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Scale 1759: "Pylygic"

Scale 1759: Pylygic, 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
Pylygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,6,7,9,10}
Forte Number9-10
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes8
Prime?yes
Deep Scaleno
Interval Vector668664
Interval Spectrump6m6n8s6d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
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{0,4,7}442.42
D{2,6,9}342.47
D♯{3,7,10}442.32
F♯{6,10,1}442.37
A{9,1,4}442.37
Minor Triadscm{0,3,7}442.37
d♯m{3,6,10}442.37
f♯m{6,9,1}442.32
gm{7,10,2}342.47
am{9,0,4}442.42
Augmented TriadsD+{2,6,10}442.32
Diminished Triads{0,3,6}242.63
c♯°{1,4,7}242.63
d♯°{3,6,9}242.74
{4,7,10}242.58
f♯°{6,9,0}242.58
{7,10,1}242.74
{9,0,3}242.63
a♯°{10,1,4}242.63
Parsimonious Voice Leading Between Common Triads of Scale 1759. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# cm->a° c#° c#° C->c#° C->e° am am C->am A A c#°->A D D D+ D+ D->D+ d#° d#° D->d#° f#m f#m D->f#m D+->d#m F# F# D+->F# gm gm D+->gm d#°->d#m d#m->D# D#->e° D#->gm f#° f#° f#°->f#m f#°->am f#m->F# f#m->A F#->g° a#° a#° F#->a#° g°->gm a°->am 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 1759 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2927
Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
3rd mode:
Scale 3511
Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
4th mode:
Scale 3803
Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
5th mode:
Scale 3949
Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
6th mode:
Scale 2011
Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic
7th mode:
Scale 3053
Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic
8th mode:
Scale 1787
Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic
9th mode:
Scale 2941
Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic

Prime

This is the prime form of this scale.

Complement

The nonatonic modal family [1759, 2927, 3511, 3803, 3949, 2011, 3053, 1787, 2941] (Forte: 9-10) is the complement of the tritonic modal family [73, 521, 577] (Forte: 3-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1759 is 3949

Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic

Transformations:

T0 1759  T0I 3949
T1 3518  T1I 3803
T2 2941  T2I 3511
T3 1787  T3I 2927
T4 3574  T4I 1759
T5 3053  T5I 3518
T6 2011  T6I 2941
T7 4022  T7I 1787
T8 3949  T8I 3574
T9 3803  T9I 3053
T10 3511  T10I 2011
T11 2927  T11I 4022

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 1757Scale 1757, Ian Ring Music Theory
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1751Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic
Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic
Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian
Scale 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic
Scale 1727Scale 1727: Sydygic, Ian Ring Music TheorySydygic
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 1887Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic
Scale 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
Scale 1503Scale 1503: Epiryllian, Ian Ring Music TheoryEpiryllian
Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
Scale 3807Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian

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.