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Scale 2373: "Dyptitonic"

Scale 2373: Dyptitonic, 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).

Common Names

Zeitler
Dyptitonic
Dozenal
Omuian

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

{0,2,6,8,11}

Forte Number

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

5-28

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: 1107

Hemitonia

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

1 (unhemitonic)

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.

4

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: 333

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

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

no

Interval Structure

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

[2, 4, 2, 3, 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.

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

Interval Spectrum

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

pm2n2s2dt2

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

Spectra Variation

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

2.4

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.

2.049

Polygon Perimeter

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

5.664

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

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(2, 8, 36)

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}110.5
Diminished Triadsg♯°{8,11,2}110.5

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

Parsimonious Voice Leading Between Common Triads of Scale 2373. Created by Ian Ring ©2019 g#° g#° bm bm g#°->bm

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 2373 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1617
Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic
3rd mode:
Scale 357
Scale 357: Banitonic, Ian Ring Music TheoryBanitonic
4th mode:
Scale 1113
Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2
5th mode:
Scale 651
Scale 651: Golitonic, Ian Ring Music TheoryGolitonic

Prime

The prime form of this scale is Scale 333

Scale 333Scale 333: Bogitonic, Ian Ring Music TheoryBogitonic

Complement

The pentatonic modal family [2373, 1617, 357, 1113, 651] (Forte: 5-28) is the complement of the heptatonic modal family [747, 1431, 1629, 1881, 2421, 2763, 3429] (Forte: 7-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2373 is 1107

Scale 1107Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2373 is chiral, and its enantiomorph is scale 1107

Scale 1107Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 2373       T0I <11,0> 1107
T1 <1,1> 651      T1I <11,1> 2214
T2 <1,2> 1302      T2I <11,2> 333
T3 <1,3> 2604      T3I <11,3> 666
T4 <1,4> 1113      T4I <11,4> 1332
T5 <1,5> 2226      T5I <11,5> 2664
T6 <1,6> 357      T6I <11,6> 1233
T7 <1,7> 714      T7I <11,7> 2466
T8 <1,8> 1428      T8I <11,8> 837
T9 <1,9> 2856      T9I <11,9> 1674
T10 <1,10> 1617      T10I <11,10> 3348
T11 <1,11> 3234      T11I <11,11> 2601
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1233      T0MI <7,0> 357
T1M <5,1> 2466      T1MI <7,1> 714
T2M <5,2> 837      T2MI <7,2> 1428
T3M <5,3> 1674      T3MI <7,3> 2856
T4M <5,4> 3348      T4MI <7,4> 1617
T5M <5,5> 2601      T5MI <7,5> 3234
T6M <5,6> 1107      T6MI <7,6> 2373
T7M <5,7> 2214      T7MI <7,7> 651
T8M <5,8> 333      T8MI <7,8> 1302
T9M <5,9> 666      T9MI <7,9> 2604
T10M <5,10> 1332      T10MI <7,10> 1113
T11M <5,11> 2664      T11MI <7,11> 2226

The transformations that map this set to itself are: T0, T6MI

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 2375Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic
Scale 2369Scale 2369: Offian, Ian Ring Music TheoryOffian
Scale 2371Scale 2371: Omoian, Ian Ring Music TheoryOmoian
Scale 2377Scale 2377: Bartók Gamma Chord, Ian Ring Music TheoryBartók Gamma Chord
Scale 2381Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
Scale 2389Scale 2389: Eskimo Hexatonic 2, Ian Ring Music TheoryEskimo Hexatonic 2
Scale 2405Scale 2405: Katalimic, Ian Ring Music TheoryKatalimic
Scale 2309Scale 2309: Ocuian, Ian Ring Music TheoryOcuian
Scale 2341Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
Scale 2437Scale 2437: Pafian, Ian Ring Music TheoryPafian
Scale 2501Scale 2501: Ralimic, Ian Ring Music TheoryRalimic
Scale 2117Scale 2117: Raga Sumukam, Ian Ring Music TheoryRaga Sumukam
Scale 2245Scale 2245: Raga Vaijayanti, Ian Ring Music TheoryRaga Vaijayanti
Scale 2629Scale 2629: Raga Shubravarni, Ian Ring Music TheoryRaga Shubravarni
Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
Scale 3397Scale 3397: Sydimic, Ian Ring Music TheorySydimic
Scale 325Scale 325: Messiaen Truncated Mode 6, Ian Ring Music TheoryMessiaen Truncated Mode 6
Scale 1349Scale 1349: Tholitonic, Ian Ring Music TheoryTholitonic

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. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.