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Scale 2415: "Lothyllic"

Scale 2415: Lothyllic, 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
Lothyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,5,6,8,11}
Forte Number8-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3795
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 735
Deep Scaleno
Interval Vector556453
Interval Spectrump5m4n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
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}242.27
G♯{8,0,3}341.91
B{11,3,6}341.91
Minor Triadsfm{5,8,0}342
g♯m{8,11,3}441.82
bm{11,2,6}342
Diminished Triads{0,3,6}242.18
{2,5,8}242.36
{5,8,11}242.09
g♯°{8,11,2}242.09
{11,2,5}242.27
Parsimonious Voice Leading Between Common Triads of Scale 2415. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C# C# C#->d° fm fm C#->fm d°->b° f°->fm g#m g#m f°->g#m fm->G# g#° g#° g#°->g#m bm bm g#°->bm g#m->G# g#m->B b°->bm bm->B

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 2415 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3255
Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
3rd mode:
Scale 3675
Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
4th mode:
Scale 3885
Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
5th mode:
Scale 1995
Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
6th mode:
Scale 3045
Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
7th mode:
Scale 1785
Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
8th mode:
Scale 735
Scale 735: Sylyllic, Ian Ring Music TheorySylyllicThis is the prime mode

Prime

The prime form of this scale is Scale 735

Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic

Complement

The octatonic modal family [2415, 3255, 3675, 3885, 1995, 3045, 1785, 735] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2415 is 3795

Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2415 is chiral, and its enantiomorph is scale 3795

Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic

Transformations:

T0 2415  T0I 3795
T1 735  T1I 3495
T2 1470  T2I 2895
T3 2940  T3I 1695
T4 1785  T4I 3390
T5 3570  T5I 2685
T6 3045  T6I 1275
T7 1995  T7I 2550
T8 3990  T8I 1005
T9 3885  T9I 2010
T10 3675  T10I 4020
T11 3255  T11I 3945

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 2413Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
Scale 2411Scale 2411: Aeolorian, Ian Ring Music TheoryAeolorian
Scale 2407Scale 2407: Zylian, Ian Ring Music TheoryZylian
Scale 2423Scale 2423, Ian Ring Music Theory
Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
Scale 2383Scale 2383: Katorian, Ian Ring Music TheoryKatorian
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 2351Scale 2351: Gynian, Ian Ring Music TheoryGynian
Scale 2479Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
Scale 2543Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
Scale 2159Scale 2159, Ian Ring Music Theory
Scale 2287Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic
Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
Scale 2927Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
Scale 3439Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian
Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

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.