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Scale 1515: "Phrygian/Locrian Mixed"

Scale 1515: Phrygian/Locrian Mixed, 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

Western Mixed
Phrygian/Locrian Mixed
Zeitler
Solyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,5,6,7,8,10}
Forte Number8-23
Rotational Symmetrynone
Reflection Axes0.5
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections1
Modes7
Prime?no
prime: 1455
Deep Scaleno
Interval Vector465472
Interval Spectrump7m4n5s6d4t2
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {5,6,7}
<5> = {7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tones[1]
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}242.3
D♯{3,7,10}341.9
F♯{6,10,1}341.9
G♯{8,0,3}242.1
Minor Triadscm{0,3,7}341.9
d♯m{3,6,10}341.9
fm{5,8,0}242.3
a♯m{10,1,5}242.1
Diminished Triads{0,3,6}242.1
{7,10,1}242.1
Parsimonious Voice Leading Between Common Triads of Scale 1515. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# G# G# cm->G# C# C# fm fm C#->fm a#m a#m C#->a#m d#m->D# F# F# d#m->F# D#->g° fm->G# F#->g° F#->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 1515 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2805
Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho
3rd mode:
Scale 1725
Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
4th mode:
Scale 1455
Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolianThis is the prime mode
5th mode:
Scale 2775
Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
6th mode:
Scale 3435
Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
7th mode:
Scale 3765
Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
8th mode:
Scale 1965
Scale 1965: Raga Mukhari, Ian Ring Music TheoryRaga Mukhari

Prime

The prime form of this scale is Scale 1455

Scale 1455Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolian

Complement

The octatonic modal family [1515, 2805, 1725, 1455, 2775, 3435, 3765, 1965] (Forte: 8-23) is the complement of the tetratonic modal family [165, 645, 1065, 1185] (Forte: 4-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1515 is 2805

Scale 2805Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho

Transformations:

T0 1515  T0I 2805
T1 3030  T1I 1515
T2 1965  T2I 3030
T3 3930  T3I 1965
T4 3765  T4I 3930
T5 3435  T5I 3765
T6 2775  T6I 3435
T7 1455  T7I 2775
T8 2910  T8I 1455
T9 1725  T9I 2910
T10 3450  T10I 1725
T11 2805  T11I 3450

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 1513Scale 1513: Stathian, Ian Ring Music TheoryStathian
Scale 1517Scale 1517: Sagyllic, Ian Ring Music TheorySagyllic
Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed
Scale 1507Scale 1507: Zynian, Ian Ring Music TheoryZynian
Scale 1511Scale 1511: Styptyllic, Ian Ring Music TheoryStyptyllic
Scale 1523Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic
Scale 1531Scale 1531: Styptygic, Ian Ring Music TheoryStyptygic
Scale 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
Scale 1499Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
Scale 1451Scale 1451: Phrygian, Ian Ring Music TheoryPhrygian
Scale 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian
Scale 1259Scale 1259: Stadian, Ian Ring Music TheoryStadian
Scale 1771Scale 1771, Ian Ring Music Theory
Scale 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic
Scale 491Scale 491: Aeolyrian, Ian Ring Music TheoryAeolyrian
Scale 1003Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
Scale 2539Scale 2539: Half-Diminished Bebop, Ian Ring Music TheoryHalf-Diminished Bebop
Scale 3563Scale 3563: Ionoptygic, Ian Ring Music TheoryIonoptygic

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.