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Scale 4093: "Aerycratic"

Scale 4093: Aerycratic, 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
Aerycratic

Analysis

Cardinality11 (undecatonic)
Pitch Class Set{0,2,3,4,5,6,7,8,9,10,11}
Forte Number11-1
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia10 (multihemitonic)
Cohemitonia9 (multicohemitonic)
Imperfections1
Modes10
Prime?no
prime: 2047
Deep Scaleno
Interval Vector10101010105
Interval Spectrump10m10n10s10d10t5
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5}
<5> = {5,6}
<6> = {6,7}
<7> = {7,8}
<8> = {8,9}
<9> = {9,10}
<10> = {10,11}
Spectra Variation0.909
Maximally Evenyes
Maximal Area Setyes
Interior Area2.933
Myhill Propertyyes
Balancedno
Ridge Tones[2]
ProprietyProper
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}353
D{2,6,9}453.07
D♯{3,7,10}452.87
E{4,8,11}452.93
F{5,9,0}453.1
G{7,11,2}452.87
G♯{8,0,3}452.93
A♯{10,2,5}353.13
B{11,3,6}452.8
Minor Triadscm{0,3,7}452.87
dm{2,5,9}453.1
d♯m{3,6,10}452.93
em{4,7,11}452.87
fm{5,8,0}453.07
gm{7,10,2}353
g♯m{8,11,3}452.8
am{9,0,4}353.13
bm{11,2,6}452.93
Augmented TriadsC+{0,4,8}552.9
D+{2,6,10}552.9
D♯+{3,7,11}652.6
Diminished Triads{0,3,6}253.2
{2,5,8}253.3
d♯°{3,6,9}253.3
{4,7,10}253.27
{5,8,11}253.3
f♯°{6,9,0}253.3
g♯°{8,11,2}253.2
{9,0,3}253.37
{11,2,5}253.37
Parsimonious Voice Leading Between Common Triads of Scale 4093. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm C+->G# am am C+->am dm dm d°->dm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m gm gm D+->gm D+->A# bm bm D+->bm d#°->d#m D# D# d#m->D# d#m->B D#->D#+ D#->e° D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 4093. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B e°->em em->E E->f° E->g#m f°->fm fm->F F->f#° F->am gm->G g#° g#° G->g#° G->bm g#°->g#m g#m->G# G#->a° a°->am A#->b° b°->bm bm->B

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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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 4093 can be rotated to make 10 other scales. The 1st mode is itself.

2nd mode:
Scale 2047
Scale 2047: Monatic, Ian Ring Music TheoryMonaticThis is the prime mode
3rd mode:
Scale 3071
Scale 3071: Solatic, Ian Ring Music TheorySolatic
4th mode:
Scale 3583
Scale 3583: Zylatic, Ian Ring Music TheoryZylatic
5th mode:
Scale 3839
Scale 3839: Mixolatic, Ian Ring Music TheoryMixolatic
6th mode:
Scale 3967
Scale 3967: Soratic, Ian Ring Music TheorySoratic
7th mode:
Scale 4031
Scale 4031: Godatic, Ian Ring Music TheoryGodatic
8th mode:
Scale 4063
Scale 4063: Eptatic, Ian Ring Music TheoryEptatic
9th mode:
Scale 4079
Scale 4079: Ionatic, Ian Ring Music TheoryIonatic
10th mode:
Scale 4087
Scale 4087: Aeolatic, Ian Ring Music TheoryAeolatic
11th mode:
Scale 4091
Scale 4091: Thydatic, Ian Ring Music TheoryThydatic

Prime

The prime form of this scale is Scale 2047

Scale 2047Scale 2047: Monatic, Ian Ring Music TheoryMonatic

Complement

The undecatonic modal family [4093, 2047, 3071, 3583, 3839, 3967, 4031, 4063, 4079, 4087, 4091] (Forte: 11-1) is the complement of the modal family [1] (Forte: 1-1)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4093 is 2047

Scale 2047Scale 2047: Monatic, Ian Ring Music TheoryMonatic

Transformations:

T0 4093  T0I 2047
T1 4091  T1I 4094
T2 4087  T2I 4093
T3 4079  T3I 4091
T4 4063  T4I 4087
T5 4031  T5I 4079
T6 3967  T6I 4063
T7 3839  T7I 4031
T8 3583  T8I 3967
T9 3071  T9I 3839
T10 2047  T10I 3583
T11 4094  T11I 3071

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 4095Scale 4095: Chromatic, Ian Ring Music TheoryChromatic
Scale 4089Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian
Scale 4091Scale 4091: Thydatic, Ian Ring Music TheoryThydatic
Scale 4085Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 4061Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
Scale 4029Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed
Scale 3965Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse
Scale 3837Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
Scale 3581Scale 3581: Epocryllian, Ian Ring Music TheoryEpocryllian
Scale 3069Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza
Scale 2045Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian

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.