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Scale 4073: "Sathygic"

Scale 4073: Sathygic, 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
Sathygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,3,5,6,7,8,9,10,11}
Forte Number9-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 767
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 767
Deep Scaleno
Interval Vector777663
Interval Spectrump6m6n7s7d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {7,8,9,10}
<8> = {9,10,11}
Spectra Variation2.444
Maximally Evenno
Maximal Area Setno
Interior Area2.683
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsD♯{3,7,10}242.43
F{5,9,0}342.43
G♯{8,0,3}442.07
B{11,3,6}342.29
Minor Triadscm{0,3,7}342.14
d♯m{3,6,10}342.43
fm{5,8,0}342.29
g♯m{8,11,3}342.14
Augmented TriadsD♯+{3,7,11}442.07
Diminished Triads{0,3,6}242.5
d♯°{3,6,9}242.57
{5,8,11}242.5
f♯°{6,9,0}242.57
{9,0,3}242.43
Parsimonious Voice Leading Between Common Triads of Scale 4073. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° D# D# d#m->D# d#m->B D#->D#+ g#m g#m D#+->g#m D#+->B fm fm f°->fm f°->g#m F F fm->F fm->G# F->f#° F->a° g#m->G# G#->a°

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 4073 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1021
Scale 1021: Ladygic, Ian Ring Music TheoryLadygic
3rd mode:
Scale 1279
Scale 1279: Sarygic, Ian Ring Music TheorySarygic
4th mode:
Scale 2687
Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
5th mode:
Scale 3391
Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
6th mode:
Scale 3743
Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
7th mode:
Scale 3919
Scale 3919: Lynygic, Ian Ring Music TheoryLynygic
8th mode:
Scale 4007
Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic
9th mode:
Scale 4051
Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic

Prime

The prime form of this scale is Scale 767

Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic

Complement

The nonatonic modal family [4073, 1021, 1279, 2687, 3391, 3743, 3919, 4007, 4051] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4073 is 767

Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 4073 is chiral, and its enantiomorph is scale 767

Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic

Transformations:

T0 4073  T0I 767
T1 4051  T1I 1534
T2 4007  T2I 3068
T3 3919  T3I 2041
T4 3743  T4I 4082
T5 3391  T5I 4069
T6 2687  T6I 4043
T7 1279  T7I 3991
T8 2558  T8I 3887
T9 1021  T9I 3679
T10 2042  T10I 3263
T11 4084  T11I 2431

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 4075Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 4065Scale 4065, Ian Ring Music Theory
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic
Scale 4081Scale 4081: Manygic, Ian Ring Music TheoryManygic
Scale 4089Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian
Scale 4041Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
Scale 4009Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 3561Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
Scale 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 2025Scale 2025, Ian Ring Music Theory

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.