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Scale 3555: "Pylyllic"

Scale 3555: Pylyllic, 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
Pylyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,5,6,7,8,10,11}
Forte Number8-6
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 495
Deep Scaleno
Interval Vector654463
Interval Spectrump6m4n4s5d6t3
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6}
<4> = {5,7}
<5> = {6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[6]
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♯{1,5,8}231.5
F♯{6,10,1}241.83
Minor Triadsfm{5,8,0}241.83
a♯m{10,1,5}231.5
Diminished Triads{5,8,11}152.5
{7,10,1}152.5
Parsimonious Voice Leading Between Common Triads of Scale 3555. Created by Ian Ring ©2019 C# C# fm fm C#->fm a#m a#m C#->a#m f°->fm F# F# F#->g° F#->a#m

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC♯, a♯m
Peripheral Verticesf°, g°

Modes

Modes are the rotational transformation of this scale. Scale 3555 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3825
Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic
3rd mode:
Scale 495
Scale 495: Bocryllic, Ian Ring Music TheoryBocryllicThis is the prime mode
4th mode:
Scale 2295
Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
5th mode:
Scale 3195
Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
6th mode:
Scale 3645
Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic
7th mode:
Scale 1935
Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic
8th mode:
Scale 3015
Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic

Prime

The prime form of this scale is Scale 495

Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic

Complement

The octatonic modal family [3555, 3825, 495, 2295, 3195, 3645, 1935, 3015] (Forte: 8-6) is the complement of the tetratonic modal family [135, 225, 2115, 3105] (Forte: 4-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3555 is 2295

Scale 2295Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic

Transformations:

T0 3555  T0I 2295
T1 3015  T1I 495
T2 1935  T2I 990
T3 3870  T3I 1980
T4 3645  T4I 3960
T5 3195  T5I 3825
T6 2295  T6I 3555
T7 495  T7I 3015
T8 990  T8I 1935
T9 1980  T9I 3870
T10 3960  T10I 3645
T11 3825  T11I 3195

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 3553Scale 3553, Ian Ring Music Theory
Scale 3557Scale 3557, Ian Ring Music Theory
Scale 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic
Scale 3563Scale 3563: Ionoptygic, Ian Ring Music TheoryIonoptygic
Scale 3571Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
Scale 3523Scale 3523, Ian Ring Music Theory
Scale 3539Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 3427Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
Scale 3299Scale 3299: Syptian, Ian Ring Music TheorySyptian
Scale 3811Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
Scale 4067Scale 4067: Aeolarygic, Ian Ring Music TheoryAeolarygic
Scale 2531Scale 2531: Danian, Ian Ring Music TheoryDanian
Scale 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
Scale 1507Scale 1507: Zynian, Ian Ring Music TheoryZynian

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.