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Scale 2269: "Pygian"

Scale 2269: Pygian, 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
Pygian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,4,6,7,11}
Forte Number7-Z37
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 443
Deep Scaleno
Interval Vector434541
Interval Spectrump4m5n4s3d4t
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {7,9,10}
<6> = {8,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tones[6]
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}242
G{7,11,2}231.75
B{11,3,6}331.5
Minor Triadscm{0,3,7}331.5
em{4,7,11}231.75
bm{11,2,6}242
Augmented TriadsD♯+{3,7,11}421.25
Diminished Triads{0,3,6}231.75
Parsimonious Voice Leading Between Common Triads of Scale 2269. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ em em C->em D#+->em Parsimonious Voice Leading Between Common Triads of Scale 2269. Created by Ian Ring ©2019 G D#+->G D#+->B bm bm G->bm bm->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
Radius2
Self-Centeredno
Central VerticesD♯+
Peripheral VerticesC, bm

Modes

Modes are the rotational transformation of this scale. Scale 2269 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1591
Scale 1591: Rodian, Ian Ring Music TheoryRodian
3rd mode:
Scale 2843
Scale 2843: Sorian, Ian Ring Music TheorySorian
4th mode:
Scale 3469
Scale 3469: Monian, Ian Ring Music TheoryMonian
5th mode:
Scale 1891
Scale 1891: Thalian, Ian Ring Music TheoryThalian
6th mode:
Scale 2993
Scale 2993: Stythian, Ian Ring Music TheoryStythian
7th mode:
Scale 443
Scale 443: Kothian, Ian Ring Music TheoryKothianThis is the prime mode

Prime

The prime form of this scale is Scale 443

Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian

Complement

The heptatonic modal family [2269, 1591, 2843, 3469, 1891, 2993, 443] (Forte: 7-Z37) is the complement of the pentatonic modal family [313, 551, 913, 2323, 3209] (Forte: 5-Z37)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2269 is 1891

Scale 1891Scale 1891: Thalian, Ian Ring Music TheoryThalian

Transformations:

T0 2269  T0I 1891
T1 443  T1I 3782
T2 886  T2I 3469
T3 1772  T3I 2843
T4 3544  T4I 1591
T5 2993  T5I 3182
T6 1891  T6I 2269
T7 3782  T7I 443
T8 3469  T8I 886
T9 2843  T9I 1772
T10 1591  T10I 3544
T11 3182  T11I 2993

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 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
Scale 2265Scale 2265: Raga Rasamanjari, Ian Ring Music TheoryRaga Rasamanjari
Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian
Scale 2261Scale 2261: Raga Caturangini, Ian Ring Music TheoryRaga Caturangini
Scale 2253Scale 2253: Raga Amarasenapriya, Ian Ring Music TheoryRaga Amarasenapriya
Scale 2285Scale 2285: Aerogian, Ian Ring Music TheoryAerogian
Scale 2301Scale 2301: Bydyllic, Ian Ring Music TheoryBydyllic
Scale 2205Scale 2205: Ionocrimic, Ian Ring Music TheoryIonocrimic
Scale 2237Scale 2237: Epothian, Ian Ring Music TheoryEpothian
Scale 2141Scale 2141, Ian Ring Music Theory
Scale 2397Scale 2397: Stagian, Ian Ring Music TheoryStagian
Scale 2525Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
Scale 2781Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
Scale 3293Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
Scale 221Scale 221, Ian Ring Music Theory
Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian

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.