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Scale 2037: "Sythygic"

Scale 2037: Sythygic, 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
Sythygic

Analysis

Cardinality

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

9 (enneatonic)

Pitch Class Set

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

{0,2,4,5,6,7,8,9,10}

Forte Number

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

9-6

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.

[1]

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.

6 (multihemitonic)

Cohemitonia

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

5 (multicohemitonic)

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.

8

Prime Form

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

no
prime: 1407

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.

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

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.

<6, 8, 6, 7, 6, 3>

Interval Spectrum

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

p6m7n6s8d6t3

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

Spectra Variation

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

2

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.

yes

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.

2.799

Polygon Perimeter

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

6.106

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.

[2]

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 TriadsC{0,4,7}242.54
D{2,6,9}342.15
F{5,9,0}442
A♯{10,2,5}242.31
Minor Triadsdm{2,5,9}442
fm{5,8,0}342.15
gm{7,10,2}242.54
am{9,0,4}242.31
Augmented TriadsC+{0,4,8}342.31
D+{2,6,10}342.31
Diminished Triads{2,5,8}242.31
{4,7,10}242.62
f♯°{6,9,0}242.31
Parsimonious Voice Leading Between Common Triads of Scale 2037. Created by Ian Ring ©2019 C C C+ C+ C->C+ C->e° fm fm C+->fm am am C+->am dm dm d°->dm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm D+->A# e°->gm fm->F F->f#° F->am

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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2037 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1533
Scale 1533: Katycrygic, Ian Ring Music TheoryKatycrygic
3rd mode:
Scale 1407
Scale 1407: Tharygic, Ian Ring Music TheoryTharygicThis is the prime mode
4th mode:
Scale 2751
Scale 2751: Sylygic, Ian Ring Music TheorySylygic
5th mode:
Scale 3423
Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
6th mode:
Scale 3759
Scale 3759: Darygic, Ian Ring Music TheoryDarygic
7th mode:
Scale 3927
Scale 3927: Monygic, Ian Ring Music TheoryMonygic
8th mode:
Scale 4011
Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
9th mode:
Scale 4053
Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic

Prime

The prime form of this scale is Scale 1407

Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic

Complement

The enneatonic modal family [2037, 1533, 1407, 2751, 3423, 3759, 3927, 4011, 4053] (Forte: 9-6) is the complement of the tritonic modal family [21, 1029, 1281] (Forte: 3-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2037 is 1533

Scale 1533Scale 1533: Katycrygic, Ian Ring Music TheoryKatycrygic

Transformations:

T0 2037  T0I 1533
T1 4074  T1I 3066
T2 4053  T2I 2037
T3 4011  T3I 4074
T4 3927  T4I 4053
T5 3759  T5I 4011
T6 3423  T6I 3927
T7 2751  T7I 3759
T8 1407  T8I 3423
T9 2814  T9I 2751
T10 1533  T10I 1407
T11 3066  T11I 2814

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 2039Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian
Scale 2033Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic
Scale 2035Scale 2035: Aerythygic, Ian Ring Music TheoryAerythygic
Scale 2041Scale 2041: Aeolacrygic, Ian Ring Music TheoryAeolacrygic
Scale 2045Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
Scale 2021Scale 2021: Katycryllic, Ian Ring Music TheoryKatycryllic
Scale 2029Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
Scale 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
Scale 1781Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic
Scale 1525Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
Scale 1013Scale 1013: Stydyllic, Ian Ring Music TheoryStydyllic
Scale 3061Scale 3061: Apinygic, Ian Ring Music TheoryApinygic
Scale 4085Scale 4085: Rechberger's Decamode, Ian Ring Music TheoryRechberger's Decamode

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.