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Scale 3319: "Tholygic"

Scale 3319: Tholygic, 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
Tholygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,4,5,6,7,10,11}
Forte Number9-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3559
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 TriadsC{0,4,7}242.64
F♯{6,10,1}342.21
G{7,11,2}342.14
A♯{10,2,5}342.21
Minor Triadsem{4,7,11}342.36
gm{7,10,2}442.07
a♯m{10,1,5}342.29
bm{11,2,6}342.21
Augmented TriadsD+{2,6,10}442
Diminished Triadsc♯°{1,4,7}242.71
{4,7,10}242.43
{7,10,1}242.43
a♯°{10,1,4}242.57
{11,2,5}242.57
Parsimonious Voice Leading Between Common Triads of Scale 3319. Created by Ian Ring ©2019 C C c#° c#° C->c#° em em C->em a#° a#° c#°->a#° D+ D+ F# F# D+->F# gm gm D+->gm A# A# D+->A# bm bm D+->bm e°->em e°->gm Parsimonious Voice Leading Between Common Triads of Scale 3319. Created by Ian Ring ©2019 G em->G F#->g° a#m a#m F#->a#m g°->gm gm->G G->bm a#°->a#m a#m->A# A#->b° b°->bm

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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 3319 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3707
Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
3rd mode:
Scale 3901
Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
4th mode:
Scale 1999
Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
5th mode:
Scale 3047
Scale 3047: Panygic, Ian Ring Music TheoryPanygic
6th mode:
Scale 3571
Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
7th mode:
Scale 3833
Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
8th mode:
Scale 991
Scale 991: Aeolygic, Ian Ring Music TheoryAeolygicThis is the prime mode
9th mode:
Scale 2543
Scale 2543: Dydygic, Ian Ring Music TheoryDydygic

Prime

The prime form of this scale is Scale 991

Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic

Complement

The nonatonic modal family [3319, 3707, 3901, 1999, 3047, 3571, 3833, 991, 2543] (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 3319 is 3559

Scale 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3319 is chiral, and its enantiomorph is scale 3559

Scale 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic

Transformations:

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

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 3317Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic
Scale 3315Scale 3315: Tcherepnin Octatonic Mode 1, Ian Ring Music TheoryTcherepnin Octatonic Mode 1
Scale 3323Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic
Scale 3327Scale 3327: Madyllian, Ian Ring Music TheoryMadyllian
Scale 3303Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic
Scale 3311Scale 3311: Mixodygic, Ian Ring Music TheoryMixodygic
Scale 3287Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3191Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
Scale 3447Scale 3447: Mogyllian, Ian Ring Music TheoryMogyllian
Scale 3575Scale 3575: Symmetrical Decatonic, Ian Ring Music TheorySymmetrical Decatonic
Scale 3831Scale 3831: Ionyllian, Ian Ring Music TheoryIonyllian
Scale 2295Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
Scale 2807Scale 2807: Zylygic, Ian Ring Music TheoryZylygic
Scale 1271Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic

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.