The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 929

Scale 929, 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

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.

5 (pentatonic)

Pitch Class Set

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

{0,5,7,8,9}

Forte Number

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

5-11

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: 185

Hemitonia

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

2 (dihemitonic)

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.

4

Prime Form

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

no
prime: 157

Deep Scale

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

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[5, 2, 1, 1, 3]

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.

<2, 2, 2, 2, 2, 0>

Interval Spectrum

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

p2m2n2s2d2

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

Spectra Variation

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

4

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.

no

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.

1.683

Polygon Perimeter

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

5.381

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".

Improper

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{5,9,0}110.5
Minor Triadsfm{5,8,0}110.5

The following pitch classes are not present in any of the common triads: {7}

Parsimonious Voice Leading Between Common Triads of Scale 929. Created by Ian Ring ©2019 fm fm F F fm->F

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

2nd mode:
Scale 157
Scale 157, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 1063
Scale 1063, Ian Ring Music Theory
4th mode:
Scale 2579
Scale 2579, Ian Ring Music Theory
5th mode:
Scale 3337
Scale 3337, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 157

Scale 157Scale 157, Ian Ring Music Theory

Complement

The pentatonic modal family [929, 157, 1063, 2579, 3337] (Forte: 5-11) is the complement of the heptatonic modal family [379, 1583, 1969, 2237, 2839, 3467, 3781] (Forte: 7-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 929 is 185

Scale 185Scale 185, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 929 is chiral, and its enantiomorph is scale 185

Scale 185Scale 185, Ian Ring Music Theory

Transformations:

T0 929  T0I 185
T1 1858  T1I 370
T2 3716  T2I 740
T3 3337  T3I 1480
T4 2579  T4I 2960
T5 1063  T5I 1825
T6 2126  T6I 3650
T7 157  T7I 3205
T8 314  T8I 2315
T9 628  T9I 535
T10 1256  T10I 1070
T11 2512  T11I 2140

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 931Scale 931: Raga Kalakanthi, Ian Ring Music TheoryRaga Kalakanthi
Scale 933Scale 933: Dadimic, Ian Ring Music TheoryDadimic
Scale 937Scale 937: Stothimic, Ian Ring Music TheoryStothimic
Scale 945Scale 945: Raga Saravati, Ian Ring Music TheoryRaga Saravati
Scale 897Scale 897, Ian Ring Music Theory
Scale 913Scale 913: Aeolyritonic, Ian Ring Music TheoryAeolyritonic
Scale 961Scale 961, Ian Ring Music Theory
Scale 993Scale 993, Ian Ring Music Theory
Scale 801Scale 801, Ian Ring Music Theory
Scale 865Scale 865, Ian Ring Music Theory
Scale 673Scale 673, Ian Ring Music Theory
Scale 417Scale 417, Ian Ring Music Theory
Scale 1441Scale 1441, Ian Ring Music Theory
Scale 1953Scale 1953, Ian Ring Music Theory
Scale 2977Scale 2977, Ian Ring Music Theory

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. 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.