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Scale 237

Scale 237, 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

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,5,6,7}
Forte Number6-Z11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1761
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 183
Deep Scaleno
Interval Vector333231
Interval Spectrump3m2n3s3d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {4,5,7,8}
<4> = {5,6,9,10}
<5> = {7,10,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area1.866
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
Minor Triadscm{0,3,7}110.5
Diminished Triads{0,3,6}110.5
Parsimonious Voice Leading Between Common Triads of Scale 237. Created by Ian Ring ©2019 cm cm c°->cm

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

2nd mode:
Scale 1083
Scale 1083, Ian Ring Music Theory
3rd mode:
Scale 2589
Scale 2589, Ian Ring Music Theory
4th mode:
Scale 1671
Scale 1671, Ian Ring Music Theory
5th mode:
Scale 2883
Scale 2883, Ian Ring Music Theory
6th mode:
Scale 3489
Scale 3489, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 183

Scale 183Scale 183, Ian Ring Music Theory

Complement

The hexatonic modal family [237, 1083, 2589, 1671, 2883, 3489] (Forte: 6-Z11) is the complement of the hexatonic modal family [303, 753, 1929, 2199, 3147, 3621] (Forte: 6-Z40)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 237 is 1761

Scale 1761Scale 1761, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 237 is chiral, and its enantiomorph is scale 1761

Scale 1761Scale 1761, Ian Ring Music Theory

Transformations:

T0 237  T0I 1761
T1 474  T1I 3522
T2 948  T2I 2949
T3 1896  T3I 1803
T4 3792  T4I 3606
T5 3489  T5I 3117
T6 2883  T6I 2139
T7 1671  T7I 183
T8 3342  T8I 366
T9 2589  T9I 732
T10 1083  T10I 1464
T11 2166  T11I 2928

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 239Scale 239, Ian Ring Music Theory
Scale 233Scale 233, Ian Ring Music Theory
Scale 235Scale 235, Ian Ring Music Theory
Scale 229Scale 229, Ian Ring Music Theory
Scale 245Scale 245: Raga Dipak, Ian Ring Music TheoryRaga Dipak
Scale 253Scale 253, Ian Ring Music Theory
Scale 205Scale 205, Ian Ring Music Theory
Scale 221Scale 221, Ian Ring Music Theory
Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 109Scale 109, Ian Ring Music Theory
Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic
Scale 493Scale 493: Rygian, Ian Ring Music TheoryRygian
Scale 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian
Scale 1261Scale 1261: Modified Blues, Ian Ring Music TheoryModified Blues
Scale 2285Scale 2285: Aerogian, Ian Ring Music TheoryAerogian

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.