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Scale 1099: "Dyritonic"

Scale 1099: Dyritonic, 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

Zeitler
Dyritonic

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

{0,1,3,6,10}

Forte Number

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

5-25

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: 2629

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.

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: 301

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.

[1, 2, 3, 1, 2, 1]

Interval Spectrum

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

p2mn3s2dt

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> = {3,5,6,7}
<3> = {5,6,7,9}
<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.

2.8

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

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♯{6,10,1}121
Minor Triadsd♯m{3,6,10}210.67
Diminished Triads{0,3,6}121
Parsimonious Voice Leading Between Common Triads of Scale 1099. Created by Ian Ring ©2019 d#m d#m c°->d#m F# F# d#m->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.

Diameter2
Radius1
Self-Centeredno
Central Verticesd♯m
Peripheral Verticesc°, F♯

Modes

Modes are the rotational transformation of this scale. Scale 1099 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2597
Scale 2597: Raga Rasranjani, Ian Ring Music TheoryRaga Rasranjani
3rd mode:
Scale 1673
Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
4th mode:
Scale 721
Scale 721: Raga Dhavalashri, Ian Ring Music TheoryRaga Dhavalashri
5th mode:
Scale 301
Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav TukhariThis is the prime mode

Prime

The prime form of this scale is Scale 301

Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari

Complement

The pentatonic modal family [1099, 2597, 1673, 721, 301] (Forte: 5-25) is the complement of the heptatonic modal family [733, 1207, 1769, 1867, 2651, 2981, 3373] (Forte: 7-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1099 is 2629

Scale 2629Scale 2629: Raga Shubravarni, Ian Ring Music TheoryRaga Shubravarni

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1099 is chiral, and its enantiomorph is scale 2629

Scale 2629Scale 2629: Raga Shubravarni, Ian Ring Music TheoryRaga Shubravarni

Transformations:

T0 1099  T0I 2629
T1 2198  T1I 1163
T2 301  T2I 2326
T3 602  T3I 557
T4 1204  T4I 1114
T5 2408  T5I 2228
T6 721  T6I 361
T7 1442  T7I 722
T8 2884  T8I 1444
T9 1673  T9I 2888
T10 3346  T10I 1681
T11 2597  T11I 3362

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 1097Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic
Scale 1101Scale 1101: Stothitonic, Ian Ring Music TheoryStothitonic
Scale 1103Scale 1103: Lynimic, Ian Ring Music TheoryLynimic
Scale 1091Scale 1091, Ian Ring Music Theory
Scale 1095Scale 1095: Phrythitonic, Ian Ring Music TheoryPhrythitonic
Scale 1107Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
Scale 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form
Scale 1035Scale 1035, Ian Ring Music Theory
Scale 1067Scale 1067, Ian Ring Music Theory
Scale 1163Scale 1163: Raga Rukmangi, Ian Ring Music TheoryRaga Rukmangi
Scale 1227Scale 1227: Thacrimic, Ian Ring Music TheoryThacrimic
Scale 1355Scale 1355: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
Scale 75Scale 75, Ian Ring Music Theory
Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic

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.