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Scale 2457: "Augmented"

Scale 2457: Augmented, Ian Ring Music Theory
This highly symmetrical scale is constructed from two interlocked augmented triads. Often referred to as just "The Augmented Scale" or "Augmented Hexatonic", it was used prominently used in Liszt's Faust Symphony. It is sometimes confused with another scale which is nicknamed Major Augmented, the 3rd mode of the Harmonic Minor.

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

Western Modern
Augmented
Messiaen
Messiaen Truncated Mode 3 Inverse
Ancient Greek
Genus Tertium
Carnatic Raga
Raga Devamani
Zeitler
Ionythimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,7,8,11}
Forte Number6-20
Rotational Symmetry4, 8 semitones
Reflection Axes1.5, 3.5, 5.5
Palindromicno
Chiralityno
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes1
Prime?no
prime: 819
Deep Scaleno
Interval Vector303630
Interval Spectrump3m6n3d3
Distribution Spectra<1> = {1,3}
<2> = {4}
<3> = {5,7}
<4> = {8}
<5> = {9,11}
Spectra Variation1
Maximally Evenno
Maximal Area Setno
Interior Area2.25
Myhill Propertyno
Balancedyes
Ridge Tones[3,7,11]
ProprietyStrictly Proper
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}331.5
E{4,8,11}331.5
G♯{8,0,3}331.5
Minor Triadscm{0,3,7}331.5
em{4,7,11}331.5
g♯m{8,11,3}331.5
Augmented TriadsC+{0,4,8}331.5
D♯+{3,7,11}331.5
Parsimonious Voice Leading Between Common Triads of Scale 2457. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E C+->G# D#+->em g#m g#m D#+->g#m em->E E->g#m g#m->G#

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2457 can be rotated to make 1 other scales. The 1st mode is itself.

2nd mode:
Scale 819
Scale 819: Augmented Inverse, Ian Ring Music TheoryAugmented InverseThis is the prime mode

Prime

The prime form of this scale is Scale 819

Scale 819Scale 819: Augmented Inverse, Ian Ring Music TheoryAugmented Inverse

Complement

The hexatonic modal family [2457, 819] (Forte: 6-20) is the complement of the hexatonic modal family [819, 2457] (Forte: 6-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2457 is 819

Scale 819Scale 819: Augmented Inverse, Ian Ring Music TheoryAugmented Inverse

Transformations:

T0 2457  T0I 819
T1 819  T1I 1638
T2 1638  T2I 3276
T3 3276  T3I 2457
T4 2457  T4I 819
T5 819  T5I 1638
T6 1638  T6I 3276
T7 3276  T7I 2457
T8 2457  T8I 819
T9 819  T9I 1638
T10 1638  T10I 3276
T11 3276  T11I 2457

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 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian
Scale 2461Scale 2461: Sagian, Ian Ring Music TheorySagian
Scale 2449Scale 2449: Zacritonic, Ian Ring Music TheoryZacritonic
Scale 2453Scale 2453: Raga Latika, Ian Ring Music TheoryRaga Latika
Scale 2441Scale 2441: Kyritonic, Ian Ring Music TheoryKyritonic
Scale 2473Scale 2473: Raga Takka, Ian Ring Music TheoryRaga Takka
Scale 2489Scale 2489: Mela Gangeyabhusani, Ian Ring Music TheoryMela Gangeyabhusani
Scale 2521Scale 2521: Mela Dhatuvardhani, Ian Ring Music TheoryMela Dhatuvardhani
Scale 2329Scale 2329: Styditonic, Ian Ring Music TheoryStyditonic
Scale 2393Scale 2393: Zathimic, Ian Ring Music TheoryZathimic
Scale 2201Scale 2201: Ionagitonic, Ian Ring Music TheoryIonagitonic
Scale 2713Scale 2713: Porimic, Ian Ring Music TheoryPorimic
Scale 2969Scale 2969: Tholian, Ian Ring Music TheoryTholian
Scale 3481Scale 3481: Katathian, Ian Ring Music TheoryKatathian
Scale 409Scale 409: Laritonic, Ian Ring Music TheoryLaritonic
Scale 1433Scale 1433: Dynimic, Ian Ring Music TheoryDynimic

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.