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Scale 2381: "Takemitsu Linea Mode 1"

Scale 2381: Takemitsu Linea Mode 1, 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

Named After Composers
Takemitsu Linea Mode 1
Takemitsu Tree Line Mode 1
Zeitler
Sorimic

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

{0,2,3,6,8,11}

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-Z49

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.

[1]

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.

no

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.

4

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: 667

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, 3, 2, 3, 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.

<2, 2, 4, 3, 2, 2>

Interval Spectrum

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

p2m3n4s2d2t2

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

Spectra Variation

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

2

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.

2.366

Polygon Perimeter

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

5.864

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.

[2]

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}231.5
B{11,3,6}321.17
Minor Triadsg♯m{8,11,3}321.17
bm{11,2,6}231.5
Diminished Triads{0,3,6}231.5
g♯°{8,11,2}231.5
Parsimonious Voice Leading Between Common Triads of Scale 2381. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B g#° g#° g#m g#m g#°->g#m bm bm g#°->bm g#m->G# g#m->B bm->B

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 Verticesg♯m, B
Peripheral Verticesc°, g♯°, G♯, bm

Modes

Modes are the rotational transformation of this scale. Scale 2381 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1619
Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan
3rd mode:
Scale 2857
Scale 2857: Stythimic, Ian Ring Music TheoryStythimic
4th mode:
Scale 869
Scale 869: Kothimic, Ian Ring Music TheoryKothimic
5th mode:
Scale 1241
Scale 1241: Pygimic, Ian Ring Music TheoryPygimic
6th mode:
Scale 667
Scale 667: Rodimic, Ian Ring Music TheoryRodimicThis is the prime mode

Prime

The prime form of this scale is Scale 667

Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic

Complement

The hexatonic modal family [2381, 1619, 2857, 869, 1241, 667] (Forte: 6-Z49) is the complement of the hexatonic modal family [619, 857, 1427, 1613, 2357, 2761] (Forte: 6-Z28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2381 is 1619

Scale 1619Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan

Transformations:

T0 2381  T0I 1619
T1 667  T1I 3238
T2 1334  T2I 2381
T3 2668  T3I 667
T4 1241  T4I 1334
T5 2482  T5I 2668
T6 869  T6I 1241
T7 1738  T7I 2482
T8 3476  T8I 869
T9 2857  T9I 1738
T10 1619  T10I 3476
T11 3238  T11I 2857

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 2383Scale 2383: Katorian, Ian Ring Music TheoryKatorian
Scale 2377Scale 2377: Bartók Gamma Chord, Ian Ring Music TheoryBartók Gamma Chord
Scale 2379Scale 2379: Raga Gurjari Todi, Ian Ring Music TheoryRaga Gurjari Todi
Scale 2373Scale 2373: Dyptitonic, Ian Ring Music TheoryDyptitonic
Scale 2389Scale 2389: Eskimo Hexatonic 2, Ian Ring Music TheoryEskimo Hexatonic 2
Scale 2397Scale 2397: Stagian, Ian Ring Music TheoryStagian
Scale 2413Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
Scale 2317Scale 2317, Ian Ring Music Theory
Scale 2349Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
Scale 2445Scale 2445: Zadimic, Ian Ring Music TheoryZadimic
Scale 2509Scale 2509: Double Harmonic Minor, Ian Ring Music TheoryDouble Harmonic Minor
Scale 2125Scale 2125, Ian Ring Music Theory
Scale 2253Scale 2253: Raga Amarasenapriya, Ian Ring Music TheoryRaga Amarasenapriya
Scale 2637Scale 2637: Raga Ranjani, Ian Ring Music TheoryRaga Ranjani
Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian
Scale 3405Scale 3405: Stynian, Ian Ring Music TheoryStynian
Scale 333Scale 333: Bogitonic, Ian Ring Music TheoryBogitonic
Scale 1357Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2

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.