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Scale 2367: "Laryllic"

Scale 2367: Laryllic, 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
Laryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,5,8,11}
Forte Number8-3
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 639
Deep Scaleno
Interval Vector656542
Interval Spectrump4m5n6s5d6t2
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {3,5,7}
<4> = {4,6,8}
<5> = {5,7,9}
<6> = {6,8,10}
<7> = {9,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.5
Myhill Propertyno
Balancedno
Ridge Tones[4]
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
E{4,8,11}341.91
G♯{8,0,3}242.09
Minor Triadsc♯m{1,4,8}242.09
fm{5,8,0}341.91
g♯m{8,11,3}342
Augmented TriadsC+{0,4,8}441.82
Diminished Triads{2,5,8}242.27
{5,8,11}242.18
g♯°{8,11,2}242.27
{11,2,5}242.36
Parsimonious Voice Leading Between Common Triads of Scale 2367. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm G# G# C+->G# C# C# c#m->C# C#->d° C#->fm d°->b° E->f° g#m g#m E->g#m f°->fm g#° g#° g#°->g#m g#°->b° g#m->G#

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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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2367 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3231
Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
3rd mode:
Scale 3663
Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
4th mode:
Scale 3879
Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
5th mode:
Scale 3987
Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic
6th mode:
Scale 4041
Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
7th mode:
Scale 1017
Scale 1017: Dythyllic, Ian Ring Music TheoryDythyllic
8th mode:
Scale 639
Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllicThis is the prime mode

Prime

The prime form of this scale is Scale 639

Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic

Complement

The octatonic modal family [2367, 3231, 3663, 3879, 3987, 4041, 1017, 639] (Forte: 8-3) is the complement of the tetratonic modal family [27, 1539, 2061, 2817] (Forte: 4-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2367 is 3987

Scale 3987Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic

Transformations:

T0 2367  T0I 3987
T1 639  T1I 3879
T2 1278  T2I 3663
T3 2556  T3I 3231
T4 1017  T4I 2367
T5 2034  T5I 639
T6 4068  T6I 1278
T7 4041  T7I 2556
T8 3987  T8I 1017
T9 3879  T9I 2034
T10 3663  T10I 4068
T11 3231  T11I 4041

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 2365Scale 2365: Sythian, Ian Ring Music TheorySythian
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 2359Scale 2359: Gadian, Ian Ring Music TheoryGadian
Scale 2351Scale 2351: Gynian, Ian Ring Music TheoryGynian
Scale 2335Scale 2335: Epydian, Ian Ring Music TheoryEpydian
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
Scale 2111Scale 2111, Ian Ring Music Theory
Scale 2239Scale 2239: Dacryllic, Ian Ring Music TheoryDacryllic
Scale 2623Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic
Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
Scale 3391Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 1343Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic

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.