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Scale 471: "Dodian"

Scale 471: Dodian, 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
Dodian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,6,7,8}
Forte Number7-15
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector442443
Interval Spectrump4m4n2s4d4t3
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {8,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tones[8]
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 TriadsC{0,4,7}221
Minor Triadsc♯m{1,4,8}221
Augmented TriadsC+{0,4,8}221
Diminished Triadsc♯°{1,4,7}221
Parsimonious Voice Leading Between Common Triads of Scale 471. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m c#°->c#m

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 471 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2283
Scale 2283: Aeolyptian, Ian Ring Music TheoryAeolyptian
3rd mode:
Scale 3189
Scale 3189: Aeolonian, Ian Ring Music TheoryAeolonian
4th mode:
Scale 1821
Scale 1821: Aeradian, Ian Ring Music TheoryAeradian
5th mode:
Scale 1479
Scale 1479: Mela Jalarnava, Ian Ring Music TheoryMela Jalarnava
6th mode:
Scale 2787
Scale 2787: Zyrian, Ian Ring Music TheoryZyrian
7th mode:
Scale 3441
Scale 3441: Thacrian, Ian Ring Music TheoryThacrian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [471, 2283, 3189, 1821, 1479, 2787, 3441] (Forte: 7-15) is the complement of the pentatonic modal family [327, 453, 1137, 2211, 3153] (Forte: 5-15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 471 is 3441

Scale 3441Scale 3441: Thacrian, Ian Ring Music TheoryThacrian

Transformations:

T0 471  T0I 3441
T1 942  T1I 2787
T2 1884  T2I 1479
T3 3768  T3I 2958
T4 3441  T4I 1821
T5 2787  T5I 3642
T6 1479  T6I 3189
T7 2958  T7I 2283
T8 1821  T8I 471
T9 3642  T9I 942
T10 3189  T10I 1884
T11 2283  T11I 3768

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 469Scale 469: Katyrimic, Ian Ring Music TheoryKatyrimic
Scale 467Scale 467: Raga Dhavalangam, Ian Ring Music TheoryRaga Dhavalangam
Scale 475Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian
Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic
Scale 455Scale 455: Messiaen Mode 5, Ian Ring Music TheoryMessiaen Mode 5
Scale 463Scale 463: Zythian, Ian Ring Music TheoryZythian
Scale 487Scale 487: Dynian, Ian Ring Music TheoryDynian
Scale 503Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic
Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic
Scale 215Scale 215, Ian Ring Music Theory
Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian
Scale 983Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic
Scale 1495Scale 1495: Messiaen Mode 6, Ian Ring Music TheoryMessiaen Mode 6
Scale 2519Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic

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.