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Scale 1877: "Aeroptian"

Scale 1877: Aeroptian, 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
Aeroptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,4,6,8,9,10}
Forte Number7-33
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections5
Modes6
Prime?no
prime: 1367
Deep Scaleno
Interval Vector262623
Interval Spectrump2m6n2s6d2t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9,10}
<6> = {10,11}
Spectra Variation1.429
Maximally Evenno
Maximal Area Setyes
Interior Area2.665
Myhill Propertyno
Balancedno
Ridge Tones[6]
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 TriadsD{2,6,9}231.4
Minor Triadsam{9,0,4}231.4
Augmented TriadsC+{0,4,8}142
D+{2,6,10}142
Diminished Triadsf♯°{6,9,0}221.2
Parsimonious Voice Leading Between Common Triads of Scale 1877. Created by Ian Ring ©2019 C+ C+ am am C+->am D D D+ D+ D->D+ f#° f#° D->f#° f#°->am

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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 Verticesf♯°
Peripheral VerticesC+, D+

Modes

Modes are the rotational transformation of this scale. Scale 1877 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1493
Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
3rd mode:
Scale 1397
Scale 1397: Major Locrian, Ian Ring Music TheoryMajor Locrian
4th mode:
Scale 1373
Scale 1373: Storian, Ian Ring Music TheoryStorian
5th mode:
Scale 1367
Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone InverseThis is the prime mode
6th mode:
Scale 2731
Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
7th mode:
Scale 3413
Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone

Prime

The prime form of this scale is Scale 1367

Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse

Complement

The heptatonic modal family [1877, 1493, 1397, 1373, 1367, 2731, 3413] (Forte: 7-33) is the complement of the pentatonic modal family [341, 1109, 1301, 1349, 1361] (Forte: 5-33)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1877 is 1373

Scale 1373Scale 1373: Storian, Ian Ring Music TheoryStorian

Transformations:

T0 1877  T0I 1373
T1 3754  T1I 2746
T2 3413  T2I 1397
T3 2731  T3I 2794
T4 1367  T4I 1493
T5 2734  T5I 2986
T6 1373  T6I 1877
T7 2746  T7I 3754
T8 1397  T8I 3413
T9 2794  T9I 2731
T10 1493  T10I 1367
T11 2986  T11I 2734

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 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale
Scale 1881Scale 1881: Katorian, Ian Ring Music TheoryKatorian
Scale 1885Scale 1885: Saptyllic, Ian Ring Music TheorySaptyllic
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
Scale 1893Scale 1893: Ionylian, Ian Ring Music TheoryIonylian
Scale 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
Scale 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic
Scale 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian
Scale 1941Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
Scale 1621Scale 1621: Scriabin's Prometheus, Ian Ring Music TheoryScriabin's Prometheus
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
Scale 1365Scale 1365: Whole Tone, Ian Ring Music TheoryWhole Tone
Scale 853Scale 853: Epothimic, Ian Ring Music TheoryEpothimic
Scale 2901Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic

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.