283Scale 2283: Aeolyptian, Ian Ring Music TheoryAeolyptian
Scale 2187Scale 2187: Ionothitonic, Ian Ring Music TheoryIonothitonic
Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 2379Scale 2379: Raga Gurjari Todi, Ian Ring Music TheoryRaga Gurjari Todi
Scale 2507Scale 2507: Todi That, Ian Ring Music TheoryTodi That
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
Scale 203Scale 203, Ian Ring Music Theory
Scale 1227Scale 1227: Thacrimic, Ian Ring Music TheoryThacrimic

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.