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Scale 989: "Phrolyllic"

Scale 989: Phrolyllic, 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
Phrolyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,6,7,8,9}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1913
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 751
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<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}242.1
D{2,6,9}242.3
G♯{8,0,3}341.9
Minor Triadscm{0,3,7}341.9
am{9,0,4}341.9
Augmented TriadsC+{0,4,8}341.9
Diminished Triads{0,3,6}242.1
d♯°{3,6,9}242.3
f♯°{6,9,0}242.1
{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 989. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° C C cm->C G# G# cm->G# C+ C+ C->C+ C+->G# am am C+->am D D D->d#° f#° f#° D->f#° f#°->am G#->a° a°->am

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 989 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1271
Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic
3rd mode:
Scale 2683
Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic
4th mode:
Scale 3389
Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
5th mode:
Scale 1871
Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
6th mode:
Scale 2983
Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
7th mode:
Scale 3539
Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic
8th mode:
Scale 3817
Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic

Prime

The prime form of this scale is Scale 751

Scale 751Scale 751, Ian Ring Music Theory

Complement

The octatonic modal family [989, 1271, 2683, 3389, 1871, 2983, 3539, 3817] (Forte: 8-Z29) is the complement of the tetratonic modal family [139, 353, 1553, 2117] (Forte: 4-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 989 is 1913

Scale 1913Scale 1913, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 989 is chiral, and its enantiomorph is scale 1913

Scale 1913Scale 1913, Ian Ring Music Theory

Transformations:

T0 989  T0I 1913
T1 1978  T1I 3826
T2 3956  T2I 3557
T3 3817  T3I 3019
T4 3539  T4I 1943
T5 2983  T5I 3886
T6 1871  T6I 3677
T7 3742  T7I 3259
T8 3389  T8I 2423
T9 2683  T9I 751
T10 1271  T10I 1502
T11 2542  T11I 3004

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 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic
Scale 985Scale 985: Mela Sucaritra, Ian Ring Music TheoryMela Sucaritra
Scale 987Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani
Scale 973Scale 973: Mela Syamalangi, Ian Ring Music TheoryMela Syamalangi
Scale 1005Scale 1005: Radyllic, Ian Ring Music TheoryRadyllic
Scale 1021Scale 1021: Ladygic, Ian Ring Music TheoryLadygic
Scale 925Scale 925: Chromatic Hypodorian, Ian Ring Music TheoryChromatic Hypodorian
Scale 957Scale 957: Phronyllic, Ian Ring Music TheoryPhronyllic
Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian
Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian
Scale 477Scale 477: Stacrian, Ian Ring Music TheoryStacrian
Scale 1501Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
Scale 3037Scale 3037: Nine Tone Scale, Ian Ring Music TheoryNine Tone Scale

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.