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Scale 749: "Aeologian"

Scale 749: Aeologian, 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

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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

Zeitler
Aeologian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,5,6,7,9}
Forte Number7-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1769
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 733
Deep Scaleno
Interval Vector345342
Interval Spectrump4m3n5s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
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 TriadsD{2,6,9}331.63
F{5,9,0}331.63
Minor Triadscm{0,3,7}231.88
dm{2,5,9}231.75
Diminished Triads{0,3,6}231.88
d♯°{3,6,9}231.75
f♯°{6,9,0}231.75
{9,0,3}231.75
Parsimonious Voice Leading Between Common Triads of Scale 749. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° cm->a° dm dm D D dm->D F F dm->F D->d#° f#° f#° D->f#° F->f#° F->a°

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

2nd mode:
Scale 1211
Scale 1211: Zadian, Ian Ring Music TheoryZadian
3rd mode:
Scale 2653
Scale 2653: Sygian, Ian Ring Music TheorySygian
4th mode:
Scale 1687
Scale 1687: Phralian, Ian Ring Music TheoryPhralian
5th mode:
Scale 2891
Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
6th mode:
Scale 3493
Scale 3493: Rathian, Ian Ring Music TheoryRathian
7th mode:
Scale 1897
Scale 1897: Ionopian, Ian Ring Music TheoryIonopian

Prime

The prime form of this scale is Scale 733

Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian

Complement

The heptatonic modal family [749, 1211, 2653, 1687, 2891, 3493, 1897] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 749 is 1769

Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 749 is chiral, and its enantiomorph is scale 1769

Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II

Transformations:

T0 749  T0I 1769
T1 1498  T1I 3538
T2 2996  T2I 2981
T3 1897  T3I 1867
T4 3794  T4I 3734
T5 3493  T5I 3373
T6 2891  T6I 2651
T7 1687  T7I 1207
T8 3374  T8I 2414
T9 2653  T9I 733
T10 1211  T10I 1466
T11 2422  T11I 2932

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 751Scale 751, Ian Ring Music Theory
Scale 745Scale 745: Kolimic, Ian Ring Music TheoryKolimic
Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian
Scale 741Scale 741: Gathimic, Ian Ring Music TheoryGathimic
Scale 757Scale 757: Ionyptian, Ian Ring Music TheoryIonyptian
Scale 765Scale 765, Ian Ring Music Theory
Scale 717Scale 717: Raga Vijayanagari, Ian Ring Music TheoryRaga Vijayanagari
Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian
Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala
Scale 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic
Scale 877Scale 877: Moravian Pistalkova, Ian Ring Music TheoryMoravian Pistalkova
Scale 1005Scale 1005: Radyllic, Ian Ring Music TheoryRadyllic
Scale 237Scale 237, Ian Ring Music Theory
Scale 493Scale 493: Rygian, Ian Ring Music TheoryRygian
Scale 1261Scale 1261: Modified Blues, Ian Ring Music TheoryModified Blues
Scale 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic

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. Special thanks to Richard Repp for helping with technical accuracy.