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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

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
Aeodyllic

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

8 (octatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,1,2,3,4,6,7,10}

Forte Number

A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

8-12

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 3941

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

5 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

3 (tricohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

4

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

7

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 763

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[1, 1, 1, 1, 2, 1, 3, 2] 9

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<5, 5, 6, 5, 4, 3>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.

p4m5n6s5d5t3

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<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 Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.5

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.616

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.002

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

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

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.

Diameter4
Radius4
Self-Centeredyes

Triadic Polychords

There is 1 way that this hexatonic scale can be split into two common triads.


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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. 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.