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Scale 3723: "Myptian"

Scale 3723: Myptian, 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

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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
Myptian

Analysis

Cardinality

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

7 (heptatonic)

Pitch Class Set

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

{0,1,3,7,9,10,11}

Forte Number

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

7-8

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.

[5]

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.

no

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

3 (tricohemitonic)

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.

5

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.

6

Prime Form

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

no
prime: 381

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.

[4, 5, 4, 4, 2, 2]

Interval Spectrum

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

p2m4n4s5d4t2

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

Spectra Variation

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

3.429

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.

2.299

Polygon Perimeter

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

5.803

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.

[10]

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

Harmonic Chords

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 TriadsD♯{3,7,10}231.4
Minor Triadscm{0,3,7}231.4
Augmented TriadsD♯+{3,7,11}221.2
Diminished Triads{7,10,1}142
{9,0,3}142
Parsimonious Voice Leading Between Common Triads of Scale 3723. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ cm->a° D# D# D#->D#+ D#->g°

view full size

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.

Diameter4
Radius2
Self-Centeredno
Central VerticesD♯+
Peripheral Verticesg°, a°

Modes

Modes are the rotational transformation of this scale. Scale 3723 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3909
Scale 3909: Rydian, Ian Ring Music TheoryRydian
3rd mode:
Scale 2001
Scale 2001: Gydian, Ian Ring Music TheoryGydian
4th mode:
Scale 381
Scale 381: Kogian, Ian Ring Music TheoryKogianThis is the prime mode
5th mode:
Scale 1119
Scale 1119: Rarian, Ian Ring Music TheoryRarian
6th mode:
Scale 2607
Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
7th mode:
Scale 3351
Scale 3351: Crater Scale, Ian Ring Music TheoryCrater Scale

Prime

The prime form of this scale is Scale 381

Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian

Complement

The heptatonic modal family [3723, 3909, 2001, 381, 1119, 2607, 3351] (Forte: 7-8) is the complement of the pentatonic modal family [93, 1047, 1857, 2571, 3333] (Forte: 5-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3723 is 2607

Scale 2607Scale 2607: Aerolian, Ian Ring Music TheoryAerolian

Transformations:

T0 3723  T0I 2607
T1 3351  T1I 1119
T2 2607  T2I 2238
T3 1119  T3I 381
T4 2238  T4I 762
T5 381  T5I 1524
T6 762  T6I 3048
T7 1524  T7I 2001
T8 3048  T8I 4002
T9 2001  T9I 3909
T10 4002  T10I 3723
T11 3909  T11I 3351

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 3721Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic
Scale 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
Scale 3727Scale 3727: Tholyllic, Ian Ring Music TheoryTholyllic
Scale 3715Scale 3715, Ian Ring Music Theory
Scale 3719Scale 3719, Ian Ring Music Theory
Scale 3731Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian
Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 3787Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
Scale 3595Scale 3595, Ian Ring Music Theory
Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian
Scale 3851Scale 3851, Ian Ring Music Theory
Scale 3979Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
Scale 3211Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic
Scale 3467Scale 3467: Katonian, Ian Ring Music TheoryKatonian
Scale 2699Scale 2699: Sythimic, Ian Ring Music TheorySythimic
Scale 1675Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali

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.