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Scale 3109

Scale 3109, 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

Cardinality5 (pentatonic)
Pitch Class Set{0,2,5,10,11}
Forte Number5-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1159
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes4
Prime?no
prime: 151
Deep Scaleno
Interval Vector222121
Interval Spectrump2mn2s2d2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {2,3,5,6,8}
<3> = {4,6,7,9,10}
<4> = {7,9,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.683
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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 TriadsA♯{10,2,5}110.5
Diminished Triads{11,2,5}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3109. Created by Ian Ring ©2019 A# A# A#->b°

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3109 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1801
Scale 1801, Ian Ring Music Theory
3rd mode:
Scale 737
Scale 737, Ian Ring Music Theory
4th mode:
Scale 151
Scale 151, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2123
Scale 2123, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 151

Scale 151Scale 151, Ian Ring Music Theory

Complement

The pentatonic modal family [3109, 1801, 737, 151, 2123] (Forte: 5-Z36) is the complement of the heptatonic modal family [367, 1777, 1931, 2231, 3013, 3163, 3629] (Forte: 7-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3109 is 1159

Scale 1159Scale 1159, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3109 is chiral, and its enantiomorph is scale 1159

Scale 1159Scale 1159, Ian Ring Music Theory

Transformations:

T0 3109  T0I 1159
T1 2123  T1I 2318
T2 151  T2I 541
T3 302  T3I 1082
T4 604  T4I 2164
T5 1208  T5I 233
T6 2416  T6I 466
T7 737  T7I 932
T8 1474  T8I 1864
T9 2948  T9I 3728
T10 1801  T10I 3361
T11 3602  T11I 2627

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 3111Scale 3111, Ian Ring Music Theory
Scale 3105Scale 3105, Ian Ring Music Theory
Scale 3107Scale 3107, Ian Ring Music Theory
Scale 3113Scale 3113, Ian Ring Music Theory
Scale 3117Scale 3117, Ian Ring Music Theory
Scale 3125Scale 3125, Ian Ring Music Theory
Scale 3077Scale 3077, Ian Ring Music Theory
Scale 3093Scale 3093, Ian Ring Music Theory
Scale 3141Scale 3141: Kanitonic, Ian Ring Music TheoryKanitonic
Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3621Scale 3621: Gylimic, Ian Ring Music TheoryGylimic
Scale 2085Scale 2085, Ian Ring Music Theory
Scale 2597Scale 2597: Raga Rasranjani, Ian Ring Music TheoryRaga Rasranjani
Scale 1061Scale 1061, 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. Special thanks to Richard Repp for helping with technical accuracy.