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Scale 3763: "Modyllic"

Scale 3763: Modyllic, 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
Modyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,4,5,7,9,10,11}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2479
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 863
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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}342
F{5,9,0}242.18
A{9,1,4}441.82
Minor Triadsem{4,7,11}242.27
am{9,0,4}341.91
a♯m{10,1,5}342
Augmented TriadsC♯+{1,5,9}341.91
Diminished Triadsc♯°{1,4,7}242.09
e°{4,7,10}242.36
g°{7,10,1}242.27
a♯°{10,1,4}242.09
Parsimonious Voice Leading Between Common Triads of Scale 3763. Created by Ian Ring ©2019 C C c#° c#° C->c#° em em C->em am am C->am A A c#°->A C#+ C#+ F F C#+->F C#+->A a#m a#m C#+->a#m e° e° e°->em g° g° e°->g° F->am g°->a#m am->A a#° a#° A->a#° a#°->a#m

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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 3763 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3929		Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
3rd mode:
Scale 1003		Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
4th mode:
Scale 2549		Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
5th mode:
Scale 1661		Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
6th mode:
Scale 1439		Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
7th mode:
Scale 2767		Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic
8th mode:
Scale 3431		Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [3763, 3929, 1003, 2549, 1661, 1439, 2767, 3431] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3763 is 2479

Scale 2479Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3763 is chiral, and its enantiomorph is scale 2479

Scale 2479Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed

Transformations:

T0 3763  T0I 2479
T1 3431  T1I 863
T2 2767  T2I 1726
T3 1439  T3I 3452
T4 2878  T4I 2809
T5 1661  T5I 1523
T6 3322  T6I 3046
T7 2549  T7I 1997
T8 1003  T8I 3994
T9 2006  T9I 3893
T10 4012  T10I 3691
T11 3929  T11I 3287

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 3761Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri
Scale 3765Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
Scale 3767Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
Scale 3771Scale 3771: Katodyllian, Ian Ring Music TheoryKatodyllian
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 3731Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 3827Scale 3827: Bodygic, Ian Ring Music TheoryBodygic
Scale 3635Scale 3635: Katygian, Ian Ring Music TheoryKatygian
Scale 3699Scale 3699: Galyllic, Ian Ring Music TheoryGalyllic
Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
Scale 4019Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari
Scale 3507Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz
Scale 2739Scale 2739: Mela Suryakanta, Ian Ring Music TheoryMela Suryakanta
Scale 1715Scale 1715: Harmonic Minor Inverse, Ian Ring Music TheoryHarmonic Minor Inverse

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.