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Scale 3437

Scale 3437, 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

Cardinality

Cardinality is the count of how many pitches are in the scale.

8 (octatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,3,5,6,8,10,11}

Forte Number

A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

8-27

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 1751

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

4 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

1 (uncohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

3

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

7

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 1463

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

[4, 5, 6, 5, 5, 3]

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.

p5m5n6s5d4t3

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

1.25

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

yes

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.732

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.071

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Proper

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 TriadsG♯{8,0,3}342.15
A♯{10,2,5}342.23
B{11,3,6}441.85
Minor Triadsd♯m{3,6,10}242.23
fm{5,8,0}342.23
g♯m{8,11,3}441.92
bm{11,2,6}441.92
Augmented TriadsD+{2,6,10}342.15
Diminished Triads{0,3,6}242.23
{2,5,8}242.31
{5,8,11}242.31
g♯°{8,11,2}242.15
{11,2,5}242.31
Parsimonious Voice Leading Between Common Triads of Scale 3437. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B fm fm d°->fm A# A# d°->A# D+ D+ d#m d#m D+->d#m D+->A# bm bm D+->bm d#m->B f°->fm g#m g#m f°->g#m fm->G# g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B A#->b° b°->bm bm->B

view full size

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3437 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1883
Scale 1883, Ian Ring Music Theory
3rd mode:
Scale 2989
Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
4th mode:
Scale 1771
Scale 1771, Ian Ring Music Theory
5th mode:
Scale 2933
Scale 2933, Ian Ring Music Theory
6th mode:
Scale 1757
Scale 1757, Ian Ring Music Theory
7th mode:
Scale 1463
Scale 1463, Ian Ring Music TheoryThis is the prime mode
8th mode:
Scale 2779
Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich

Prime

The prime form of this scale is Scale 1463

Scale 1463Scale 1463, Ian Ring Music Theory

Complement

The octatonic modal family [3437, 1883, 2989, 1771, 2933, 1757, 1463, 2779] (Forte: 8-27) is the complement of the tetratonic modal family [293, 593, 649, 1097] (Forte: 4-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3437 is 1751

Scale 1751Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3437 is chiral, and its enantiomorph is scale 1751

Scale 1751Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic

Transformations:

T0 3437  T0I 1751
T1 2779  T1I 3502
T2 1463  T2I 2909
T3 2926  T3I 1723
T4 1757  T4I 3446
T5 3514  T5I 2797
T6 2933  T6I 1499
T7 1771  T7I 2998
T8 3542  T8I 1901
T9 2989  T9I 3802
T10 1883  T10I 3509
T11 3766  T11I 2923

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 3439Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
Scale 3433Scale 3433: Thonian, Ian Ring Music TheoryThonian
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse
Scale 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
Scale 3405Scale 3405: Stynian, Ian Ring Music TheoryStynian
Scale 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 3373Scale 3373: Lodian, Ian Ring Music TheoryLodian
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 3565Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
Scale 3181Scale 3181: Rolian, Ian Ring Music TheoryRolian
Scale 3309Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
Scale 3693Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 2413Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
Scale 2925Scale 2925: Diminished, Ian Ring Music TheoryDiminished
Scale 1389Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian

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.