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Scale 3301: "Chromatic Mixolydian Inverse"

Scale 3301: Chromatic Mixolydian Inverse, 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

Western Chromatic
Chromatic Mixolydian Inverse
Zeitler
Phrynian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,5,6,7,10,11}
Forte Number7-20
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1255
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?no
prime: 743
Deep Scaleno
Interval Vector433452
Interval Spectrump5m4n3s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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 TriadsG{7,11,2}231.5
A♯{10,2,5}231.5
Minor Triadsgm{7,10,2}231.5
bm{11,2,6}321.17
Augmented TriadsD+{2,6,10}321.17
Diminished Triads{11,2,5}231.5
Parsimonious Voice Leading Between Common Triads of Scale 3301. Created by Ian Ring ©2019 D+ D+ gm gm D+->gm A# A# D+->A# bm bm D+->bm Parsimonious Voice Leading Between Common Triads of Scale 3301. Created by Ian Ring ©2019 G gm->G G->bm A#->b° b°->bm

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
Radius2
Self-Centeredno
Central VerticesD+, bm
Peripheral Verticesgm, G, A♯, b°

Modes

Modes are the rotational transformation of this scale. Scale 3301 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1849
Scale 1849: Chromatic Hypodorian Inverse, Ian Ring Music TheoryChromatic Hypodorian Inverse
3rd mode:
Scale 743
Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian InverseThis is the prime mode
4th mode:
Scale 2419
Scale 2419: Raga Lalita, Ian Ring Music TheoryRaga Lalita
5th mode:
Scale 3257
Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata
6th mode:
Scale 919
Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse
7th mode:
Scale 2507
Scale 2507: Todi That, Ian Ring Music TheoryTodi That

Prime

The prime form of this scale is Scale 743

Scale 743Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian Inverse

Complement

The heptatonic modal family [3301, 1849, 743, 2419, 3257, 919, 2507] (Forte: 7-20) is the complement of the pentatonic modal family [355, 395, 1585, 2225, 2245] (Forte: 5-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3301 is 1255

Scale 1255Scale 1255: Chromatic Mixolydian, Ian Ring Music TheoryChromatic Mixolydian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3301 is chiral, and its enantiomorph is scale 1255

Scale 1255Scale 1255: Chromatic Mixolydian, Ian Ring Music TheoryChromatic Mixolydian

Transformations:

T0 3301  T0I 1255
T1 2507  T1I 2510
T2 919  T2I 925
T3 1838  T3I 1850
T4 3676  T4I 3700
T5 3257  T5I 3305
T6 2419  T6I 2515
T7 743  T7I 935
T8 1486  T8I 1870
T9 2972  T9I 3740
T10 1849  T10I 3385
T11 3698  T11I 2675

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 3303Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic
Scale 3297Scale 3297, Ian Ring Music Theory
Scale 3299Scale 3299: Syptian, Ian Ring Music TheorySyptian
Scale 3305Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
Scale 3309Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
Scale 3317Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic
Scale 3269Scale 3269: Raga Malarani, Ian Ring Music TheoryRaga Malarani
Scale 3285Scale 3285: Mela Citrambari, Ian Ring Music TheoryMela Citrambari
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3557Scale 3557, Ian Ring Music Theory
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 2277Scale 2277: Kagimic, Ian Ring Music TheoryKagimic
Scale 2789Scale 2789: Zolian, Ian Ring Music TheoryZolian
Scale 1253Scale 1253: Zolimic, Ian Ring Music TheoryZolimic

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.