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Scale 3263: "Pyrygic"

Scale 3263: Pyrygic, 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

41161837294116105072918310504116183
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
Pyrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,5,7,10,11}
Forte Number9-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 4007
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 767
Deep Scaleno
Interval Vector777663
Interval Spectrump6m6n7s7d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {7,8,9,10}
<8> = {9,10,11}
Spectra Variation2.444
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 TriadsC{0,4,7}342.43
D♯{3,7,10}342.14
G{7,11,2}342.14
A♯{10,2,5}342.29
Minor Triadscm{0,3,7}242.43
em{4,7,11}342.29
gm{7,10,2}442.07
a♯m{10,1,5}342.43
Augmented TriadsD♯+{3,7,11}442.07
Diminished Triadsc♯°{1,4,7}242.57
{4,7,10}242.5
{7,10,1}242.43
a♯°{10,1,4}242.57
{11,2,5}242.5
Parsimonious Voice Leading Between Common Triads of Scale 3263. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ c#° c#° C->c#° em em C->em a#° a#° c#°->a#° D# D# D#->D#+ D#->e° gm gm D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3263. Created by Ian Ring ©2019 G D#+->G e°->em g°->gm a#m a#m g°->a#m gm->G A# A# gm->A# G->b° a#°->a#m a#m->A# A#->b°

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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 3263 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3679
Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
3rd mode:
Scale 3887
Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
4th mode:
Scale 3991
Scale 3991: Badygic, Ian Ring Music TheoryBadygic
5th mode:
Scale 4043
Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
6th mode:
Scale 4069
Scale 4069: Starygic, Ian Ring Music TheoryStarygic
7th mode:
Scale 2041
Scale 2041: Aeolacrygic, Ian Ring Music TheoryAeolacrygic
8th mode:
Scale 767
Scale 767: Raptygic, Ian Ring Music TheoryRaptygicThis is the prime mode
9th mode:
Scale 2431
Scale 2431: Gythygic, Ian Ring Music TheoryGythygic

Prime

The prime form of this scale is Scale 767

Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic

Complement

The nonatonic modal family [3263, 3679, 3887, 3991, 4043, 4069, 2041, 767, 2431] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3263 is 4007

Scale 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3263 is chiral, and its enantiomorph is scale 4007

Scale 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic

Transformations:

T0 3263  T0I 4007
T1 2431  T1I 3919
T2 767  T2I 3743
T3 1534  T3I 3391
T4 3068  T4I 2687
T5 2041  T5I 1279
T6 4082  T6I 2558
T7 4069  T7I 1021
T8 4043  T8I 2042
T9 3991  T9I 4084
T10 3887  T10I 4073
T11 3679  T11I 4051

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 3261Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
Scale 3259Scale 3259, Ian Ring Music Theory
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3247Scale 3247: Aeolonyllic, Ian Ring Music TheoryAeolonyllic
Scale 3231Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3327Scale 3327: Madyllian, Ian Ring Music TheoryMadyllian
Scale 3135Scale 3135, Ian Ring Music Theory
Scale 3199Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic
Scale 3391Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
Scale 3519Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
Scale 3775Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian
Scale 2239Scale 2239: Dacryllic, Ian Ring Music TheoryDacryllic
Scale 2751Scale 2751: Sylygic, Ian Ring Music TheorySylygic
Scale 1215Scale 1215, Ian Ring Music Theory

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.