The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3885: "Styryllic"

Scale 3885: Styryllic, 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
Styryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,5,8,9,10,11}
Forte Number8-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1695
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 735
Deep Scaleno
Interval Vector556453
Interval Spectrump5m4n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
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 TriadsF{5,9,0}341.91
G♯{8,0,3}341.91
A♯{10,2,5}242.27
Minor Triadsdm{2,5,9}342
fm{5,8,0}441.82
g♯m{8,11,3}342
Diminished Triads{2,5,8}242.09
{5,8,11}242.09
g♯°{8,11,2}242.27
{9,0,3}242.18
{11,2,5}242.36
Parsimonious Voice Leading Between Common Triads of Scale 3885. Created by Ian Ring ©2019 dm dm d°->dm fm fm d°->fm F F dm->F A# A# dm->A# f°->fm g#m g#m f°->g#m fm->F G# G# fm->G# F->a° g#° g#° g#°->g#m g#°->b° g#m->G# G#->a° A#->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3885 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1995
Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
3rd mode:
Scale 3045
Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
4th mode:
Scale 1785
Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
5th mode:
Scale 735
Scale 735: Sylyllic, Ian Ring Music TheorySylyllicThis is the prime mode
6th mode:
Scale 2415
Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
7th mode:
Scale 3255
Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
8th mode:
Scale 3675
Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic

Prime

The prime form of this scale is Scale 735

Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic

Complement

The octatonic modal family [3885, 1995, 3045, 1785, 735, 2415, 3255, 3675] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3885 is 1695

Scale 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3885 is chiral, and its enantiomorph is scale 1695

Scale 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic

Transformations:

T0 3885  T0I 1695
T1 3675  T1I 3390
T2 3255  T2I 2685
T3 2415  T3I 1275
T4 735  T4I 2550
T5 1470  T5I 1005
T6 2940  T6I 2010
T7 1785  T7I 4020
T8 3570  T8I 3945
T9 3045  T9I 3795
T10 1995  T10I 3495
T11 3990  T11I 2895

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 3887Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
Scale 3881Scale 3881: Morian, Ian Ring Music TheoryMorian
Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 3901Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
Scale 3853Scale 3853, Ian Ring Music Theory
Scale 3869Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
Scale 3373Scale 3373: Lodian, Ian Ring Music TheoryLodian
Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian

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.