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Scale 2287: "Lodyllic"

Scale 2287: Lodyllic, 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
Lodyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,5,6,7,11}
Forte Number8-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3811
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 479
Deep Scaleno
Interval Vector654553
Interval Spectrump5m5n4s5d6t3
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation2.75
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsG{7,11,2}231.57
B{11,3,6}321.29
Minor Triadscm{0,3,7}241.86
bm{11,2,6}331.43
Augmented TriadsD♯+{3,7,11}331.43
Diminished Triads{0,3,6}231.71
{11,2,5}142.14
Parsimonious Voice Leading Between Common Triads of Scale 2287. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ Parsimonious Voice Leading Between Common Triads of Scale 2287. Created by Ian Ring ©2019 G D#+->G D#+->B bm bm G->bm b°->bm bm->B

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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
Radius2
Self-Centeredno
Central VerticesB
Peripheral Verticescm, b°

Modes

Modes are the rotational transformation of this scale. Scale 2287 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3191
Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
3rd mode:
Scale 3643
Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
4th mode:
Scale 3869
Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic
5th mode:
Scale 1991
Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic
6th mode:
Scale 3043
Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
7th mode:
Scale 3569
Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic
8th mode:
Scale 479
Scale 479: Kocryllic, Ian Ring Music TheoryKocryllicThis is the prime mode

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [2287, 3191, 3643, 3869, 1991, 3043, 3569, 479] (Forte: 8-5) is the complement of the tetratonic modal family [71, 449, 2083, 3089] (Forte: 4-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2287 is 3811

Scale 3811Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2287 is chiral, and its enantiomorph is scale 3811

Scale 3811Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic

Transformations:

T0 2287  T0I 3811
T1 479  T1I 3527
T2 958  T2I 2959
T3 1916  T3I 1823
T4 3832  T4I 3646
T5 3569  T5I 3197
T6 3043  T6I 2299
T7 1991  T7I 503
T8 3982  T8I 1006
T9 3869  T9I 2012
T10 3643  T10I 4024
T11 3191  T11I 3953

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 2285Scale 2285: Aerogian, Ian Ring Music TheoryAerogian
Scale 2283Scale 2283: Aeolyptian, Ian Ring Music TheoryAeolyptian
Scale 2279Scale 2279: Dyrian, Ian Ring Music TheoryDyrian
Scale 2295Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
Scale 2303Scale 2303: Stanygic, Ian Ring Music TheoryStanygic
Scale 2255Scale 2255: Dylian, Ian Ring Music TheoryDylian
Scale 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian
Scale 2159Scale 2159, Ian Ring Music Theory
Scale 2415Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
Scale 2543Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
Scale 2799Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic
Scale 3311Scale 3311: Mixodygic, Ian Ring Music TheoryMixodygic
Scale 239Scale 239, Ian Ring Music Theory
Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic

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.