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Scale 1861: "Phrygimic"

Scale 1861: Phrygimic, 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
Phrygimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,6,8,9,10}
Forte Number6-21
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1117
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections5
Modes5
Prime?no
prime: 349
Deep Scaleno
Interval Vector242412
Interval Spectrumpm4n2s4d2t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {8,10,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.232
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}210.67
Augmented TriadsD+{2,6,10}121
Diminished Triadsf♯°{6,9,0}121
Parsimonious Voice Leading Between Common Triads of Scale 1861. Created by Ian Ring ©2019 D D D+ D+ D->D+ f#° f#° D->f#°

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.

Diameter2
Radius1
Self-Centeredno
Central VerticesD
Peripheral VerticesD+, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 1861 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1489
Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti
3rd mode:
Scale 349
Scale 349: Borimic, Ian Ring Music TheoryBorimicThis is the prime mode
4th mode:
Scale 1111
Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic
5th mode:
Scale 2603
Scale 2603: Gadimic, Ian Ring Music TheoryGadimic
6th mode:
Scale 3349
Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic

Prime

The prime form of this scale is Scale 349

Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic

Complement

The hexatonic modal family [1861, 1489, 349, 1111, 2603, 3349] (Forte: 6-21) is the complement of the hexatonic modal family [349, 1111, 1489, 1861, 2603, 3349] (Forte: 6-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1861 is 1117

Scale 1117Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1861 is chiral, and its enantiomorph is scale 1117

Scale 1117Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic

Transformations:

T0 1861  T0I 1117
T1 3722  T1I 2234
T2 3349  T2I 373
T3 2603  T3I 746
T4 1111  T4I 1492
T5 2222  T5I 2984
T6 349  T6I 1873
T7 698  T7I 3746
T8 1396  T8I 3397
T9 2792  T9I 2699
T10 1489  T10I 1303
T11 2978  T11I 2606

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 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian
Scale 1857Scale 1857, Ian Ring Music Theory
Scale 1859Scale 1859, Ian Ring Music Theory
Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
Scale 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1893Scale 1893: Ionylian, Ian Ring Music TheoryIonylian
Scale 1797Scale 1797, Ian Ring Music Theory
Scale 1829Scale 1829: Pathimic, Ian Ring Music TheoryPathimic
Scale 1925Scale 1925, Ian Ring Music Theory
Scale 1989Scale 1989: Dydian, Ian Ring Music TheoryDydian
Scale 1605Scale 1605: Zanitonic, Ian Ring Music TheoryZanitonic
Scale 1733Scale 1733: Raga Sarasvati, Ian Ring Music TheoryRaga Sarasvati
Scale 1349Scale 1349: Tholitonic, Ian Ring Music TheoryTholitonic
Scale 837Scale 837: Epaditonic, Ian Ring Music TheoryEpaditonic
Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
Scale 3909Scale 3909: Rydian, Ian Ring Music TheoryRydian

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.