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Scale 2041: "Aeolacrygic"

Scale 2041: Aeolacrygic, 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
Aeolacrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,3,4,5,6,7,8,9,10}
Forte Number9-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1021
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 767
Deep Scaleno
Interval Vector777663
Interval Spectrump6m6n7s7d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {7,8,9,10}
<8> = {9,10,11}
Spectra Variation2.444
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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}342.14
D♯{3,7,10}342.29
F{5,9,0}342.43
G♯{8,0,3}342.14
Minor Triadscm{0,3,7}442.07
d♯m{3,6,10}342.43
fm{5,8,0}242.43
am{9,0,4}342.29
Augmented TriadsC+{0,4,8}442.07
Diminished Triads{0,3,6}242.43
d♯°{3,6,9}242.57
{4,7,10}242.5
f♯°{6,9,0}242.57
{9,0,3}242.5
Parsimonious Voice Leading Between Common Triads of Scale 2041. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ C->e° fm fm C+->fm C+->G# am am C+->am d#° d#° d#°->d#m f#° f#° d#°->f#° d#m->D# D#->e° F F fm->F F->f#° F->am G#->a° a°->am

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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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2041 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 767
Scale 767: Raptygic, Ian Ring Music TheoryRaptygicThis is the prime mode
3rd mode:
Scale 2431
Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
4th mode:
Scale 3263
Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
5th mode:
Scale 3679
Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
6th mode:
Scale 3887
Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
7th mode:
Scale 3991
Scale 3991: Badygic, Ian Ring Music TheoryBadygic
8th mode:
Scale 4043
Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
9th mode:
Scale 4069
Scale 4069: Starygic, Ian Ring Music TheoryStarygic

Prime

The prime form of this scale is Scale 767

Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic

Complement

The nonatonic modal family [2041, 767, 2431, 3263, 3679, 3887, 3991, 4043, 4069] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2041 is 1021

Scale 1021Scale 1021: Ladygic, Ian Ring Music TheoryLadygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2041 is chiral, and its enantiomorph is scale 1021

Scale 1021Scale 1021: Ladygic, Ian Ring Music TheoryLadygic

Transformations:

T0 2041  T0I 1021
T1 4082  T1I 2042
T2 4069  T2I 4084
T3 4043  T3I 4073
T4 3991  T4I 4051
T5 3887  T5I 4007
T6 3679  T6I 3919
T7 3263  T7I 3743
T8 2431  T8I 3391
T9 767  T9I 2687
T10 1534  T10I 1279
T11 3068  T11I 2558

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 2043Scale 2043: Maqam Tarzanuyn, Ian Ring Music TheoryMaqam Tarzanuyn
Scale 2045Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
Scale 2033Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic
Scale 2037Scale 2037: Sythygic, Ian Ring Music TheorySythygic
Scale 2025Scale 2025, Ian Ring Music Theory
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 1977Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
Scale 1913Scale 1913, Ian Ring Music Theory
Scale 1785Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
Scale 1529Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
Scale 1017Scale 1017: Dythyllic, Ian Ring Music TheoryDythyllic
Scale 3065Scale 3065: Zothygic, Ian Ring Music TheoryZothygic
Scale 4089Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.