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Scale 3449: "Bacryllic"

Scale 3449: Bacryllic, 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
Bacryllic

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

{0,3,4,5,6,8,10,11}

Forte Number

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

8-16

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: 983

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.

2

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: 943

Deep Scale

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

no

Interval Formula

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

[3, 1, 1, 1, 2, 2, 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, 4, 5, 6, 3>

Interval Spectrum

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

p6m5n4s5d5t3

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}
<3> = {3,4,5}
<4> = {5,6,7}
<5> = {7,8,9}
<6> = {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.

1.75

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 TriadsE{4,8,11}331.67
G♯{8,0,3}331.67
B{11,3,6}341.89
Minor Triadsd♯m{3,6,10}152.67
fm{5,8,0}252.33
g♯m{8,11,3}331.56
Augmented TriadsC+{0,4,8}341.78
Diminished Triads{0,3,6}242
{5,8,11}242.22
Parsimonious Voice Leading Between Common Triads of Scale 3449. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ E E C+->E fm fm C+->fm C+->G# d#m d#m d#m->B E->f° g#m g#m E->g#m f°->fm g#m->G# g#m->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.

Diameter5
Radius3
Self-Centeredno
Central VerticesE, g♯m, G♯
Peripheral Verticesd♯m, fm

Modes

Modes are the rotational transformation of this scale. Scale 3449 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 943
Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllicThis is the prime mode
3rd mode:
Scale 2519
Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic
4th mode:
Scale 3307
Scale 3307: Boptyllic, Ian Ring Music TheoryBoptyllic
5th mode:
Scale 3701
Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
6th mode:
Scale 1949
Scale 1949: Mathyllic, Ian Ring Music TheoryMathyllic
7th mode:
Scale 1511
Scale 1511: Styptyllic, Ian Ring Music TheoryStyptyllic
8th mode:
Scale 2803
Scale 2803: Raga Bhatiyar, Ian Ring Music TheoryRaga Bhatiyar

Prime

The prime form of this scale is Scale 943

Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic

Complement

The octatonic modal family [3449, 943, 2519, 3307, 3701, 1949, 1511, 2803] (Forte: 8-16) is the complement of the tetratonic modal family [163, 389, 1121, 2129] (Forte: 4-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3449 is 983

Scale 983Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3449 is chiral, and its enantiomorph is scale 983

Scale 983Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic

Transformations:

T0 3449  T0I 983
T1 2803  T1I 1966
T2 1511  T2I 3932
T3 3022  T3I 3769
T4 1949  T4I 3443
T5 3898  T5I 2791
T6 3701  T6I 1487
T7 3307  T7I 2974
T8 2519  T8I 1853
T9 943  T9I 3706
T10 1886  T10I 3317
T11 3772  T11I 2539

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 3451Scale 3451: Garygic, Ian Ring Music TheoryGarygic
Scale 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
Scale 3441Scale 3441: Thacrian, Ian Ring Music TheoryThacrian
Scale 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse
Scale 3433Scale 3433: Thonian, Ian Ring Music TheoryThonian
Scale 3417Scale 3417: Golian, Ian Ring Music TheoryGolian
Scale 3385Scale 3385: Chromatic Phrygian, Ian Ring Music TheoryChromatic Phrygian
Scale 3513Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
Scale 3577Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian
Scale 3321Scale 3321: Epagyllic, Ian Ring Music TheoryEpagyllic
Scale 3705Scale 3705: Messiaen Mode 4 Inverse, Ian Ring Music TheoryMessiaen Mode 4 Inverse
Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 2425Scale 2425: Rorian, Ian Ring Music TheoryRorian
Scale 2937Scale 2937: Phragyllic, Ian Ring Music TheoryPhragyllic
Scale 1401Scale 1401: Pagian, Ian Ring Music TheoryPagian

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. 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.