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Scale 347: "Barimic"

Scale 347: Barimic, 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
Barimic

Analysis

Cardinality

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

6 (hexatonic)

Pitch Class Set

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

{0,1,3,4,6,8}

Forte Number

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

6-Z24

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: 2897

Hemitonia

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

2 (dihemitonic)

Cohemitonia

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

0 (ancohemitonic)

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.

5

Prime Form

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

yes

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.

[1, 2, 1, 2, 2, 4]

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.

<2, 3, 3, 3, 3, 1>

Interval Spectrum

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

p3m3n3s3d2t

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> = {1,2,4}
<2> = {3,4,5,6}
<3> = {4,5,7,8}
<4> = {6,7,8,9}
<5> = {8,10,11}

Spectra Variation

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

2.667

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.

2.232

Polygon Perimeter

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

5.767

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 TriadsG♯{8,0,3}221
Minor Triadsc♯m{1,4,8}131.5
Augmented TriadsC+{0,4,8}221
Diminished Triads{0,3,6}131.5
Parsimonious Voice Leading Between Common Triads of Scale 347. Created by Ian Ring ©2019 G# G# c°->G# C+ C+ c#m c#m C+->c#m C+->G#

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.

Diameter3
Radius2
Self-Centeredno
Central VerticesC+, G♯
Peripheral Verticesc°, c♯m

Triad Polychords

Also known as Bi-Triadic Hexatonics (a term coined by mDecks), and related to Generic Modality Compression (a method for guitar by Mick Goodrick and Tim Miller), these are two common triads that when combined use all the tones in this scale.

There is 1 way that this hexatonic scale can be split into two common triads.


Diminished: {0, 3, 6}
Minor: {1, 4, 8}

Modes

Modes are the rotational transformation of this scale. Scale 347 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2221
Scale 2221: Raga Sindhura Kafi, Ian Ring Music TheoryRaga Sindhura Kafi
3rd mode:
Scale 1579
Scale 1579: Sagimic, Ian Ring Music TheorySagimic
4th mode:
Scale 2837
Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
5th mode:
Scale 1733
Scale 1733: Raga Sarasvati, Ian Ring Music TheoryRaga Sarasvati
6th mode:
Scale 1457
Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [347, 2221, 1579, 2837, 1733, 1457] (Forte: 6-Z24) is the complement of the hexatonic modal family [599, 697, 1481, 1829, 2347, 3221] (Forte: 6-Z46)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 347 is 2897

Scale 2897Scale 2897: Rycrimic, Ian Ring Music TheoryRycrimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 347 is chiral, and its enantiomorph is scale 2897

Scale 2897Scale 2897: Rycrimic, Ian Ring Music TheoryRycrimic

Transformations:

T0 347  T0I 2897
T1 694  T1I 1699
T2 1388  T2I 3398
T3 2776  T3I 2701
T4 1457  T4I 1307
T5 2914  T5I 2614
T6 1733  T6I 1133
T7 3466  T7I 2266
T8 2837  T8I 437
T9 1579  T9I 874
T10 3158  T10I 1748
T11 2221  T11I 3496

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 345Scale 345: Gylitonic, Ian Ring Music TheoryGylitonic
Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 339Scale 339: Zaptitonic, Ian Ring Music TheoryZaptitonic
Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic
Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi
Scale 363Scale 363: Soptimic, Ian Ring Music TheorySoptimic
Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian
Scale 283Scale 283: Aerylitonic, Ian Ring Music TheoryAerylitonic
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 411Scale 411: Lygimic, Ian Ring Music TheoryLygimic
Scale 475Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian
Scale 91Scale 91, Ian Ring Music Theory
Scale 219Scale 219: Istrian, Ian Ring Music TheoryIstrian
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian
Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian
Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian

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.