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Scale 415: "Aeoladian"

Scale 415: Aeoladian, 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
Aeoladian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,4,7,8}
Forte Number7-6
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3889
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector533442
Interval Spectrump4m4n3s3d5t2
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {7,8,10}
<6> = {8,9,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.183
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 TriadsC{0,4,7}321.17
G♯{8,0,3}231.5
Minor Triadscm{0,3,7}231.5
c♯m{1,4,8}231.5
Augmented TriadsC+{0,4,8}321.17
Diminished Triadsc♯°{1,4,7}231.5
Parsimonious Voice Leading Between Common Triads of Scale 415. Created by Ian Ring ©2019 cm cm C C cm->C G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m C+->G# 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.

Diameter3
Radius2
Self-Centeredno
Central VerticesC, C+
Peripheral Verticescm, c♯°, c♯m, G♯

Modes

Modes are the rotational transformation of this scale. Scale 415 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2255
Scale 2255: Dylian, Ian Ring Music TheoryDylian
3rd mode:
Scale 3175
Scale 3175: Eponian, Ian Ring Music TheoryEponian
4th mode:
Scale 3635
Scale 3635: Katygian, Ian Ring Music TheoryKatygian
5th mode:
Scale 3865
Scale 3865: Starian, Ian Ring Music TheoryStarian
6th mode:
Scale 995
Scale 995: Phrathian, Ian Ring Music TheoryPhrathian
7th mode:
Scale 2545
Scale 2545: Thycrian, Ian Ring Music TheoryThycrian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [415, 2255, 3175, 3635, 3865, 995, 2545] (Forte: 7-6) is the complement of the pentatonic modal family [103, 899, 2099, 2497, 3097] (Forte: 5-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 415 is 3889

Scale 3889Scale 3889: Parian, Ian Ring Music TheoryParian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 415 is chiral, and its enantiomorph is scale 3889

Scale 3889Scale 3889: Parian, Ian Ring Music TheoryParian

Transformations:

T0 415  T0I 3889
T1 830  T1I 3683
T2 1660  T2I 3271
T3 3320  T3I 2447
T4 2545  T4I 799
T5 995  T5I 1598
T6 1990  T6I 3196
T7 3980  T7I 2297
T8 3865  T8I 499
T9 3635  T9I 998
T10 3175  T10I 1996
T11 2255  T11I 3992

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 413Scale 413: Ganimic, Ian Ring Music TheoryGanimic
Scale 411Scale 411: Lygimic, Ian Ring Music TheoryLygimic
Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic
Scale 399Scale 399: Zynimic, Ian Ring Music TheoryZynimic
Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian
Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic
Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic
Scale 287Scale 287: Gynimic, Ian Ring Music TheoryGynimic
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 159Scale 159, Ian Ring Music Theory
Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian
Scale 927Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllic
Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic

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.