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Scale 615: "Phrothimic"

Scale 615: Phrothimic, 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

Zeitler
Phrothimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,5,6,9}
Forte Number6-Z44
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3273
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?yes
Deep Scaleno
Interval Vector313431
Interval Spectrump3m4n3sd3t
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {5,7}
<4> = {6,8,10}
<5> = {9,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.25
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsD{2,6,9}231.5
F{5,9,0}231.5
Minor Triadsdm{2,5,9}231.5
f♯m{6,9,1}321.17
Augmented TriadsC♯+{1,5,9}321.17
Diminished Triadsf♯°{6,9,0}231.5
Parsimonious Voice Leading Between Common Triads of Scale 615. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m D D dm->D D->f#m f#° f#° F->f#° f#°->f#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
Radius2
Self-Centeredno
Central VerticesC♯+, f♯m
Peripheral Verticesdm, D, F, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 615 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2355
Scale 2355: Raga Lalita, Ian Ring Music TheoryRaga Lalita
3rd mode:
Scale 3225
Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic
4th mode:
Scale 915
Scale 915: Raga Kalagada, Ian Ring Music TheoryRaga Kalagada
5th mode:
Scale 2505
Scale 2505: Mydimic, Ian Ring Music TheoryMydimic
6th mode:
Scale 825
Scale 825: Thyptimic, Ian Ring Music TheoryThyptimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [615, 2355, 3225, 915, 2505, 825] (Forte: 6-Z44) is the complement of the hexatonic modal family [411, 867, 1587, 2253, 2481, 2841] (Forte: 6-Z19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 615 is 3273

Scale 3273Scale 3273: Raga Jivantini, Ian Ring Music TheoryRaga Jivantini

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 615 is chiral, and its enantiomorph is scale 3273

Scale 3273Scale 3273: Raga Jivantini, Ian Ring Music TheoryRaga Jivantini

Transformations:

T0 615  T0I 3273
T1 1230  T1I 2451
T2 2460  T2I 807
T3 825  T3I 1614
T4 1650  T4I 3228
T5 3300  T5I 2361
T6 2505  T6I 627
T7 915  T7I 1254
T8 1830  T8I 2508
T9 3660  T9I 921
T10 3225  T10I 1842
T11 2355  T11I 3684

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 613Scale 613: Phralitonic, Ian Ring Music TheoryPhralitonic
Scale 611Scale 611: Anchihoye, Ian Ring Music TheoryAnchihoye
Scale 619Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian Hexatonic
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 631Scale 631: Zygian, Ian Ring Music TheoryZygian
Scale 583Scale 583: Aeritonic, Ian Ring Music TheoryAeritonic
Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic
Scale 551Scale 551: Aeoloditonic, Ian Ring Music TheoryAeoloditonic
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 743Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian Inverse
Scale 871Scale 871: Locrian Double-flat 3 Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 3 Double-flat 7
Scale 103Scale 103, Ian Ring Music Theory
Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic
Scale 1127Scale 1127: Eparimic, Ian Ring Music TheoryEparimic
Scale 1639Scale 1639: Aeolothian, Ian Ring Music TheoryAeolothian
Scale 2663Scale 2663: Lalian, Ian Ring Music TheoryLalian

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.