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Scale 2491: "Layllic"

Scale 2491: Layllic, 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
Layllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,5,7,8,11}
Forte Number8-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2995
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 887
Deep Scaleno
Interval Vector545752
Interval Spectrump5m7n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.75
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}431.77
C♯{1,5,8}252.62
E{4,8,11}431.77
G♯{8,0,3}331.92
Minor Triadscm{0,3,7}342.15
c♯m{1,4,8}342.08
em{4,7,11}342
fm{5,8,0}342.08
g♯m{8,11,3}342.15
Augmented TriadsC+{0,4,8}531.54
D♯+{3,7,11}352.38
Diminished Triadsc♯°{1,4,7}242.31
{5,8,11}242.31
Parsimonious Voice Leading Between Common Triads of Scale 2491. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# c#°->c#m C# C# c#m->C# C#->fm D#+->em g#m g#m D#+->g#m em->E E->f° E->g#m f°->fm g#m->G#

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC, C+, E, G♯
Peripheral VerticesC♯, D♯+

Modes

Modes are the rotational transformation of this scale. Scale 2491 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3293
Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
3rd mode:
Scale 1847
Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
4th mode:
Scale 2971
Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
5th mode:
Scale 3533
Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
6th mode:
Scale 1907
Scale 1907: Lynyllic, Ian Ring Music TheoryLynyllic
7th mode:
Scale 3001
Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
8th mode:
Scale 887
Scale 887: Sathyllic, Ian Ring Music TheorySathyllicThis is the prime mode

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [2491, 3293, 1847, 2971, 3533, 1907, 3001, 887] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2491 is 2995

Scale 2995Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2491 is chiral, and its enantiomorph is scale 2995

Scale 2995Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra

Transformations:

T0 2491  T0I 2995
T1 887  T1I 1895
T2 1774  T2I 3790
T3 3548  T3I 3485
T4 3001  T4I 2875
T5 1907  T5I 1655
T6 3814  T6I 3310
T7 3533  T7I 2525
T8 2971  T8I 955
T9 1847  T9I 1910
T10 3694  T10I 3820
T11 3293  T11I 3545

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 2489Scale 2489: Mela Gangeyabhusani, Ian Ring Music TheoryMela Gangeyabhusani
Scale 2493Scale 2493: Manyllic, Ian Ring Music TheoryManyllic
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
Scale 2483Scale 2483: Double Harmonic, Ian Ring Music TheoryDouble Harmonic
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian
Scale 2523Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale
Scale 2555Scale 2555: Bythygic, Ian Ring Music TheoryBythygic
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian
Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
Scale 3003Scale 3003: Genus Chromaticum, Ian Ring Music TheoryGenus Chromaticum
Scale 3515Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian
Scale 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian

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.