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Scale 2831

Scale 2831, 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).

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,8,9,11}
Forte Number7-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3611
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 223
Deep Scaleno
Interval Vector544332
Interval Spectrump3m3n4s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area1.933
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 TriadsG♯{8,0,3}221
Minor Triadsg♯m{8,11,3}221
Diminished Triadsg♯°{8,11,2}131.5
{9,0,3}131.5
Parsimonious Voice Leading Between Common Triads of Scale 2831. Created by Ian Ring ©2019 g#° g#° g#m g#m g#°->g#m G# G# g#m->G# G#->a°

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
Radius2
Self-Centeredno
Central Verticesg♯m, G♯
Peripheral Verticesg♯°, a°

Modes

Modes are the rotational transformation of this scale. Scale 2831 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3463
Scale 3463, Ian Ring Music Theory
3rd mode:
Scale 3779
Scale 3779, Ian Ring Music Theory
4th mode:
Scale 3937
Scale 3937, Ian Ring Music Theory
5th mode:
Scale 251
Scale 251, Ian Ring Music Theory
6th mode:
Scale 2173
Scale 2173, Ian Ring Music Theory
7th mode:
Scale 1567
Scale 1567, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 223

Scale 223Scale 223, Ian Ring Music Theory

Complement

The heptatonic modal family [2831, 3463, 3779, 3937, 251, 2173, 1567] (Forte: 7-4) is the complement of the pentatonic modal family [79, 961, 2087, 3091, 3593] (Forte: 5-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2831 is 3611

Scale 3611Scale 3611, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2831 is chiral, and its enantiomorph is scale 3611

Scale 3611Scale 3611, Ian Ring Music Theory

Transformations:

T0 2831  T0I 3611
T1 1567  T1I 3127
T2 3134  T2I 2159
T3 2173  T3I 223
T4 251  T4I 446
T5 502  T5I 892
T6 1004  T6I 1784
T7 2008  T7I 3568
T8 4016  T8I 3041
T9 3937  T9I 1987
T10 3779  T10I 3974
T11 3463  T11I 3853

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 2829Scale 2829, Ian Ring Music Theory
Scale 2827Scale 2827, Ian Ring Music Theory
Scale 2823Scale 2823, Ian Ring Music Theory
Scale 2839Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
Scale 2847Scale 2847: Phracryllic, Ian Ring Music TheoryPhracryllic
Scale 2863Scale 2863: Aerogyllic, Ian Ring Music TheoryAerogyllic
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
Scale 2575Scale 2575, Ian Ring Music Theory
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 2319Scale 2319, Ian Ring Music Theory
Scale 3343Scale 3343, Ian Ring Music Theory
Scale 3855Scale 3855, Ian Ring Music Theory
Scale 783Scale 783, Ian Ring Music Theory
Scale 1807Scale 1807, Ian Ring Music Theory

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.