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Scale 137: "Ute Tritonic"

Scale 137: Ute Tritonic, 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).

Common Names

Carnatic Raga
Ute Tritonic
Chord Names
Minor Triad
Exoticisms
Peruvian Tritonic 2

Analysis

Cardinality

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

3 (tritonic)

Pitch Class Set

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

{0,3,7}

Forte Number

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

3-11

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: 545

Hemitonia

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

0 (anhemitonic)

Cohemitonia

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

0 (ancohemitonic)

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.

2

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.

2

Prime Form

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

yes

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.

[3, 4, 5] 9

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.

<0, 0, 1, 1, 1, 0>

Interval Spectrum

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

pmn

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

Spectra Variation

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

1.333

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.

1.183

Polygon Perimeter

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

5.078

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".

Strictly 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
Minor Triadscm{0,3,7}000

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 137 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 529
Scale 529: Raga Bilwadala, Ian Ring Music TheoryRaga Bilwadala
3rd mode:
Scale 289
Scale 289, Ian Ring Music Theory

Prime

This is the prime form of this scale.

Complement

The tritonic modal family [137, 529, 289] (Forte: 3-11) is the complement of the enneatonic modal family [1775, 1915, 1975, 2935, 3005, 3035, 3515, 3565, 3805] (Forte: 9-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 137 is 545

Scale 545Scale 545, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 137 is chiral, and its enantiomorph is scale 545

Scale 545Scale 545, Ian Ring Music Theory

Transformations:

T0 137  T0I 545
T1 274  T1I 1090
T2 548  T2I 2180
T3 1096  T3I 265
T4 2192  T4I 530
T5 289  T5I 1060
T6 578  T6I 2120
T7 1156  T7I 145
T8 2312  T8I 290
T9 529  T9I 580
T10 1058  T10I 1160
T11 2116  T11I 2320

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 139Scale 139, Ian Ring Music Theory
Scale 141Scale 141, Ian Ring Music Theory
Scale 129Scale 129: Niagari, Ian Ring Music TheoryNiagari
Scale 133Scale 133: Suspended Second Triad, Ian Ring Music TheorySuspended Second Triad
Scale 145Scale 145: Raga Malasri, Ian Ring Music TheoryRaga Malasri
Scale 153Scale 153, Ian Ring Music Theory
Scale 169Scale 169: Vietnamese Tetratonic, Ian Ring Music TheoryVietnamese Tetratonic
Scale 201Scale 201, Ian Ring Music Theory
Scale 9Scale 9: Minor Third Ditone, Ian Ring Music TheoryMinor Third Ditone
Scale 73Scale 73: Diminished Triad, Ian Ring Music TheoryDiminished Triad
Scale 265Scale 265, Ian Ring Music Theory
Scale 393Scale 393: Lothic, Ian Ring Music TheoryLothic
Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic
Scale 1161Scale 1161: Bi Yu, Ian Ring Music TheoryBi Yu
Scale 2185Scale 2185: Dygic, Ian Ring Music TheoryDygic

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.