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Scale 2527: "Phradygic"

Scale 2527: Phradygic, 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
Phradygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,6,7,8,11}
Forte Number9-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3955
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 959
Deep Scaleno
Interval Vector766773
Interval Spectrump7m7n6s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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}442.07
E{4,8,11}342.2
G{7,11,2}352.4
G♯{8,0,3}342.07
B{11,3,6}352.4
Minor Triadscm{0,3,7}431.87
c♯m{1,4,8}263
em{4,7,11}332
g♯m{8,11,3}442
bm{11,2,6}263
Augmented TriadsC+{0,4,8}452.27
D♯+{3,7,11}541.8
Diminished Triads{0,3,6}242.47
c♯°{1,4,7}252.8
g♯°{8,11,2}252.6
Parsimonious Voice Leading Between Common Triads of Scale 2527. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E C+->G# c#°->c#m D#+->em Parsimonious Voice Leading Between Common Triads of Scale 2527. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B em->E E->g#m g#° g#° G->g#° bm bm G->bm g#°->g#m g#m->G# bm->B

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.

Diameter6
Radius3
Self-Centeredno
Central Verticescm, em
Peripheral Verticesc♯m, bm

Modes

Modes are the rotational transformation of this scale. Scale 2527 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3311
Scale 3311: Mixodygic, Ian Ring Music TheoryMixodygic
3rd mode:
Scale 3703
Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
4th mode:
Scale 3899
Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
5th mode:
Scale 3997
Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
6th mode:
Scale 2023
Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
7th mode:
Scale 3059
Scale 3059: Madygic, Ian Ring Music TheoryMadygic
8th mode:
Scale 3577
Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic
9th mode:
Scale 959
Scale 959: Katylygic, Ian Ring Music TheoryKatylygicThis is the prime mode

Prime

The prime form of this scale is Scale 959

Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic

Complement

The nonatonic modal family [2527, 3311, 3703, 3899, 3997, 2023, 3059, 3577, 959] (Forte: 9-4) is the complement of the tritonic modal family [35, 385, 2065] (Forte: 3-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2527 is 3955

Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2527 is chiral, and its enantiomorph is scale 3955

Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic

Transformations:

T0 2527  T0I 3955
T1 959  T1I 3815
T2 1918  T2I 3535
T3 3836  T3I 2975
T4 3577  T4I 1855
T5 3059  T5I 3710
T6 2023  T6I 3325
T7 4046  T7I 2555
T8 3997  T8I 1015
T9 3899  T9I 2030
T10 3703  T10I 4060
T11 3311  T11I 4025

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 2525Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
Scale 2523Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale
Scale 2519Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic
Scale 2511Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic
Scale 2543Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
Scale 2559Scale 2559: Zogyllian, Ian Ring Music TheoryZogyllian
Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
Scale 3039Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian
Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic
Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

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.