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Scale 1431: "Phragian"

Scale 1431: Phragian, 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

Zeitler
Phragian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,7,8,10}
Forte Number7-28
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3381
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes6
Prime?no
prime: 747
Deep Scaleno
Interval Vector344433
Interval Spectrump3m4n4s4d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
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{0,4,7}331.63
Minor Triadsc♯m{1,4,8}331.63
gm{7,10,2}231.88
Augmented TriadsC+{0,4,8}231.75
Diminished Triadsc♯°{1,4,7}231.75
{4,7,10}231.75
{7,10,1}231.88
a♯°{10,1,4}231.75
Parsimonious Voice Leading Between Common Triads of Scale 1431. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° C->e° c#m c#m C+->c#m c#°->c#m a#° a#° c#m->a#° gm gm e°->gm g°->gm g°->a#°

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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 1431 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2763
Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
3rd mode:
Scale 3429
Scale 3429: Marian, Ian Ring Music TheoryMarian
4th mode:
Scale 1881
Scale 1881: Katorian, Ian Ring Music TheoryKatorian
5th mode:
Scale 747
Scale 747: Lynian, Ian Ring Music TheoryLynianThis is the prime mode
6th mode:
Scale 2421
Scale 2421: Malian, Ian Ring Music TheoryMalian
7th mode:
Scale 1629
Scale 1629: Synian, Ian Ring Music TheorySynian

Prime

The prime form of this scale is Scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Complement

The heptatonic modal family [1431, 2763, 3429, 1881, 747, 2421, 1629] (Forte: 7-28) is the complement of the pentatonic modal family [333, 837, 1107, 1233, 2601] (Forte: 5-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1431 is 3381

Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1431 is chiral, and its enantiomorph is scale 3381

Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian

Transformations:

T0 1431  T0I 3381
T1 2862  T1I 2667
T2 1629  T2I 1239
T3 3258  T3I 2478
T4 2421  T4I 861
T5 747  T5I 1722
T6 1494  T6I 3444
T7 2988  T7I 2793
T8 1881  T8I 1491
T9 3762  T9I 2982
T10 3429  T10I 1869
T11 2763  T11I 3738

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 1429Scale 1429: Bythimic, Ian Ring Music TheoryBythimic
Scale 1427Scale 1427: Lolimic, Ian Ring Music TheoryLolimic
Scale 1435Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam
Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
Scale 1415Scale 1415, Ian Ring Music Theory
Scale 1423Scale 1423: Doptian, Ian Ring Music TheoryDoptian
Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
Scale 1463Scale 1463, Ian Ring Music Theory
Scale 1495Scale 1495: Messiaen Mode 6, Ian Ring Music TheoryMessiaen Mode 6
Scale 1303Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic
Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse
Scale 1175Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian
Scale 1943Scale 1943, Ian Ring Music Theory
Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic
Scale 919Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse
Scale 2455Scale 2455: Bothian, Ian Ring Music TheoryBothian
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic

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.