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Scale 1247: "Aeodyllic"

Scale 1247: Aeodyllic, 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
Aeodyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,6,7,10}
Forte Number8-12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3941
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 763
Deep Scaleno
Interval Vector556543
Interval Spectrump4m5n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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}342.17
D♯{3,7,10}441.83
F♯{6,10,1}342.17
Minor Triadscm{0,3,7}342
d♯m{3,6,10}342
gm{7,10,2}342
Augmented TriadsD+{2,6,10}342
Diminished Triads{0,3,6}242.33
c♯°{1,4,7}242.33
{4,7,10}242.17
{7,10,1}242.33
a♯°{10,1,4}242.33
Parsimonious Voice Leading Between Common Triads of Scale 1247. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# c#° c#° C->c#° C->e° a#° a#° c#°->a#° D+ D+ D+->d#m F# F# D+->F# gm gm D+->gm d#m->D# D#->e° D#->gm F#->g° F#->a#° g°->gm

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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 1247 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2671
Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
3rd mode:
Scale 3383
Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
4th mode:
Scale 3739
Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
5th mode:
Scale 3917
Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
6th mode:
Scale 2003
Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
7th mode:
Scale 3049
Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
8th mode:
Scale 893
Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic

Prime

The prime form of this scale is Scale 763

Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic

Complement

The octatonic modal family [1247, 2671, 3383, 3739, 3917, 2003, 3049, 893] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1247 is 3941

Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1247 is chiral, and its enantiomorph is scale 3941

Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic

Transformations:

T0 1247  T0I 3941
T1 2494  T1I 3787
T2 893  T2I 3479
T3 1786  T3I 2863
T4 3572  T4I 1631
T5 3049  T5I 3262
T6 2003  T6I 2429
T7 4006  T7I 763
T8 3917  T8I 1526
T9 3739  T9I 3052
T10 3383  T10I 2009
T11 2671  T11I 4018

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 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian
Scale 1243Scale 1243: Epylian, Ian Ring Music TheoryEpylian
Scale 1239Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
Scale 1231Scale 1231: Logian, Ian Ring Music TheoryLogian
Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic
Scale 1279Scale 1279: Sarygic, Ian Ring Music TheorySarygic
Scale 1183Scale 1183: Sadian, Ian Ring Music TheorySadian
Scale 1215Scale 1215, Ian Ring Music Theory
Scale 1119Scale 1119: Rarian, Ian Ring Music TheoryRarian
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic
Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 223Scale 223, Ian Ring Music Theory
Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic

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.