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Scale 349: "Borimic"

Scale 349: Borimic, 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
Borimic

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

{0,2,3,4,6,8}

Forte Number

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

6-21

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: 1873

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.

1 (uncohemitonic)

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.

5

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.

[2, 1, 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, 4, 2, 4, 1, 2>

Interval Spectrum

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

pm4n2s4d2t2

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

Spectra Variation

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

3

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}210.67
Augmented TriadsC+{0,4,8}121
Diminished Triads{0,3,6}121

The following pitch classes are not present in any of the common triads: {2}

Parsimonious Voice Leading Between Common Triads of Scale 349. Created by Ian Ring ©2019 G# G# c°->G# C+ C+ 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.

Diameter2
Radius1
Self-Centeredno
Central VerticesG♯
Peripheral Verticesc°, C+

Modes

Modes are the rotational transformation of this scale. Scale 349 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1111
Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic
3rd mode:
Scale 2603
Scale 2603: Gadimic, Ian Ring Music TheoryGadimic
4th mode:
Scale 3349
Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic
5th mode:
Scale 1861
Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
6th mode:
Scale 1489
Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [349, 1111, 2603, 3349, 1861, 1489] (Forte: 6-21) is the complement of the hexatonic modal family [349, 1111, 1489, 1861, 2603, 3349] (Forte: 6-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 349 is 1873

Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 349 is chiral, and its enantiomorph is scale 1873

Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic

Transformations:

T0 349  T0I 1873
T1 698  T1I 3746
T2 1396  T2I 3397
T3 2792  T3I 2699
T4 1489  T4I 1303
T5 2978  T5I 2606
T6 1861  T6I 1117
T7 3722  T7I 2234
T8 3349  T8I 373
T9 2603  T9I 746
T10 1111  T10I 1492
T11 2222  T11I 2984

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 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 345Scale 345: Gylitonic, Ian Ring Music TheoryGylitonic
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 341Scale 341: Bothitonic, Ian Ring Music TheoryBothitonic
Scale 333Scale 333: Bogitonic, Ian Ring Music TheoryBogitonic
Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic
Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian
Scale 285Scale 285: Zaritonic, Ian Ring Music TheoryZaritonic
Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic
Scale 413Scale 413: Ganimic, Ian Ring Music TheoryGanimic
Scale 477Scale 477: Stacrian, Ian Ring Music TheoryStacrian
Scale 93Scale 93, Ian Ring Music Theory
Scale 221Scale 221, Ian Ring Music Theory
Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic
Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian
Scale 1373Scale 1373: Storian, Ian Ring Music TheoryStorian
Scale 2397Scale 2397: Stagian, Ian Ring Music TheoryStagian

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.