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Scale 3515: "Moorish Phrygian"

Scale 3515: Moorish Phrygian, 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

Exoticisms
Moorish Phrygian
Western Mixed
Phrygian/Double Harmonic Major Mixed
Zeitler
Katodygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,4,5,7,8,10,11}
Forte Number9-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2999
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes8
Prime?no
prime: 1775
Deep Scaleno
Interval Vector667773
Interval Spectrump7m7n7s6d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {5,6}
<5> = {6,7}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.111
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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}442.17
C♯{1,5,8}342.5
D♯{3,7,10}342.56
E{4,8,11}442.17
G♯{8,0,3}342.39
Minor Triadscm{0,3,7}342.44
c♯m{1,4,8}442.28
em{4,7,11}442.22
fm{5,8,0}342.39
g♯m{8,11,3}342.44
a♯m{10,1,5}342.67
Augmented TriadsC+{0,4,8}542
D♯+{3,7,11}442.33
Diminished Triadsc♯°{1,4,7}242.56
{4,7,10}242.67
{5,8,11}242.67
{7,10,1}242.72
a♯°{10,1,4}242.72
Parsimonious Voice Leading Between Common Triads of Scale 3515. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# c#°->c#m C# C# c#m->C# a#° a#° c#m->a#° C#->fm a#m a#m C#->a#m D# D# D#->D#+ D#->e° D#->g° D#+->em g#m g#m D#+->g#m e°->em em->E E->f° E->g#m f°->fm g°->a#m g#m->G# a#°->a#m

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3515 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3805
Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
3rd mode:
Scale 1975
Scale 1975: Ionocrygic, Ian Ring Music TheoryIonocrygic
4th mode:
Scale 3035
Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
5th mode:
Scale 3565
Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
6th mode:
Scale 1915
Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
7th mode:
Scale 3005
Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic
8th mode:
Scale 1775
Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygicThis is the prime mode
9th mode:
Scale 2935
Scale 2935: Modygic, Ian Ring Music TheoryModygic

Prime

The prime form of this scale is Scale 1775

Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic

Complement

The nonatonic modal family [3515, 3805, 1975, 3035, 3565, 1915, 3005, 1775, 2935] (Forte: 9-11) is the complement of the tritonic modal family [137, 289, 529] (Forte: 3-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3515 is 2999

Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3515 is chiral, and its enantiomorph is scale 2999

Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed

Transformations:

T0 3515  T0I 2999
T1 2935  T1I 1903
T2 1775  T2I 3806
T3 3550  T3I 3517
T4 3005  T4I 2939
T5 1915  T5I 1783
T6 3830  T6I 3566
T7 3565  T7I 3037
T8 3035  T8I 1979
T9 1975  T9I 3958
T10 3950  T10I 3821
T11 3805  T11I 3547

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 3513Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
Scale 3517Scale 3517: Epocrygic, Ian Ring Music TheoryEpocrygic
Scale 3519Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
Scale 3507Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz
Scale 3511Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 3547Scale 3547: Sadygic, Ian Ring Music TheorySadygic
Scale 3579Scale 3579: Zyphyllian, Ian Ring Music TheoryZyphyllian
Scale 3387Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
Scale 3451Scale 3451: Garygic, Ian Ring Music TheoryGarygic
Scale 3259Scale 3259, Ian Ring Music Theory
Scale 3771Scale 3771: Katodyllian, Ian Ring Music TheoryKatodyllian
Scale 4027Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
Scale 2491Scale 2491: Layllic, Ian Ring Music TheoryLayllic
Scale 3003Scale 3003: Genus Chromaticum, Ian Ring Music TheoryGenus Chromaticum
Scale 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian

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.