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Scale 2777: "Aeolian Harmonic"

Scale 2777: Aeolian Harmonic, 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

Western Modern
Aeolian Harmonic
Western Altered
Lydian Sharp 2
Carnatic Mela
Mela Kosalam
Carnatic Raga
Raga Kusumakaram
Zeitler
Bycrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,4,6,7,9,11}
Forte Number7-32
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 875
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 TriadsC{0,4,7}331.7
B{11,3,6}331.8
Minor Triadscm{0,3,7}431.6
em{4,7,11}232
am{9,0,4}331.8
Augmented TriadsD♯+{3,7,11}331.7
Diminished Triads{0,3,6}231.9
d♯°{3,6,9}232
f♯°{6,9,0}232
{9,0,3}231.9
Parsimonious Voice Leading Between Common Triads of Scale 2777. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ cm->a° em em C->em am am C->am d#° d#° f#° f#° d#°->f#° d#°->B D#+->em D#+->B f#°->am a°->am

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 2777 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 859
Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrianThis is the prime mode
3rd mode:
Scale 2477
Scale 2477: Harmonic Minor, Ian Ring Music TheoryHarmonic Minor
4th mode:
Scale 1643
Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
5th mode:
Scale 2869
Scale 2869: Major Augmented, Ian Ring Music TheoryMajor Augmented
6th mode:
Scale 1741
Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
7th mode:
Scale 1459
Scale 1459: Phrygian Dominant, Ian Ring Music TheoryPhrygian Dominant

Prime

The prime form of this scale is Scale 859

Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian

Complement

The heptatonic modal family [2777, 859, 2477, 1643, 2869, 1741, 1459] (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 2777 is 875

Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2777 is chiral, and its enantiomorph is scale 875

Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7

Transformations:

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

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 2779Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich
Scale 2781Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
Scale 2769Scale 2769: Dyrimic, Ian Ring Music TheoryDyrimic
Scale 2773Scale 2773: Lydian, Ian Ring Music TheoryLydian
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 2793Scale 2793: Eporian, Ian Ring Music TheoryEporian
Scale 2809Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
Scale 2713Scale 2713: Porimic, Ian Ring Music TheoryPorimic
Scale 2745Scale 2745: Mela Sulini, Ian Ring Music TheoryMela Sulini
Scale 2649Scale 2649: Aeolythimic, Ian Ring Music TheoryAeolythimic
Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
Scale 2265Scale 2265: Raga Rasamanjari, Ian Ring Music TheoryRaga Rasamanjari
Scale 2521Scale 2521: Mela Dhatuvardhani, Ian Ring Music TheoryMela Dhatuvardhani
Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 729Scale 729: Stygimic, Ian Ring Music TheoryStygimic
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major

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.