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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

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,1,3,5,7,8,10}

Forte Number

A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

7-35

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

[4]

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

no

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

2 (dihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

0 (ancohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

1

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

6

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 1387

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

yes

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[1, 2, 2, 2, 1, 2, 2]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<2, 5, 4, 3, 6, 1>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.

p6m3n4s5d2t

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2}
<2> = {3,4}
<3> = {5,6}
<4> = {6,7}
<5> = {8,9}
<6> = {10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

0.857

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

yes

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

yes

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.665

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.035

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

yes

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

[8]

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Proper

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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: Quartal Octamode, Ian Ring Music TheoryQuartal Octamode
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. 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.