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Scale 2695: "RAKIAN"

Scale 2695: RAKIAN, 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).

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

{0,1,2,7,9,11}

Forte Number

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

6-9

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: 3115

Hemitonia

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

3 (trihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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.

no
prime: 175

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.

[3, 4, 2, 2, 3, 1]

Interval Spectrum

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

p3m2n2s4d3t

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

Spectra Variation

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

4

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.

1.866

Polygon Perimeter

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

5.485

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{7,11,2}000

The following pitch classes are not present in any of the common triads: {0,1,9}

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 2695 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3395
Scale 3395: VEPIAN, Ian Ring Music TheoryVEPIAN
3rd mode:
Scale 3745
Scale 3745: XUVIAN, Ian Ring Music TheoryXUVIAN
4th mode:
Scale 245
Scale 245: Raga Dipak, Ian Ring Music TheoryRaga Dipak
5th mode:
Scale 1085
Scale 1085: GOZIAN, Ian Ring Music TheoryGOZIAN
6th mode:
Scale 1295
Scale 1295: HUYIAN, Ian Ring Music TheoryHUYIAN

Prime

The prime form of this scale is Scale 175

Scale 175Scale 175: BEWIAN, Ian Ring Music TheoryBEWIAN

Complement

The hexatonic modal family [2695, 3395, 3745, 245, 1085, 1295] (Forte: 6-9) is the complement of the hexatonic modal family [175, 1505, 1925, 2135, 3115, 3605] (Forte: 6-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2695 is 3115

Scale 3115Scale 3115: TIHIAN, Ian Ring Music TheoryTIHIAN

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2695 is chiral, and its enantiomorph is scale 3115

Scale 3115Scale 3115: TIHIAN, Ian Ring Music TheoryTIHIAN

Transformations:

T0 2695  T0I 3115
T1 1295  T1I 2135
T2 2590  T2I 175
T3 1085  T3I 350
T4 2170  T4I 700
T5 245  T5I 1400
T6 490  T6I 2800
T7 980  T7I 1505
T8 1960  T8I 3010
T9 3920  T9I 1925
T10 3745  T10I 3850
T11 3395  T11I 3605

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 2693Scale 2693: Lahuzu 5 Tone Type 3, Ian Ring Music TheoryLahuzu 5 Tone Type 3
Scale 2691Scale 2691: RAHIAN, Ian Ring Music TheoryRAHIAN
Scale 2699Scale 2699: Sythimic, Ian Ring Music TheorySythimic
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 2711Scale 2711: Stolian, Ian Ring Music TheoryStolian
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 2759Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani
Scale 2567Scale 2567: PUHIAN, Ian Ring Music TheoryPUHIAN
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 2823Scale 2823: RULIAN, Ian Ring Music TheoryRULIAN
Scale 2951Scale 2951: SILIAN, Ian Ring Music TheorySILIAN
Scale 2183Scale 2183: NENIAN, Ian Ring Music TheoryNENIAN
Scale 2439Scale 2439: PAGIAN, Ian Ring Music TheoryPAGIAN
Scale 3207Scale 3207: UCOIAN, Ian Ring Music TheoryUCOIAN
Scale 3719Scale 3719: XOFIAN, Ian Ring Music TheoryXOFIAN
Scale 647Scale 647: DUZIAN, Ian Ring Music TheoryDUZIAN
Scale 1671Scale 1671: KEMIAN, Ian Ring Music TheoryKEMIAN

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.