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Scale 2877: "Phrylyllic"

Scale 2877: Phrylyllic, 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
Phrylyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,5,8,9,11}
Forte Number8-18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1947
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 879
Deep Scaleno
Interval Vector546553
Interval Spectrump5m5n6s4d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
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 TriadsE{4,8,11}342.08
F{5,9,0}342
G♯{8,0,3}342.08
Minor Triadsdm{2,5,9}342.23
fm{5,8,0}441.92
g♯m{8,11,3}342.15
am{9,0,4}342.08
Augmented TriadsC+{0,4,8}441.85
Diminished Triads{2,5,8}242.31
{5,8,11}242.31
g♯°{8,11,2}242.38
{9,0,3}242.46
{11,2,5}242.46
Parsimonious Voice Leading Between Common Triads of Scale 2877. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm G# G# C+->G# am am C+->am dm dm d°->dm d°->fm F F dm->F dm->b° E->f° g#m g#m E->g#m f°->fm fm->F F->am g#° g#° g#°->g#m g#°->b° g#m->G# G#->a° a°->am

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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 2877 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1743
Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
3rd mode:
Scale 2919
Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
4th mode:
Scale 3507
Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz
5th mode:
Scale 3801
Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
6th mode:
Scale 987
Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
7th mode:
Scale 2541
Scale 2541: Algerian, Ian Ring Music TheoryAlgerian
8th mode:
Scale 1659
Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban

Prime

The prime form of this scale is Scale 879

Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic

Complement

The octatonic modal family [2877, 1743, 2919, 3507, 3801, 987, 2541, 1659] (Forte: 8-18) is the complement of the tetratonic modal family [147, 609, 777, 2121] (Forte: 4-18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2877 is 1947

Scale 1947Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2877 is chiral, and its enantiomorph is scale 1947

Scale 1947Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic

Transformations:

T0 2877  T0I 1947
T1 1659  T1I 3894
T2 3318  T2I 3693
T3 2541  T3I 3291
T4 987  T4I 2487
T5 1974  T5I 879
T6 3948  T6I 1758
T7 3801  T7I 3516
T8 3507  T8I 2937
T9 2919  T9I 1779
T10 1743  T10I 3558
T11 3486  T11I 3021

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 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
Scale 2873Scale 2873: Ionian Augmented Sharp 2, Ian Ring Music TheoryIonian Augmented Sharp 2
Scale 2875Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic
Scale 2869Scale 2869: Ionian Augmented, Ian Ring Music TheoryIonian Augmented
Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 2845Scale 2845: Baptian, Ian Ring Music TheoryBaptian
Scale 2909Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
Scale 2941Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
Scale 3005Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic
Scale 2621Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
Scale 2749Scale 2749: Katagyllic, Ian Ring Music TheoryKatagyllic
Scale 2365Scale 2365: Sythian, Ian Ring Music TheorySythian
Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
Scale 3901Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
Scale 829Scale 829: Lygian, Ian Ring Music TheoryLygian
Scale 1853Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.