The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3227: "Aeolocrian"

Scale 3227: Aeolocrian, 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
Aeolocrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,7,10,11}
Forte Number7-16
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2855
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 623
Deep Scaleno
Interval Vector435432
Interval Spectrump3m4n5s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,8,9,10}
<6> = {9,10,11}
Spectra Variation2.857
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 TriadsC{0,4,7}331.67
D♯{3,7,10}331.67
Minor Triadscm{0,3,7}231.89
em{4,7,11}331.67
Augmented TriadsD♯+{3,7,11}331.67
Diminished Triadsc♯°{1,4,7}231.89
{4,7,10}231.89
{7,10,1}231.89
a♯°{10,1,4}232
Parsimonious Voice Leading Between Common Triads of Scale 3227. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ c#° c#° C->c#° em em C->em a#° a#° c#°->a#° D# D# D#->D#+ D#->e° D#->g° D#+->em e°->em g°->a#°

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3227 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3661
Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
3rd mode:
Scale 1939
Scale 1939: Dathian, Ian Ring Music TheoryDathian
4th mode:
Scale 3017
Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
5th mode:
Scale 889
Scale 889: Borian, Ian Ring Music TheoryBorian
6th mode:
Scale 623
Scale 623: Sycrian, Ian Ring Music TheorySycrianThis is the prime mode
7th mode:
Scale 2359
Scale 2359: Gadian, Ian Ring Music TheoryGadian

Prime

The prime form of this scale is Scale 623

Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian

Complement

The heptatonic modal family [3227, 3661, 1939, 3017, 889, 623, 2359] (Forte: 7-16) is the complement of the pentatonic modal family [155, 865, 1555, 2125, 2825] (Forte: 5-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3227 is 2855

Scale 2855Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3227 is chiral, and its enantiomorph is scale 2855

Scale 2855Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain

Transformations:

T0 3227  T0I 2855
T1 2359  T1I 1615
T2 623  T2I 3230
T3 1246  T3I 2365
T4 2492  T4I 635
T5 889  T5I 1270
T6 1778  T6I 2540
T7 3556  T7I 985
T8 3017  T8I 1970
T9 1939  T9I 3940
T10 3878  T10I 3785
T11 3661  T11I 3475

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 3225Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic
Scale 3229Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian
Scale 3231Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
Scale 3219Scale 3219: Ionaphimic, Ian Ring Music TheoryIonaphimic
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3211Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3259Scale 3259, Ian Ring Music Theory
Scale 3291Scale 3291: Lygyllic, Ian Ring Music TheoryLygyllic
Scale 3099Scale 3099, Ian Ring Music Theory
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3355Scale 3355: Bagian, Ian Ring Music TheoryBagian
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
Scale 2203Scale 2203: Dorimic, Ian Ring Music TheoryDorimic
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 1179Scale 1179: Sonimic, Ian Ring Music TheorySonimic

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.