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Scale 3793: "Aeopian"

Scale 3793: Aeopian, 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
Aeopian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,4,6,7,9,10,11}
Forte Number7-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 367
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 367
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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}221.2
Minor Triadsem{4,7,11}231.4
am{9,0,4}231.4
Diminished Triads{4,7,10}142
f♯°{6,9,0}142
Parsimonious Voice Leading Between Common Triads of Scale 3793. Created by Ian Ring ©2019 C C em em C->em am am C->am e°->em f#° f#° f#°->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.

Diameter4
Radius2
Self-Centeredno
Central VerticesC
Peripheral Verticese°, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 3793 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 493
Scale 493: Rygian, Ian Ring Music TheoryRygian
3rd mode:
Scale 1147
Scale 1147: Epynian, Ian Ring Music TheoryEpynian
4th mode:
Scale 2621
Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
5th mode:
Scale 1679
Scale 1679: Kydian, Ian Ring Music TheoryKydian
6th mode:
Scale 2887
Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
7th mode:
Scale 3491
Scale 3491: Tharian, Ian Ring Music TheoryTharian

Prime

The prime form of this scale is Scale 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Complement

The heptatonic modal family [3793, 493, 1147, 2621, 1679, 2887, 3491] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3793 is 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3793 is chiral, and its enantiomorph is scale 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Transformations:

T0 3793  T0I 367
T1 3491  T1I 734
T2 2887  T2I 1468
T3 1679  T3I 2936
T4 3358  T4I 1777
T5 2621  T5I 3554
T6 1147  T6I 3013
T7 2294  T7I 1931
T8 493  T8I 3862
T9 986  T9I 3629
T10 1972  T10I 3163
T11 3944  T11I 2231

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 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 3777Scale 3777, Ian Ring Music Theory
Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 3825Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic
Scale 3729Scale 3729: Starimic, Ian Ring Music TheoryStarimic
Scale 3761Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri
Scale 3665Scale 3665: Stalimic, Ian Ring Music TheoryStalimic
Scale 3921Scale 3921: Pythian, Ian Ring Music TheoryPythian
Scale 4049Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic
Scale 3281Scale 3281: Raga Vijayavasanta, Ian Ring Music TheoryRaga Vijayavasanta
Scale 3537Scale 3537: Katogian, Ian Ring Music TheoryKatogian
Scale 2769Scale 2769: Dyrimic, Ian Ring Music TheoryDyrimic
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari

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.