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Scale 379: "Aeragian"

Scale 379: Aeragian, 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

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
Aeragian

Analysis

Cardinality

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

7 (heptatonic)

Pitch Class Set

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

{0,1,3,4,5,6,8}

Forte Number

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

7-11

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: 3025

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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.

3

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.

6

Prime Form

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

yes

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, 2, 1, 1, 1, 2, 4]

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.

<4, 4, 4, 4, 4, 1>

Interval Spectrum

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

p4m4n4s4d4t

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> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}

Spectra Variation

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

3.143

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.

2.299

Polygon Perimeter

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

5.803

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♯{1,5,8}241.83
G♯{8,0,3}231.5
Minor Triadsc♯m{1,4,8}231.5
fm{5,8,0}231.5
Augmented TriadsC+{0,4,8}321.17
Diminished Triads{0,3,6}142.17
Parsimonious Voice Leading Between Common Triads of Scale 379. Created by Ian Ring ©2019 G# G# c°->G# C+ C+ c#m c#m C+->c#m fm fm C+->fm C+->G# C# C# c#m->C# C#->fm

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
Radius2
Self-Centeredno
Central VerticesC+
Peripheral Verticesc°, C♯

Modes

Modes are the rotational transformation of this scale. Scale 379 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2237
Scale 2237: Epothian, Ian Ring Music TheoryEpothian
3rd mode:
Scale 1583
Scale 1583: Salian, Ian Ring Music TheorySalian
4th mode:
Scale 2839
Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
5th mode:
Scale 3467
Scale 3467: Katonian, Ian Ring Music TheoryKatonian
6th mode:
Scale 3781
Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
7th mode:
Scale 1969
Scale 1969: Stylian, Ian Ring Music TheoryStylian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [379, 2237, 1583, 2839, 3467, 3781, 1969] (Forte: 7-11) is the complement of the pentatonic modal family [157, 929, 1063, 2579, 3337] (Forte: 5-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 379 is 3025

Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 379 is chiral, and its enantiomorph is scale 3025

Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian

Transformations:

T0 379  T0I 3025
T1 758  T1I 1955
T2 1516  T2I 3910
T3 3032  T3I 3725
T4 1969  T4I 3355
T5 3938  T5I 2615
T6 3781  T6I 1135
T7 3467  T7I 2270
T8 2839  T8I 445
T9 1583  T9I 890
T10 3166  T10I 1780
T11 2237  T11I 3560

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 377Scale 377: Kathimic, Ian Ring Music TheoryKathimic
Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian
Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic
Scale 371Scale 371: Rythimic, Ian Ring Music TheoryRythimic
Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian
Scale 363Scale 363: Soptimic, Ian Ring Music TheorySoptimic
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian
Scale 507Scale 507: Moryllic, Ian Ring Music TheoryMoryllic
Scale 123Scale 123, Ian Ring Music Theory
Scale 251Scale 251, Ian Ring Music Theory
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 891Scale 891: Ionilyllic, Ian Ring Music TheoryIonilyllic
Scale 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale
Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic

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.