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Scale 619: "Double-Phrygian Hexatonic"

Scale 619: Double-Phrygian Hexatonic, 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

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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 Modern
Double-Phrygian Hexatonic
Hexatonic Double Phrygian
Zeitler
Parimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,5,6,9}
Forte Number6-Z28
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?yes
Deep Scaleno
Interval Vector224322
Interval Spectrump2m3n4s2d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,6}
<3> = {5,6,7}
<4> = {6,8,9}
<5> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[6]
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 TriadsF{5,9,0}331.43
Minor Triadsf♯m{6,9,1}331.43
Augmented TriadsC♯+{1,5,9}231.57
Diminished Triadsc°{0,3,6}231.71
d♯°{3,6,9}231.57
f♯°{6,9,0}231.57
a°{9,0,3}231.57
Parsimonious Voice Leading Between Common Triads of Scale 619. Created by Ian Ring ©2019 c° c° d#° d#° c°->d#° a° a° c°->a° C#+ C#+ F F C#+->F f#m f#m C#+->f#m d#°->f#m f#° f#° F->f#° F->a° f#°->f#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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 619 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2357		Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
3rd mode:
Scale 1613		Scale 1613: Thylimic, Ian Ring Music TheoryThylimic
4th mode:
Scale 1427		Scale 1427: Lolimic, Ian Ring Music TheoryLolimic
5th mode:
Scale 2761		Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
6th mode:
Scale 857		Scale 857: Aeolydimic, Ian Ring Music TheoryAeolydimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [619, 2357, 1613, 1427, 2761, 857] (Forte: 6-Z28) is the complement of the hexatonic modal family [667, 869, 1241, 1619, 2381, 2857] (Forte: 6-Z49)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 619 is 2761

Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic

Transformations:

T0 619  T0I 2761
T1 1238  T1I 1427
T2 2476  T2I 2854
T3 857  T3I 1613
T4 1714  T4I 3226
T5 3428  T5I 2357
T6 2761  T6I 619
T7 1427  T7I 1238
T8 2854  T8I 2476
T9 1613  T9I 857
T10 3226  T10I 1714
T11 2357  T11I 3428

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 617Scale 617: Katycritonic, Ian Ring Music TheoryKatycritonic
Scale 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 611Scale 611: Anchihoye, Ian Ring Music TheoryAnchihoye
Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic
Scale 627Scale 627: Mogimic, Ian Ring Music TheoryMogimic
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic
Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic
Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian
Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
Scale 107Scale 107, Ian Ring Music Theory
Scale 363Scale 363: Soptimic, Ian Ring Music TheorySoptimic
Scale 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form
Scale 1643Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
Scale 2667Scale 2667: Byrian, Ian Ring Music TheoryByrian

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.