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Scale 1863: "Pycrian"

Scale 1863: Pycrian, 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
Pycrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,6,8,9,10}
Forte Number7-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3165
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 375
Deep Scaleno
Interval Vector443532
Interval Spectrump3m5n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsD{2,6,9}221.2
F♯{6,10,1}221.2
Minor Triadsf♯m{6,9,1}321
Augmented TriadsD+{2,6,10}231.4
Diminished Triadsf♯°{6,9,0}131.6
Parsimonious Voice Leading Between Common Triads of Scale 1863. Created by Ian Ring ©2019 D D D+ D+ D->D+ f#m f#m D->f#m F# F# D+->F# f#° f#° f#°->f#m f#m->F#

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.

Diameter3
Radius2
Self-Centeredno
Central VerticesD, f♯m, F♯
Peripheral VerticesD+, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 1863 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2979
Scale 2979: Gyptian, Ian Ring Music TheoryGyptian
3rd mode:
Scale 3537
Scale 3537: Katogian, Ian Ring Music TheoryKatogian
4th mode:
Scale 477
Scale 477: Stacrian, Ian Ring Music TheoryStacrian
5th mode:
Scale 1143
Scale 1143: Styrian, Ian Ring Music TheoryStyrian
6th mode:
Scale 2619
Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
7th mode:
Scale 3357
Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian

Prime

The prime form of this scale is Scale 375

Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian

Complement

The heptatonic modal family [1863, 2979, 3537, 477, 1143, 2619, 3357] (Forte: 7-13) is the complement of the pentatonic modal family [279, 369, 1809, 2187, 3141] (Forte: 5-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1863 is 3165

Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1863 is chiral, and its enantiomorph is scale 3165

Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian

Transformations:

T0 1863  T0I 3165
T1 3726  T1I 2235
T2 3357  T2I 375
T3 2619  T3I 750
T4 1143  T4I 1500
T5 2286  T5I 3000
T6 477  T6I 1905
T7 954  T7I 3810
T8 1908  T8I 3525
T9 3816  T9I 2955
T10 3537  T10I 1815
T11 2979  T11I 3630

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 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 1859Scale 1859, Ian Ring Music Theory
Scale 1867Scale 1867: Solian, Ian Ring Music TheorySolian
Scale 1871Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
Scale 1799Scale 1799, Ian Ring Music Theory
Scale 1831Scale 1831: Pothian, Ian Ring Music TheoryPothian
Scale 1927Scale 1927, Ian Ring Music Theory
Scale 1991Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic
Scale 1607Scale 1607: Epytimic, Ian Ring Music TheoryEpytimic
Scale 1735Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam
Scale 1351Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic
Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic

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.