The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3883: "Kyryllic"

Scale 3883: Kyryllic, 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
Kyryllic

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

{0,1,3,5,8,9,10,11}

Forte Number

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

8-11

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: 2719

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.

4 (multicohemitonic)

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: 703

Deep Scale

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

no

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, 6, 5, 5, 5, 2]

Interval Spectrum

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

p5m5n5s6d5t2

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> = {3,4,5,6,7}
<4> = {4,5,6,7,8}
<5> = {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.

2.75

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

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}231.78
F{5,9,0}331.56
G♯{8,0,3}341.78
Minor Triadsfm{5,8,0}431.44
g♯m{8,11,3}252.33
a♯m{10,1,5}152.67
Augmented TriadsC♯+{1,5,9}341.89
Diminished Triads{5,8,11}242
{9,0,3}231.89
Parsimonious Voice Leading Between Common Triads of Scale 3883. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F a#m a#m C#+->a#m f°->fm g#m g#m f°->g#m fm->F G# G# fm->G# F->a° g#m->G# G#->a°

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♯, fm, F, a°
Peripheral Verticesg♯m, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3883 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3989
Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic
3rd mode:
Scale 2021
Scale 2021: Katycryllic, Ian Ring Music TheoryKatycryllic
4th mode:
Scale 1529
Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
5th mode:
Scale 703
Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllicThis is the prime mode
6th mode:
Scale 2399
Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
7th mode:
Scale 3247
Scale 3247: Aeolonyllic, Ian Ring Music TheoryAeolonyllic
8th mode:
Scale 3671
Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic

Prime

The prime form of this scale is Scale 703

Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic

Complement

The octatonic modal family [3883, 3989, 2021, 1529, 703, 2399, 3247, 3671] (Forte: 8-11) is the complement of the tetratonic modal family [43, 1409, 1541, 2069] (Forte: 4-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3883 is 2719

Scale 2719Scale 2719: Zocryllic, Ian Ring Music TheoryZocryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3883 is chiral, and its enantiomorph is scale 2719

Scale 2719Scale 2719: Zocryllic, Ian Ring Music TheoryZocryllic

Transformations:

T0 3883  T0I 2719
T1 3671  T1I 1343
T2 3247  T2I 2686
T3 2399  T3I 1277
T4 703  T4I 2554
T5 1406  T5I 1013
T6 2812  T6I 2026
T7 1529  T7I 4052
T8 3058  T8I 4009
T9 2021  T9I 3923
T10 4042  T10I 3751
T11 3989  T11I 3407

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 3881Scale 3881: Morian, Ian Ring Music TheoryMorian
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 3887Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
Scale 3899Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
Scale 3851Scale 3851, Ian Ring Music Theory
Scale 3867Scale 3867: Storyllic, Ian Ring Music TheoryStoryllic
Scale 3915Scale 3915, Ian Ring Music Theory
Scale 3947Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 3627Scale 3627: Kalian, Ian Ring Music TheoryKalian
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 3371Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
Scale 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 1835Scale 1835: Byptian, Ian Ring Music TheoryByptian

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.