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Scale 151

Scale 151, 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).

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,1,2,4,7}
Forte Number5-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3361
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes4
Prime?yes
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 TriadsC{0,4,7}110.5
Diminished Triadsc♯°{1,4,7}110.5
Parsimonious Voice Leading Between Common Triads of Scale 151. Created by Ian Ring ©2019 C C c#° c#° C->c#°

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 151 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2123
Scale 2123, Ian Ring Music Theory
3rd mode:
Scale 3109
Scale 3109, Ian Ring Music Theory
4th mode:
Scale 1801
Scale 1801, Ian Ring Music Theory
5th mode:
Scale 737
Scale 737, Ian Ring Music Theory

Prime

This is the prime form of this scale.

Complement

The pentatonic modal family [151, 2123, 3109, 1801, 737] (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 151 is 3361

Scale 3361Scale 3361, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 151 is chiral, and its enantiomorph is scale 3361

Scale 3361Scale 3361, Ian Ring Music Theory

Transformations:

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

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 149Scale 149: Eskimo Tetratonic, Ian Ring Music TheoryEskimo Tetratonic
Scale 147Scale 147, Ian Ring Music Theory
Scale 155Scale 155, Ian Ring Music Theory
Scale 159Scale 159, Ian Ring Music Theory
Scale 135Scale 135, Ian Ring Music Theory
Scale 143Scale 143, Ian Ring Music Theory
Scale 167Scale 167, Ian Ring Music Theory
Scale 183Scale 183, Ian Ring Music Theory
Scale 215Scale 215, Ian Ring Music Theory
Scale 23Scale 23, Ian Ring Music Theory
Scale 87Scale 87, Ian Ring Music Theory
Scale 279Scale 279: Poditonic, Ian Ring Music TheoryPoditonic
Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic
Scale 663Scale 663: Phrynimic, Ian Ring Music TheoryPhrynimic
Scale 1175Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.