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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

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
Dozenal
Yogian

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

8 (octatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,3,5,8,9,10,11}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

8-13

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 1695

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

5 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

3 (tricohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

3

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

7

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 735

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

[2, 1, 2, 3, 1, 1, 1, 1]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<5, 5, 6, 4, 5, 3>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p5m4n6s5d5t3

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<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 Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.5

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.616

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.002

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(36, 72, 151)

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: Sideways Scale, Ian Ring Music TheorySideways Scale
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:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 3885       T0I <11,0> 1695
T1 <1,1> 3675      T1I <11,1> 3390
T2 <1,2> 3255      T2I <11,2> 2685
T3 <1,3> 2415      T3I <11,3> 1275
T4 <1,4> 735      T4I <11,4> 2550
T5 <1,5> 1470      T5I <11,5> 1005
T6 <1,6> 2940      T6I <11,6> 2010
T7 <1,7> 1785      T7I <11,7> 4020
T8 <1,8> 3570      T8I <11,8> 3945
T9 <1,9> 3045      T9I <11,9> 3795
T10 <1,10> 1995      T10I <11,10> 3495
T11 <1,11> 3990      T11I <11,11> 2895
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1695      T0MI <7,0> 3885
T1M <5,1> 3390      T1MI <7,1> 3675
T2M <5,2> 2685      T2MI <7,2> 3255
T3M <5,3> 1275      T3MI <7,3> 2415
T4M <5,4> 2550      T4MI <7,4> 735
T5M <5,5> 1005      T5MI <7,5> 1470
T6M <5,6> 2010      T6MI <7,6> 2940
T7M <5,7> 4020      T7MI <7,7> 1785
T8M <5,8> 3945      T8MI <7,8> 3570
T9M <5,9> 3795      T9MI <7,9> 3045
T10M <5,10> 3495      T10MI <7,10> 1995
T11M <5,11> 2895      T11MI <7,11> 3990

The transformations that map this set to itself are: T0, T0MI

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: Yomian, Ian Ring Music TheoryYomian
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. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.