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Scale 1451: "Phrygian"

Scale 1451: 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

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
Phrygian
Ancient Greek
Greek Dorian
Greek Medieval Hypoaeolian
Medieval
Medieval Phrygian
Unknown / Unsorted
Neapolitan Minor
Bilashkhani Todi
Ghanta
In
Hindustani
Bhairavi That
Bhairavi Theta
Carnatic Mela
Mela Hanumatodi
Carnatic Raga
Raga Asavari
Raga Asaveri
Turkish
Makam Kurd
Gregorian Numbered
Gregorian Number 3
Japanese
Zokuso
Modern Greek
Ousak
Western Modern
Major Inverse
Zeitler
Phrygian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,5,7,8,10}
Forte Number7-35
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections1
Modes6
Prime?no
prime: 1387
Deep Scaleyes
Interval Vector254361
Interval Spectrump6m3n4s5d2t
Distribution Spectra<1> = {1,2}
<2> = {3,4}
<3> = {5,6}
<4> = {6,7}
<5> = {8,9}
<6> = {10,11}
Spectra Variation0.857
Maximally Evenyes
Maximal Area Setyes
Interior Area2.665
Myhill Propertyyes
Balancedno
Ridge Tones[8]
ProprietyProper
Heliotonicyes

Harmonic Chords

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}231.71
D♯{3,7,10}231.71
G♯{8,0,3}231.71
Minor Triadscm{0,3,7}231.71
fm{5,8,0}231.71
a♯m{10,1,5}231.71
Diminished Triads{7,10,1}231.71
Parsimonious Voice Leading Between Common Triads of Scale 1451. Created by Ian Ring ©2019 cm cm D# D# cm->D# G# G# cm->G# C# C# fm fm C#->fm a#m a#m C#->a#m D#->g° fm->G# 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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1451 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2773
Scale 2773: Lydian, Ian Ring Music TheoryLydian
3rd mode:
Scale 1717
Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
4th mode:
Scale 1453
Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
5th mode:
Scale 1387
Scale 1387: Locrian, Ian Ring Music TheoryLocrianThis is the prime mode
6th mode:
Scale 2741
Scale 2741: Major, Ian Ring Music TheoryMajor
7th mode:
Scale 1709
Scale 1709: Dorian, Ian Ring Music TheoryDorian

Prime

The prime form of this scale is Scale 1387

Scale 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian

Complement

The heptatonic modal family [1451, 2773, 1717, 1453, 1387, 2741, 1709] (Forte: 7-35) is the complement of the pentatonic modal family [661, 677, 1189, 1193, 1321] (Forte: 5-35)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1451 is 2741

Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor

Transformations:

T0 1451  T0I 2741
T1 2902  T1I 1387
T2 1709  T2I 2774
T3 3418  T3I 1453
T4 2741  T4I 2906
T5 1387  T5I 1717
T6 2774  T6I 3434
T7 1453  T7I 2773
T8 2906  T8I 1451
T9 1717  T9I 2902
T10 3434  T10I 1709
T11 2773  T11I 3418

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 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 1453Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
Scale 1455Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolian
Scale 1443Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti
Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
Scale 1459Scale 1459: Phrygian Dominant, Ian Ring Music TheoryPhrygian Dominant
Scale 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian
Scale 1419Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi
Scale 1435Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam
Scale 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
Scale 1515Scale 1515: Phrygian/Locrian Mixed, Ian Ring Music TheoryPhrygian/Locrian Mixed
Scale 1323Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
Scale 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian
Scale 1195Scale 1195: Raga Gandharavam, Ian Ring Music TheoryRaga Gandharavam
Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
Scale 1963Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic
Scale 427Scale 427: Raga Suddha Simantini, Ian Ring Music TheoryRaga Suddha Simantini
Scale 939Scale 939: Mela Senavati, Ian Ring Music TheoryMela Senavati
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel

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.