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Scale 3287: "Phrathyllic"

Scale 3287: Phrathyllic, 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
Phrathyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,6,7,10,11}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3431
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 863
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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 TriadsC{0,4,7}242.27
F♯{6,10,1}342
G{7,11,2}341.91
Minor Triadsem{4,7,11}342
gm{7,10,2}441.82
bm{11,2,6}242.18
Augmented TriadsD+{2,6,10}341.91
Diminished Triadsc♯°{1,4,7}242.36
{4,7,10}242.09
{7,10,1}242.09
a♯°{10,1,4}242.27
Parsimonious Voice Leading Between Common Triads of Scale 3287. Created by Ian Ring ©2019 C C c#° c#° C->c#° em em C->em a#° a#° c#°->a#° D+ D+ F# F# D+->F# gm gm D+->gm bm bm D+->bm e°->em e°->gm Parsimonious Voice Leading Between Common Triads of Scale 3287. Created by Ian Ring ©2019 G em->G F#->g° F#->a#° g°->gm gm->G G->bm

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3287 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3691
Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
3rd mode:
Scale 3893
Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
4th mode:
Scale 1997
Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
5th mode:
Scale 1523
Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic
6th mode:
Scale 2809
Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
7th mode:
Scale 863
Scale 863: Pyryllic, Ian Ring Music TheoryPyryllicThis is the prime mode
8th mode:
Scale 2479
Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [3287, 3691, 3893, 1997, 1523, 2809, 863, 2479] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3287 is 3431

Scale 3431Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3287 is chiral, and its enantiomorph is scale 3431

Scale 3431Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic

Transformations:

T0 3287  T0I 3431
T1 2479  T1I 2767
T2 863  T2I 1439
T3 1726  T3I 2878
T4 3452  T4I 1661
T5 2809  T5I 3322
T6 1523  T6I 2549
T7 3046  T7I 1003
T8 1997  T8I 2006
T9 3994  T9I 4012
T10 3893  T10I 3929
T11 3691  T11I 3763

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 3285Scale 3285: Mela Citrambari, Ian Ring Music TheoryMela Citrambari
Scale 3283Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari
Scale 3291Scale 3291: Lygyllic, Ian Ring Music TheoryLygyllic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3271Scale 3271: Mela Raghupriya, Ian Ring Music TheoryMela Raghupriya
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
Scale 3303Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic
Scale 3319Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 3799Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
Scale 2263Scale 2263: Lycrian, Ian Ring Music TheoryLycrian
Scale 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 1239Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian

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.