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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

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
Sythygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,4,5,6,7,8,9,10}
Forte Number9-6
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1407
Deep Scaleno
Interval Vector686763
Interval Spectrump6m7n6s8d6t3
Distribution Spectra<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 Variation2
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tones[2]
ProprietyImproper
Heliotonicno

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

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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 nonatonic 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: Sydyllian, Ian Ring Music TheorySydyllian

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.