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Scale 3349: "Aeolocrimic"

Scale 3349: Aeolocrimic, 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
Aeolocrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,4,8,10,11}
Forte Number6-21
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1303
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections5
Modes5
Prime?no
prime: 349
Deep Scaleno
Interval Vector242412
Interval Spectrumpm4n2s4d2t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {8,10,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.232
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 TriadsE{4,8,11}210.67
Augmented TriadsC+{0,4,8}121
Diminished Triadsg♯°{8,11,2}121
Parsimonious Voice Leading Between Common Triads of Scale 3349. Created by Ian Ring ©2019 C+ C+ E E C+->E g#° g#° E->g#°

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
Radius1
Self-Centeredno
Central VerticesE
Peripheral VerticesC+, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 3349 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1861
Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
3rd mode:
Scale 1489
Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti
4th mode:
Scale 349
Scale 349: Borimic, Ian Ring Music TheoryBorimicThis is the prime mode
5th mode:
Scale 1111
Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic
6th mode:
Scale 2603
Scale 2603: Gadimic, Ian Ring Music TheoryGadimic

Prime

The prime form of this scale is Scale 349

Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic

Complement

The hexatonic modal family [3349, 1861, 1489, 349, 1111, 2603] (Forte: 6-21) is the complement of the hexatonic modal family [349, 1111, 1489, 1861, 2603, 3349] (Forte: 6-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3349 is 1303

Scale 1303Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3349 is chiral, and its enantiomorph is scale 1303

Scale 1303Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic

Transformations:

T0 3349  T0I 1303
T1 2603  T1I 2606
T2 1111  T2I 1117
T3 2222  T3I 2234
T4 349  T4I 373
T5 698  T5I 746
T6 1396  T6I 1492
T7 2792  T7I 2984
T8 1489  T8I 1873
T9 2978  T9I 3746
T10 1861  T10I 3397
T11 3722  T11I 2699

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 3351Scale 3351: Karian, Ian Ring Music TheoryKarian
Scale 3345Scale 3345: Zylitonic, Ian Ring Music TheoryZylitonic
Scale 3347Scale 3347: Synimic, Ian Ring Music TheorySynimic
Scale 3353Scale 3353: Phraptimic, Ian Ring Music TheoryPhraptimic
Scale 3357Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian
Scale 3333Scale 3333, Ian Ring Music Theory
Scale 3341Scale 3341, Ian Ring Music Theory
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian
Scale 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
Scale 3477Scale 3477: Kyptian, Ian Ring Music TheoryKyptian
Scale 3093Scale 3093, Ian Ring Music Theory
Scale 3221Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic
Scale 3605Scale 3605, Ian Ring Music Theory
Scale 3861Scale 3861: Phroptian, Ian Ring Music TheoryPhroptian
Scale 2325Scale 2325: Pynitonic, Ian Ring Music TheoryPynitonic
Scale 2837Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
Scale 1301Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic

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.