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Scale 3957: "Porygic"

Scale 3957: Porygic, 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
Porygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,4,5,6,8,9,10,11}
Forte Number9-8
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1503
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1503
Deep Scaleno
Interval Vector676764
Interval Spectrump6m7n6s7d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.556
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
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}342.33
E{4,8,11}342.47
F{5,9,0}442.07
A♯{10,2,5}342.33
Minor Triadsdm{2,5,9}442.07
fm{5,8,0}442.2
am{9,0,4}242.47
bm{11,2,6}342.47
Augmented TriadsC+{0,4,8}342.4
D+{2,6,10}342.4
Diminished Triadsd°{2,5,8}242.33
f°{5,8,11}242.53
f♯°{6,9,0}242.47
g♯°{8,11,2}242.53
b°{11,2,5}242.67
Parsimonious Voice Leading Between Common Triads of Scale 3957. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm am am C+->am d° d° dm dm d°->dm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° D+->A# bm bm D+->bm f° f° E->f° g#° g#° E->g#° f°->fm fm->F F->f#° F->am g#°->bm b° b° A#->b° b°->bm

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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 3957 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2013		Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
3rd mode:
Scale 1527		Scale 1527: Aeolyrigic, Ian Ring Music TheoryAeolyrigic
4th mode:
Scale 2811		Scale 2811: Barygic, Ian Ring Music TheoryBarygic
5th mode:
Scale 3453		Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
6th mode:
Scale 1887		Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic
7th mode:
Scale 2991		Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
8th mode:
Scale 3543		Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
9th mode:
Scale 3819		Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic

Prime

The prime form of this scale is Scale 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Complement

The nonatonic modal family [3957, 2013, 1527, 2811, 3453, 1887, 2991, 3543, 3819] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3957 is 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3957 is chiral, and its enantiomorph is scale 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Transformations:

T0 3957  T0I 1503
T1 3819  T1I 3006
T2 3543  T2I 1917
T3 2991  T3I 3834
T4 1887  T4I 3573
T5 3774  T5I 3051
T6 3453  T6I 2007
T7 2811  T7I 4014
T8 1527  T8I 3933
T9 3054  T9I 3771
T10 2013  T10I 3447
T11 4026  T11I 2799

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 3959Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
Scale 3953Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 3965Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 4021Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
Scale 4085Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
Scale 3701Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse
Scale 2933Scale 2933, Ian Ring Music Theory
Scale 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic

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.