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Scale 2119

Scale 2119, 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.

5 (pentatonic)

Pitch Class Set

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

{0,1,2,6,11}

Forte Number

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

5-5

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: 3139

Hemitonia

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

3 (trihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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: 143

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.

[1, 1, 4, 5, 1]

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.

<3, 2, 1, 1, 2, 1>

Interval Spectrum

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

p2mns2d3t

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

Spectra Variation

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

4.4

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.

1.433

Polygon Perimeter

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

5.217

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
Minor Triadsbm{11,2,6}000

The following pitch classes are not present in any of the common triads: {0,1}

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 2119 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3107
Scale 3107, Ian Ring Music Theory
3rd mode:
Scale 3601
Scale 3601, Ian Ring Music Theory
4th mode:
Scale 481
Scale 481, Ian Ring Music Theory
5th mode:
Scale 143
Scale 143, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 143

Scale 143Scale 143, Ian Ring Music Theory

Complement

The pentatonic modal family [2119, 3107, 3601, 481, 143] (Forte: 5-5) is the complement of the heptatonic modal family [239, 1927, 2167, 3011, 3131, 3553, 3613] (Forte: 7-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2119 is 3139

Scale 3139Scale 3139, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2119 is chiral, and its enantiomorph is scale 3139

Scale 3139Scale 3139, Ian Ring Music Theory

Transformations:

T0 2119  T0I 3139
T1 143  T1I 2183
T2 286  T2I 271
T3 572  T3I 542
T4 1144  T4I 1084
T5 2288  T5I 2168
T6 481  T6I 241
T7 962  T7I 482
T8 1924  T8I 964
T9 3848  T9I 1928
T10 3601  T10I 3856
T11 3107  T11I 3617

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 2117Scale 2117: Raga Sumukam, Ian Ring Music TheoryRaga Sumukam
Scale 2115Scale 2115, Ian Ring Music Theory
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 2127Scale 2127, Ian Ring Music Theory
Scale 2135Scale 2135, Ian Ring Music Theory
Scale 2151Scale 2151, Ian Ring Music Theory
Scale 2055Scale 2055, Ian Ring Music Theory
Scale 2087Scale 2087, Ian Ring Music Theory
Scale 2183Scale 2183, Ian Ring Music Theory
Scale 2247Scale 2247: Raga Vijayasri, Ian Ring Music TheoryRaga Vijayasri
Scale 2375Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 71Scale 71, Ian Ring Music Theory
Scale 1095Scale 1095: Phrythitonic, Ian Ring Music TheoryPhrythitonic

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.