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Scale 3267

Scale 3267, 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

Cardinality6 (hexatonic)
Pitch Class Set{0,1,6,7,10,11}
Forte Number6-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2151
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 207
Deep Scaleno
Interval Vector422232
Interval Spectrump3m2n2s2d4t2
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6}
<3> = {3,5,7,9}
<4> = {6,8,10}
<5> = {7,9,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area1.75
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 TriadsF♯{6,10,1}110.5
Diminished Triads{7,10,1}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3267. Created by Ian Ring ©2019 F# F# F#->g°

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 3267 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3681
Scale 3681, Ian Ring Music Theory
3rd mode:
Scale 243
Scale 243, Ian Ring Music Theory
4th mode:
Scale 2169
Scale 2169, Ian Ring Music Theory
5th mode:
Scale 783
Scale 783, Ian Ring Music Theory
6th mode:
Scale 2439
Scale 2439, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 207

Scale 207Scale 207, Ian Ring Music Theory

Complement

The hexatonic modal family [3267, 3681, 243, 2169, 783, 2439] (Forte: 6-5) is the complement of the hexatonic modal family [207, 963, 2151, 2529, 3123, 3609] (Forte: 6-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3267 is 2151

Scale 2151Scale 2151, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3267 is chiral, and its enantiomorph is scale 2151

Scale 2151Scale 2151, Ian Ring Music Theory

Transformations:

T0 3267  T0I 2151
T1 2439  T1I 207
T2 783  T2I 414
T3 1566  T3I 828
T4 3132  T4I 1656
T5 2169  T5I 3312
T6 243  T6I 2529
T7 486  T7I 963
T8 972  T8I 1926
T9 1944  T9I 3852
T10 3888  T10I 3609
T11 3681  T11I 3123

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 3265Scale 3265, Ian Ring Music Theory
Scale 3269Scale 3269: Raga Malarani, Ian Ring Music TheoryRaga Malarani
Scale 3271Scale 3271: Mela Raghupriya, Ian Ring Music TheoryMela Raghupriya
Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
Scale 3283Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari
Scale 3299Scale 3299: Syptian, Ian Ring Music TheorySyptian
Scale 3203Scale 3203, Ian Ring Music Theory
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3139Scale 3139, Ian Ring Music Theory
Scale 3395Scale 3395, Ian Ring Music Theory
Scale 3523Scale 3523, Ian Ring Music Theory
Scale 3779Scale 3779, Ian Ring Music Theory
Scale 2243Scale 2243, Ian Ring Music Theory
Scale 2755Scale 2755, Ian Ring Music Theory
Scale 1219Scale 1219, 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.