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Scale 2869: "Major Augmented"

Scale 2869: Major Augmented, Ian Ring Music Theory
So called because of its augmented fifth, The Major Augmented scale is the 3rd mode of the Harmonic Minor. Not to be confused with the Augmented Scale.

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

Western Modern
Major Augmented
Ionian Augmented
Western Altered
Ionian Sharp 5
Zeitler
Phrothian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,4,5,8,9,11}
Forte Number7-32
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1435
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes6
Prime?no
prime: 859
Deep Scaleno
Interval Vector335442
Interval Spectrump4m4n5s3d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9}
<6> = {9,10,11}
Spectra Variation1.429
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
Heliotonicyes

Harmonic Chords

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 TriadsE{4,8,11}331.8
F{5,9,0}331.7
Minor Triadsdm{2,5,9}331.8
fm{5,8,0}431.6
am{9,0,4}232
Augmented TriadsC+{0,4,8}331.7
Diminished Triads{2,5,8}231.9
{5,8,11}231.9
g♯°{8,11,2}232
{11,2,5}232
Parsimonious Voice Leading Between Common Triads of Scale 2869. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm am am C+->am dm dm d°->dm d°->fm F F dm->F dm->b° E->f° g#° g#° E->g#° f°->fm fm->F F->am g#°->b°

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 2869 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1741
Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
3rd mode:
Scale 1459
Scale 1459: Phrygian Dominant, Ian Ring Music TheoryPhrygian Dominant
4th mode:
Scale 2777
Scale 2777: Aeolian Harmonic, Ian Ring Music TheoryAeolian Harmonic
5th mode:
Scale 859
Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrianThis is the prime mode
6th mode:
Scale 2477
Scale 2477: Harmonic Minor, Ian Ring Music TheoryHarmonic Minor
7th mode:
Scale 1643
Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6

Prime

The prime form of this scale is Scale 859

Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian

Complement

The heptatonic modal family [2869, 1741, 1459, 2777, 859, 2477, 1643] (Forte: 7-32) is the complement of the pentatonic modal family [595, 665, 805, 1225, 2345] (Forte: 5-32)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2869 is 1435

Scale 1435Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2869 is chiral, and its enantiomorph is scale 1435

Scale 1435Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam

Transformations:

T0 2869  T0I 1435
T1 1643  T1I 2870
T2 3286  T2I 1645
T3 2477  T3I 3290
T4 859  T4I 2485
T5 1718  T5I 875
T6 3436  T6I 1750
T7 2777  T7I 3500
T8 1459  T8I 2905
T9 2918  T9I 1715
T10 1741  T10I 3430
T11 3482  T11I 2765

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 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 2865Scale 2865: Solimic, Ian Ring Music TheorySolimic
Scale 2867Scale 2867: Socrian, Ian Ring Music TheorySocrian
Scale 2873Scale 2873: Ionian Augmented Sharp 2, Ian Ring Music TheoryIonian Augmented Sharp 2
Scale 2877Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic
Scale 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 2837Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
Scale 2901Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented
Scale 2933Scale 2933, Ian Ring Music Theory
Scale 2997Scale 2997: Major Bebop, Ian Ring Music TheoryMajor Bebop
Scale 2613Scale 2613: Raga Hamsa Vinodini, Ian Ring Music TheoryRaga Hamsa Vinodini
Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor
Scale 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 821Scale 821: Aeranimic, Ian Ring Music TheoryAeranimic
Scale 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian

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.