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Scale 109

Scale 109, 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{0,2,3,5,6}
Forte Number5-10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1729
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 91
Deep Scaleno
Interval Vector223111
Interval Spectrumpmn3s2d2t
Distribution Spectra<1> = {1,2,6}
<2> = {3,7,8}
<3> = {4,5,9}
<4> = {6,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.366
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
Diminished Triads{0,3,6}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 109 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1051
Scale 1051, Ian Ring Music Theory
3rd mode:
Scale 2573
Scale 2573, Ian Ring Music Theory
4th mode:
Scale 1667
Scale 1667, Ian Ring Music Theory
5th mode:
Scale 2881
Scale 2881, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 91

Scale 91Scale 91, Ian Ring Music Theory

Complement

The pentatonic modal family [109, 1051, 2573, 1667, 2881] (Forte: 5-10) is the complement of the heptatonic modal family [607, 761, 1993, 2351, 3223, 3659, 3877] (Forte: 7-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 109 is 1729

Scale 1729Scale 1729, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 109 is chiral, and its enantiomorph is scale 1729

Scale 1729Scale 1729, Ian Ring Music Theory

Transformations:

T0 109  T0I 1729
T1 218  T1I 3458
T2 436  T2I 2821
T3 872  T3I 1547
T4 1744  T4I 3094
T5 3488  T5I 2093
T6 2881  T6I 91
T7 1667  T7I 182
T8 3334  T8I 364
T9 2573  T9I 728
T10 1051  T10I 1456
T11 2102  T11I 2912

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 111Scale 111, Ian Ring Music Theory
Scale 105Scale 105, Ian Ring Music Theory
Scale 107Scale 107, Ian Ring Music Theory
Scale 101Scale 101, Ian Ring Music Theory
Scale 117Scale 117, Ian Ring Music Theory
Scale 125Scale 125, Ian Ring Music Theory
Scale 77Scale 77, Ian Ring Music Theory
Scale 93Scale 93, Ian Ring Music Theory
Scale 45Scale 45, Ian Ring Music Theory
Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 237Scale 237, Ian Ring Music Theory
Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic
Scale 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 2157Scale 2157, 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.