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Scale 1663: "Lydygic"

Scale 1663: Lydygic, 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
Lydygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,5,6,9,10}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 4045
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 895
Deep Scaleno
Interval Vector767763
Interval Spectrump6m7n7s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2.222
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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 TriadsD{2,6,9}442.24
F{5,9,0}342.35
F♯{6,10,1}342.24
A{9,1,4}342.35
A♯{10,2,5}342.35
Minor Triadsdm{2,5,9}342.24
d♯m{3,6,10}342.53
f♯m{6,9,1}442.12
am{9,0,4}342.53
a♯m{10,1,5}442.24
Augmented TriadsC♯+{1,5,9}542
D+{2,6,10}442.24
Diminished Triads{0,3,6}242.76
d♯°{3,6,9}252.71
f♯°{6,9,0}242.59
{9,0,3}242.76
a♯°{10,1,4}252.71
Parsimonious Voice Leading Between Common Triads of Scale 1663. Created by Ian Ring ©2019 d#m d#m c°->d#m c°->a° C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m A A C#+->A a#m a#m C#+->a#m D D dm->D A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° D->f#m D+->d#m F# F# D+->F# D+->A# d#°->d#m f#° f#° F->f#° am am F->am f#°->f#m f#m->F# F#->a#m a°->am am->A a#° a#° A->a#° a#°->a#m a#m->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.

Diameter5
Radius4
Self-Centeredno
Central Verticesc°, C♯+, dm, D, D+, d♯m, F, f♯°, f♯m, F♯, a°, am, A, a♯m, A♯
Peripheral Verticesd♯°, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 1663 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2879
Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
3rd mode:
Scale 3487
Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
4th mode:
Scale 3791
Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
5th mode:
Scale 3943
Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
6th mode:
Scale 4019
Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
7th mode:
Scale 4057
Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
8th mode:
Scale 1019
Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
9th mode:
Scale 2557
Scale 2557: Dothygic, Ian Ring Music TheoryDothygic

Prime

The prime form of this scale is Scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Complement

The nonatonic modal family [1663, 2879, 3487, 3791, 3943, 4019, 4057, 1019, 2557] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1663 is 4045

Scale 4045Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1663 is chiral, and its enantiomorph is scale 4045

Scale 4045Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic

Transformations:

T0 1663  T0I 4045
T1 3326  T1I 3995
T2 2557  T2I 3895
T3 1019  T3I 3695
T4 2038  T4I 3295
T5 4076  T5I 2495
T6 4057  T6I 895
T7 4019  T7I 1790
T8 3943  T8I 3580
T9 3791  T9I 3065
T10 3487  T10I 2035
T11 2879  T11I 4070

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 1661Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
Scale 1659Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban
Scale 1655Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic
Scale 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
Scale 1727Scale 1727: Sydygic, Ian Ring Music TheorySydygic
Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian
Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian
Scale 1151Scale 1151: Mythyllic, Ian Ring Music TheoryMythyllic
Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic
Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic
Scale 2687Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
Scale 3711Scale 3711: Dycryllian, Ian Ring Music TheoryDycryllian

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.