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Scale 4057: "Phrygic"

Scale 4057: Phrygic, 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
Phrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,3,4,6,7,8,9,10,11}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 895
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 895
Deep Scaleno
Interval Vector767763
Interval Spectrump6m7n7s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2.222
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}342.24
D♯{3,7,10}342.35
E{4,8,11}342.35
G♯{8,0,3}442.24
B{11,3,6}342.35
Minor Triadscm{0,3,7}442.12
d♯m{3,6,10}342.53
em{4,7,11}442.24
g♯m{8,11,3}342.24
am{9,0,4}342.53
Augmented TriadsC+{0,4,8}442.24
D♯+{3,7,11}542
Diminished Triads{0,3,6}242.59
d♯°{3,6,9}242.76
{4,7,10}252.71
f♯°{6,9,0}242.76
{9,0,3}252.71
Parsimonious Voice Leading Between Common Triads of Scale 4057. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E C+->G# am am C+->am d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° D# D# d#m->D# d#m->B D#->D#+ D#->e° D#+->em g#m g#m D#+->g#m D#+->B e°->em em->E E->g#m f#°->am g#m->G# G#->a° a°->am

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.

Diameter5
Radius4
Self-Centeredno
Central Verticesc°, cm, C, C+, d♯°, d♯m, D♯, D♯+, em, E, f♯°, g♯m, G♯, am, B
Peripheral Verticese°, a°

Modes

Modes are the rotational transformation of this scale. Scale 4057 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1019
Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
3rd mode:
Scale 2557
Scale 2557: Dothygic, Ian Ring Music TheoryDothygic
4th mode:
Scale 1663
Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
5th mode:
Scale 2879
Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
6th mode:
Scale 3487
Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
7th mode:
Scale 3791
Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
8th mode:
Scale 3943
Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
9th mode:
Scale 4019
Scale 4019: Lonygic, Ian Ring Music TheoryLonygic

Prime

The prime form of this scale is Scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Complement

The nonatonic modal family [4057, 1019, 2557, 1663, 2879, 3487, 3791, 3943, 4019] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4057 is 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 4057 is chiral, and its enantiomorph is scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Transformations:

T0 4057  T0I 895
T1 4019  T1I 1790
T2 3943  T2I 3580
T3 3791  T3I 3065
T4 3487  T4I 2035
T5 2879  T5I 4070
T6 1663  T6I 4045
T7 3326  T7I 3995
T8 2557  T8I 3895
T9 1019  T9I 3695
T10 2038  T10I 3295
T11 4076  T11I 2495

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 4059Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
Scale 4061Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
Scale 4049Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
Scale 4041Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
Scale 4073Scale 4073: Sathygic, Ian Ring Music TheorySathygic
Scale 4089Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian
Scale 3993Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
Scale 4025Scale 4025: Kalygic, Ian Ring Music TheoryKalygic
Scale 3929Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 3545Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic
Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.