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Scale 561: "Phratic"

Scale 561: Phratic, 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
Phratic

Analysis

Cardinality4 (tetratonic)
Pitch Class Set{0,4,5,9}
Forte Number4-20
Rotational Symmetrynone
Reflection Axes4.5
Palindromicno
Chiralityno
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes3
Prime?no
prime: 291
Deep Scaleno
Interval Vector101220
Interval Spectrump2m2nd
Distribution Spectra<1> = {1,3,4}
<2> = {5,7}
<3> = {8,9,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area1.616
Myhill Propertyno
Balancedno
Ridge Tones[9]
ProprietyStrictly Proper
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 TriadsF{5,9,0}110.5
Minor Triadsam{9,0,4}110.5
Parsimonious Voice Leading Between Common Triads of Scale 561. Created by Ian Ring ©2019 F F am am F->am

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 561 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 291
Scale 291: Raga Lavangi, Ian Ring Music TheoryRaga LavangiThis is the prime mode
3rd mode:
Scale 2193
Scale 2193: Thaptic, Ian Ring Music TheoryThaptic
4th mode:
Scale 393
Scale 393: Lothic, Ian Ring Music TheoryLothic

Prime

The prime form of this scale is Scale 291

Scale 291Scale 291: Raga Lavangi, Ian Ring Music TheoryRaga Lavangi

Complement

The tetratonic modal family [561, 291, 2193, 393] (Forte: 4-20) is the complement of the octatonic modal family [951, 1767, 1851, 2523, 2931, 2973, 3309, 3513] (Forte: 8-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 561 is 393

Scale 393Scale 393: Lothic, Ian Ring Music TheoryLothic

Transformations:

T0 561  T0I 393
T1 1122  T1I 786
T2 2244  T2I 1572
T3 393  T3I 3144
T4 786  T4I 2193
T5 1572  T5I 291
T6 3144  T6I 582
T7 2193  T7I 1164
T8 291  T8I 2328
T9 582  T9I 561
T10 1164  T10I 1122
T11 2328  T11I 2244

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 563Scale 563: Thacritonic, Ian Ring Music TheoryThacritonic
Scale 565Scale 565: Aeolyphritonic, Ian Ring Music TheoryAeolyphritonic
Scale 569Scale 569: Mothitonic, Ian Ring Music TheoryMothitonic
Scale 545Scale 545, Ian Ring Music Theory
Scale 553Scale 553: Rothic, Ian Ring Music TheoryRothic
Scale 529Scale 529: Raga Bilwadala, Ian Ring Music TheoryRaga Bilwadala
Scale 593Scale 593: Saric, Ian Ring Music TheorySaric
Scale 625Scale 625: Ionyptitonic, Ian Ring Music TheoryIonyptitonic
Scale 689Scale 689: Raga Nagasvaravali, Ian Ring Music TheoryRaga Nagasvaravali
Scale 817Scale 817: Zothitonic, Ian Ring Music TheoryZothitonic
Scale 49Scale 49, Ian Ring Music Theory
Scale 305Scale 305: Gonic, Ian Ring Music TheoryGonic
Scale 1073Scale 1073, Ian Ring Music Theory
Scale 1585Scale 1585: Raga Khamaji Durga, Ian Ring Music TheoryRaga Khamaji Durga
Scale 2609Scale 2609: Raga Bhinna Shadja, Ian Ring Music TheoryRaga Bhinna Shadja

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.