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Scale 3755: "Phryryllic"

Scale 3755: Phryryllic, 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
Phryryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,5,7,9,10,11}
Forte Number8-21
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 1375
Deep Scaleno
Interval Vector474643
Interval Spectrump4m6n4s7d4t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tones[10]
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♯{3,7,10}242
F{5,9,0}242
Minor Triadscm{0,3,7}242
a♯m{10,1,5}242
Augmented TriadsC♯+{1,5,9}242
D♯+{3,7,11}242
Diminished Triads{7,10,1}242
{9,0,3}242
Parsimonious Voice Leading Between Common Triads of Scale 3755. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ cm->a° C#+ C#+ F F C#+->F a#m a#m C#+->a#m D# D# D#->D#+ D#->g° F->a° g°->a#m

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 3755 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3925
Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
3rd mode:
Scale 2005
Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
4th mode:
Scale 1525
Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
5th mode:
Scale 1405
Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
6th mode:
Scale 1375
Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllicThis is the prime mode
7th mode:
Scale 2735
Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
8th mode:
Scale 3415
Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic

Prime

The prime form of this scale is Scale 1375

Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic

Complement

The octatonic modal family [3755, 3925, 2005, 1525, 1405, 1375, 2735, 3415] (Forte: 8-21) is the complement of the tetratonic modal family [85, 1045, 1285, 1345] (Forte: 4-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3755 is 2735

Scale 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic

Transformations:

T0 3755  T0I 2735
T1 3415  T1I 1375
T2 2735  T2I 2750
T3 1375  T3I 1405
T4 2750  T4I 2810
T5 1405  T5I 1525
T6 2810  T6I 3050
T7 1525  T7I 2005
T8 3050  T8I 4010
T9 2005  T9I 3925
T10 4010  T10I 3755
T11 3925  T11I 3415

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 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
Scale 3759Scale 3759: Darygic, Ian Ring Music TheoryDarygic
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
Scale 3771Scale 3771: Stophygic, Ian Ring Music TheoryStophygic
Scale 3723Scale 3723: Myptian, Ian Ring Music TheoryMyptian
Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
Scale 3787Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
Scale 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
Scale 3627Scale 3627: Kalian, Ian Ring Music TheoryKalian
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel
Scale 2731Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2

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.