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Scale 411: "Lygimic"

Scale 411: Lygimic, 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

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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
Lygimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,4,7,8}
Forte Number6-Z19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2865
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes5
Prime?yes
Deep Scaleno
Interval Vector313431
Interval Spectrump3m4n3sd3t
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,4,5}
<3> = {4,5,6,7,8}
<4> = {7,8,9}
<5> = {8,9,10,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
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}321.17
G♯{8,0,3}231.5
Minor Triadscm{0,3,7}231.5
c♯m{1,4,8}231.5
Augmented TriadsC+{0,4,8}321.17
Diminished Triadsc♯°{1,4,7}231.5
Parsimonious Voice Leading Between Common Triads of Scale 411. Created by Ian Ring ©2019 cm cm C C cm->C G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m C+->G# c#°->c#m

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.

Diameter3
Radius2
Self-Centeredno
Central VerticesC, C+
Peripheral Verticescm, c♯°, c♯m, G♯

Modes

Modes are the rotational transformation of this scale. Scale 411 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2253
Scale 2253: Raga Amarasenapriya, Ian Ring Music TheoryRaga Amarasenapriya
3rd mode:
Scale 1587
Scale 1587: Raga Rudra Pancama, Ian Ring Music TheoryRaga Rudra Pancama
4th mode:
Scale 2841
Scale 2841: Sothimic, Ian Ring Music TheorySothimic
5th mode:
Scale 867
Scale 867: Phrocrimic, Ian Ring Music TheoryPhrocrimic
6th mode:
Scale 2481
Scale 2481: Raga Paraju, Ian Ring Music TheoryRaga Paraju

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [411, 2253, 1587, 2841, 867, 2481] (Forte: 6-Z19) is the complement of the hexatonic modal family [615, 825, 915, 2355, 2505, 3225] (Forte: 6-Z44)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 411 is 2865

Scale 2865Scale 2865: Solimic, Ian Ring Music TheorySolimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 411 is chiral, and its enantiomorph is scale 2865

Scale 2865Scale 2865: Solimic, Ian Ring Music TheorySolimic

Transformations:

T0 411  T0I 2865
T1 822  T1I 1635
T2 1644  T2I 3270
T3 3288  T3I 2445
T4 2481  T4I 795
T5 867  T5I 1590
T6 1734  T6I 3180
T7 3468  T7I 2265
T8 2841  T8I 435
T9 1587  T9I 870
T10 3174  T10I 1740
T11 2253  T11I 3480

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 409Scale 409: Laritonic, Ian Ring Music TheoryLaritonic
Scale 413Scale 413: Ganimic, Ian Ring Music TheoryGanimic
Scale 415Scale 415: Aeoladian, Ian Ring Music TheoryAeoladian
Scale 403Scale 403: Raga Reva, Ian Ring Music TheoryRaga Reva
Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic
Scale 395Scale 395: Phrygian Pentatonic, Ian Ring Music TheoryPhrygian Pentatonic
Scale 427Scale 427: Raga Suddha Simantini, Ian Ring Music TheoryRaga Suddha Simantini
Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian
Scale 475Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian
Scale 283Scale 283: Aerylitonic, Ian Ring Music TheoryAerylitonic
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 155Scale 155, Ian Ring Music Theory
Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic
Scale 923Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
Scale 1435Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam
Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian

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.