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Scale 3961: "Zathygic"

Scale 3961: Zathygic, 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
Zathygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,3,4,5,6,8,9,10,11}
Forte Number9-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 991
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 991
Deep Scaleno
Interval Vector766674
Interval Spectrump7m6n6s6d7t4
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation1.778
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 TriadsE{4,8,11}342.21
F{5,9,0}342.29
G♯{8,0,3}442.07
B{11,3,6}342.36
Minor Triadsd♯m{3,6,10}242.64
fm{5,8,0}342.21
g♯m{8,11,3}342.14
am{9,0,4}342.21
Augmented TriadsC+{0,4,8}442
Diminished Triads{0,3,6}242.43
d♯°{3,6,9}242.71
{5,8,11}242.57
f♯°{6,9,0}242.57
{9,0,3}242.43
Parsimonious Voice Leading Between Common Triads of Scale 3961. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ E E C+->E fm fm C+->fm C+->G# am am C+->am d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° d#m->B E->f° g#m g#m E->g#m f°->fm F F fm->F F->f#° F->am g#m->G# g#m->B G#->a° a°->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 3961 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1007
Scale 1007: Epitygic, Ian Ring Music TheoryEpitygic
3rd mode:
Scale 2551
Scale 2551: Thocrygic, Ian Ring Music TheoryThocrygic
4th mode:
Scale 3323
Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic
5th mode:
Scale 3709
Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic
6th mode:
Scale 1951
Scale 1951: Marygic, Ian Ring Music TheoryMarygic
7th mode:
Scale 3023
Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
8th mode:
Scale 3559
Scale 3559: Thophygic, Ian Ring Music TheoryThophygic
9th mode:
Scale 3827
Scale 3827: Bodygic, Ian Ring Music TheoryBodygic

Prime

The prime form of this scale is Scale 991

Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic

Complement

The nonatonic modal family [3961, 1007, 2551, 3323, 3709, 1951, 3023, 3559, 3827] (Forte: 9-5) is the complement of the tritonic modal family [67, 193, 2081] (Forte: 3-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3961 is 991

Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3961 is chiral, and its enantiomorph is scale 991

Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic

Transformations:

T0 3961  T0I 991
T1 3827  T1I 1982
T2 3559  T2I 3964
T3 3023  T3I 3833
T4 1951  T4I 3571
T5 3902  T5I 3047
T6 3709  T6I 1999
T7 3323  T7I 3998
T8 2551  T8I 3901
T9 1007  T9I 3707
T10 2014  T10I 3319
T11 4028  T11I 2543

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 3963Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
Scale 3965Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse
Scale 3953Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3929Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
Scale 3897Scale 3897: Kalyllic, Ian Ring Music TheoryKalyllic
Scale 4025Scale 4025: Kalygic, Ian Ring Music TheoryKalygic
Scale 4089Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian
Scale 3705Scale 3705: Messiaen Mode 4 Inverse, Ian Ring Music TheoryMessiaen Mode 4 Inverse
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
Scale 3449Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
Scale 2937Scale 2937: Phragyllic, Ian Ring Music TheoryPhragyllic
Scale 1913Scale 1913, 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.

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.