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Scale 3431: "Zyptyllic"

Scale 3431: Zyptyllic, 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
Zyptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,5,6,8,10,11}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3287
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♯{1,5,8}342
F♯{6,10,1}242.18
A♯{10,2,5}441.82
Minor Triadsfm{5,8,0}242.27
a♯m{10,1,5}341.91
bm{11,2,6}342
Augmented TriadsD+{2,6,10}341.91
Diminished Triads{2,5,8}242.09
{5,8,11}242.36
g♯°{8,11,2}242.27
{11,2,5}242.09
Parsimonious Voice Leading Between Common Triads of Scale 3431. Created by Ian Ring ©2019 C# C# C#->d° fm fm C#->fm a#m a#m C#->a#m A# A# d°->A# D+ D+ F# F# D+->F# D+->A# bm bm D+->bm f°->fm g#° g#° f°->g#° F#->a#m g#°->bm a#m->A# A#->b° b°->bm

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 3431 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3763
Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
3rd mode:
Scale 3929
Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
4th mode:
Scale 1003
Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
5th mode:
Scale 2549
Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
6th mode:
Scale 1661
Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
7th mode:
Scale 1439
Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
8th mode:
Scale 2767
Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [3431, 3763, 3929, 1003, 2549, 1661, 1439, 2767] (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 3431 is 3287

Scale 3287Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3431 is chiral, and its enantiomorph is scale 3287

Scale 3287Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic

Transformations:

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

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 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3427Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 3439Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
Scale 3447Scale 3447: Kynygic, Ian Ring Music TheoryKynygic
Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 3495Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
Scale 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3303Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic
Scale 3687Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic
Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
Scale 2407Scale 2407: Zylian, Ian Ring Music TheoryZylian
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 1383Scale 1383: Pynian, Ian Ring Music TheoryPynian

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. Special thanks to Richard Repp for helping with technical accuracy.