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Scale 4015: "Phradyllian"

Scale 4015: Phradyllian, 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
Phradyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,5,7,8,9,10,11}
Forte Number10-2
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia7 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1535
Deep Scaleno
Interval Vector898884
Interval Spectrump8m8n8s9d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {7,8,9}
<8> = {8,9,10}
<9> = {10,11}
Spectra Variation1.6
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
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 TriadsC♯{1,5,8}352.7
D♯{3,7,10}252.8
F{5,9,0}352.7
G{7,11,2}452.6
G♯{8,0,3}452.6
A♯{10,2,5}452.6
Minor Triadscm{0,3,7}252.8
dm{2,5,9}352.7
fm{5,8,0}452.6
gm{7,10,2}452.6
g♯m{8,11,3}452.6
a♯m{10,1,5}352.7
Augmented TriadsC♯+{1,5,9}452.6
D♯+{3,7,11}452.6
Diminished Triads{2,5,8}253
{5,8,11}252.8
{7,10,1}252.9
g♯°{8,11,2}252.8
{9,0,3}252.9
{11,2,5}252.8
Parsimonious Voice Leading Between Common Triads of Scale 4015. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F a#m a#m C#+->a#m d°->dm A# A# dm->A# D# D# D#->D#+ gm gm D#->gm Parsimonious Voice Leading Between Common Triads of Scale 4015. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m f°->fm f°->g#m fm->F fm->G# F->a° g°->gm g°->a#m gm->G gm->A# g#° g#° G->g#° G->b° g#°->g#m g#m->G# G#->a° a#m->A# A#->b°

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
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 4015 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 4055
Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
3rd mode:
Scale 4075
Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
4th mode:
Scale 4085
Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
5th mode:
Scale 2045
Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
6th mode:
Scale 1535
Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllianThis is the prime mode
7th mode:
Scale 2815
Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
8th mode:
Scale 3455
Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
9th mode:
Scale 3775
Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian
10th mode:
Scale 3935
Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian

Prime

The prime form of this scale is Scale 1535

Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian

Complement

The decatonic modal family [4015, 4055, 4075, 4085, 2045, 1535, 2815, 3455, 3775, 3935] (Forte: 10-2) is the complement of the modal family [5, 1025] (Forte: 2-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4015 is 3775

Scale 3775Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian

Transformations:

T0 4015  T0I 3775
T1 3935  T1I 3455
T2 3775  T2I 2815
T3 3455  T3I 1535
T4 2815  T4I 3070
T5 1535  T5I 2045
T6 3070  T6I 4090
T7 2045  T7I 4085
T8 4090  T8I 4075
T9 4085  T9I 4055
T10 4075  T10I 4015
T11 4055  T11I 3935

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 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic
Scale 4023Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
Scale 4031Scale 4031: Godatic, Ian Ring Music TheoryGodatic
Scale 3983Scale 3983: Thyptygic, Ian Ring Music TheoryThyptygic
Scale 3999Scale 3999: Dydyllian, Ian Ring Music TheoryDydyllian
Scale 4047Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian
Scale 4079Scale 4079: Ionatic, Ian Ring Music TheoryIonatic
Scale 3887Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
Scale 3951Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
Scale 3759Scale 3759: Darygic, Ian Ring Music TheoryDarygic
Scale 3503Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
Scale 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
Scale 1967Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed

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.