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Scale 2321: "Zyphic"

Scale 2321: Zyphic, 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
Zyphic

Analysis

Cardinality

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

4 (tetratonic)

Pitch Class Set

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

{0,4,8,11}

Forte Number

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

4-19

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: 275

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.

3

Prime Form

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

no
prime: 275

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.

[4, 4, 3, 1] 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.

<1, 0, 1, 3, 1, 0>

Interval Spectrum

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

pm3nd

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

Spectra Variation

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

2.5

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.

1.616

Polygon Perimeter

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

5.396

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".

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
Major TriadsE{4,8,11}110.5
Augmented TriadsC+{0,4,8}110.5
Parsimonious Voice Leading Between Common Triads of Scale 2321. Created by Ian Ring ©2019 C+ C+ E E C+->E

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 2321 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 401
Scale 401: Epogic, Ian Ring Music TheoryEpogic
3rd mode:
Scale 281
Scale 281: Lanic, Ian Ring Music TheoryLanic
4th mode:
Scale 547
Scale 547: Pyrric, Ian Ring Music TheoryPyrric

Prime

The prime form of this scale is Scale 275

Scale 275Scale 275: Dalic, Ian Ring Music TheoryDalic

Complement

The tetratonic modal family [2321, 401, 281, 547] (Forte: 4-19) is the complement of the octatonic modal family [887, 1847, 1907, 2491, 2971, 3001, 3293, 3533] (Forte: 8-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2321 is 275

Scale 275Scale 275: Dalic, Ian Ring Music TheoryDalic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2321 is chiral, and its enantiomorph is scale 275

Scale 275Scale 275: Dalic, Ian Ring Music TheoryDalic

Transformations:

T0 2321  T0I 275
T1 547  T1I 550
T2 1094  T2I 1100
T3 2188  T3I 2200
T4 281  T4I 305
T5 562  T5I 610
T6 1124  T6I 1220
T7 2248  T7I 2440
T8 401  T8I 785
T9 802  T9I 1570
T10 1604  T10I 3140
T11 3208  T11I 2185

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 2323Scale 2323: Doptitonic, Ian Ring Music TheoryDoptitonic
Scale 2325Scale 2325: Pynitonic, Ian Ring Music TheoryPynitonic
Scale 2329Scale 2329: Styditonic, Ian Ring Music TheoryStyditonic
Scale 2305Scale 2305, Ian Ring Music Theory
Scale 2313Scale 2313, Ian Ring Music Theory
Scale 2337Scale 2337, Ian Ring Music Theory
Scale 2353Scale 2353: Raga Girija, Ian Ring Music TheoryRaga Girija
Scale 2385Scale 2385: Aeolanitonic, Ian Ring Music TheoryAeolanitonic
Scale 2449Scale 2449: Zacritonic, Ian Ring Music TheoryZacritonic
Scale 2065Scale 2065, Ian Ring Music Theory
Scale 2193Scale 2193: Major Seventh, Ian Ring Music TheoryMajor Seventh
Scale 2577Scale 2577, Ian Ring Music Theory
Scale 2833Scale 2833: Dolitonic, Ian Ring Music TheoryDolitonic
Scale 3345Scale 3345: Zylitonic, Ian Ring Music TheoryZylitonic
Scale 273Scale 273: Augmented Triad, Ian Ring Music TheoryAugmented Triad
Scale 1297Scale 1297: Aeolic, Ian Ring Music TheoryAeolic

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.