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Scale 1775: "Lyrygic"

Scale 1775: Lyrygic, 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
Lyrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,5,6,7,9,10}
Forte Number9-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3821
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes8
Prime?yes
Deep Scaleno
Interval Vector667773
Interval Spectrump7m7n7s6d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {5,6}
<5> = {6,7}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.111
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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}442.17
D♯{3,7,10}342.5
F{5,9,0}342.56
F♯{6,10,1}442.17
A♯{10,2,5}342.39
Minor Triadscm{0,3,7}342.67
dm{2,5,9}342.44
d♯m{3,6,10}442.28
f♯m{6,9,1}442.22
gm{7,10,2}342.39
a♯m{10,1,5}342.44
Augmented TriadsC♯+{1,5,9}442.33
D+{2,6,10}542
Diminished Triads{0,3,6}242.72
d♯°{3,6,9}242.56
f♯°{6,9,0}242.67
{7,10,1}242.67
{9,0,3}242.72
Parsimonious Voice Leading Between Common Triads of Scale 1775. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# cm->a° C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m 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# gm gm D+->gm D+->A# d#°->d#m d#m->D# D#->gm f#° f#° F->f#° F->a° f#°->f#m f#m->F# F#->g° F#->a#m g°->gm 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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1775 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2935
Scale 2935: Modygic, Ian Ring Music TheoryModygic
3rd mode:
Scale 3515
Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
4th mode:
Scale 3805
Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
5th mode:
Scale 1975
Scale 1975: Ionocrygic, Ian Ring Music TheoryIonocrygic
6th mode:
Scale 3035
Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
7th mode:
Scale 3565
Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
8th mode:
Scale 1915
Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
9th mode:
Scale 3005
Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic

Prime

This is the prime form of this scale.

Complement

The nonatonic modal family [1775, 2935, 3515, 3805, 1975, 3035, 3565, 1915, 3005] (Forte: 9-11) is the complement of the tritonic modal family [137, 289, 529] (Forte: 3-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1775 is 3821

Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1775 is chiral, and its enantiomorph is scale 3821

Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic

Transformations:

T0 1775  T0I 3821
T1 3550  T1I 3547
T2 3005  T2I 2999
T3 1915  T3I 1903
T4 3830  T4I 3806
T5 3565  T5I 3517
T6 3035  T6I 2939
T7 1975  T7I 1783
T8 3950  T8I 3566
T9 3805  T9I 3037
T10 3515  T10I 1979
T11 2935  T11I 3958

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 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
Scale 1771Scale 1771, Ian Ring Music Theory
Scale 1767Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic
Scale 1783Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian
Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 1711Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh
Scale 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
Scale 1903Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic
Scale 2031Scale 2031: Gadyllian, Ian Ring Music TheoryGadyllian
Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic
Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed
Scale 751Scale 751, Ian Ring Music Theory
Scale 2799Scale 2799: Lyryllian, Ian Ring Music TheoryLyryllian
Scale 3823Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian

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.