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Scale 3987: "Loryllic"

Scale 3987: Loryllic, 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
Loryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,4,7,8,9,10,11}
Forte Number8-3
Rotational Symmetrynone
Reflection Axes4
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[8]
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}341.91
E{4,8,11}242.09
A{9,1,4}342
Minor Triadsc♯m{1,4,8}341.91
em{4,7,11}342
am{9,0,4}242.09
Augmented TriadsC+{0,4,8}441.82
Diminished Triadsc♯°{1,4,7}242.18
{4,7,10}242.27
{7,10,1}242.36
a♯°{10,1,4}242.27
Parsimonious Voice Leading Between Common Triads of Scale 3987. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E am am C+->am c#°->c#m A A c#m->A e°->em e°->g° em->E a#° a#° g°->a#° am->A A->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 3987 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 4041
Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
3rd mode:
Scale 1017
Scale 1017: Dythyllic, Ian Ring Music TheoryDythyllic
4th mode:
Scale 639
Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllicThis is the prime mode
5th mode:
Scale 2367
Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
6th mode:
Scale 3231
Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
7th mode:
Scale 3663
Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
8th mode:
Scale 3879
Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic

Prime

The prime form of this scale is Scale 639

Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic

Complement

The octatonic modal family [3987, 4041, 1017, 639, 2367, 3231, 3663, 3879] (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 3987 is 2367

Scale 2367Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic

Transformations:

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

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 3985Scale 3985: Thadian, Ian Ring Music TheoryThadian
Scale 3989Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic
Scale 3991Scale 3991: Badygic, Ian Ring Music TheoryBadygic
Scale 3995Scale 3995: Ionygic, Ian Ring Music TheoryIonygic
Scale 3971Scale 3971, Ian Ring Music Theory
Scale 3979Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
Scale 4019Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
Scale 4051Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic
Scale 3859Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
Scale 3923Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic
Scale 3731Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian
Scale 3475Scale 3475: Kylian, Ian Ring Music TheoryKylian
Scale 2963Scale 2963: Bygian, Ian Ring Music TheoryBygian
Scale 1939Scale 1939: Dathian, Ian Ring Music TheoryDathian

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.