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Scale 3291: "Lygyllic"

Scale 3291: Lygyllic, 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
Lygyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,6,7,10,11}
Forte Number8-18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2919
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 879
Deep Scaleno
Interval Vector546553
Interval Spectrump5m5n6s4d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
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}342.15
D♯{3,7,10}441.92
F♯{6,10,1}342.23
B{11,3,6}342.08
Minor Triadscm{0,3,7}342.08
d♯m{3,6,10}342
em{4,7,11}342.08
Augmented TriadsD♯+{3,7,11}441.85
Diminished Triads{0,3,6}242.46
c♯°{1,4,7}242.38
{4,7,10}242.31
{7,10,1}242.31
a♯°{10,1,4}242.46
Parsimonious Voice Leading Between Common Triads of Scale 3291. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ c#° c#° C->c#° em em C->em a#° a#° c#°->a#° d#m d#m D# D# d#m->D# F# F# d#m->F# d#m->B D#->D#+ D#->e° D#->g° D#+->em D#+->B e°->em F#->g° F#->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 3291 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3693
Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
3rd mode:
Scale 1947
Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic
4th mode:
Scale 3021
Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
5th mode:
Scale 1779
Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
6th mode:
Scale 2937
Scale 2937: Phragyllic, Ian Ring Music TheoryPhragyllic
7th mode:
Scale 879
Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllicThis is the prime mode
8th mode:
Scale 2487
Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic

Prime

The prime form of this scale is Scale 879

Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic

Complement

The octatonic modal family [3291, 3693, 1947, 3021, 1779, 2937, 879, 2487] (Forte: 8-18) is the complement of the tetratonic modal family [147, 609, 777, 2121] (Forte: 4-18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3291 is 2919

Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3291 is chiral, and its enantiomorph is scale 2919

Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic

Transformations:

T0 3291  T0I 2919
T1 2487  T1I 1743
T2 879  T2I 3486
T3 1758  T3I 2877
T4 3516  T4I 1659
T5 2937  T5I 3318
T6 1779  T6I 2541
T7 3558  T7I 987
T8 3021  T8I 1974
T9 1947  T9I 3948
T10 3894  T10I 3801
T11 3693  T11I 3507

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 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
Scale 3293Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3283Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari
Scale 3287Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
Scale 3307Scale 3307: Boptyllic, Ian Ring Music TheoryBoptyllic
Scale 3323Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic
Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 3259Scale 3259, Ian Ring Music Theory
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3547Scale 3547: Sadygic, Ian Ring Music TheorySadygic
Scale 3803Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian
Scale 2779Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich
Scale 1243Scale 1243: Epylian, Ian Ring Music TheoryEpylian

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.