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Scale 2841: "Sothimic"

Scale 2841: Sothimic, 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

Zeitler
Sothimic

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

{0,3,4,8,9,11}

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-Z19

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: 795

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.

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.

no
prime: 411

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, 4, 1, 2, 1] 9

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, 1, 3, 4, 3, 1>

Interval Spectrum

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

p3m4n3sd3t

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

Spectra Variation

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

2.333

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.

2.116

Polygon Perimeter

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

5.699

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}231.5
G♯{8,0,3}321.17
Minor Triadsg♯m{8,11,3}231.5
am{9,0,4}231.5
Augmented TriadsC+{0,4,8}321.17
Diminished Triads{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 2841. Created by Ian Ring ©2019 C+ C+ E E C+->E G# G# C+->G# am am C+->am g#m g#m E->g#m g#m->G# G#->a° a°->am

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 VerticesE, g♯m, a°, am

Triadic Polychords

There are 2 ways that this hexatonic scale can be split into two common triads.


Major: {4, 8, 11}
Diminished: {9, 0, 3}

Minor: {8, 11, 3}
Minor: {9, 0, 4}

Modes

Modes are the rotational transformation of this scale. Scale 2841 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 867
Scale 867: Phrocrimic, Ian Ring Music TheoryPhrocrimic
3rd mode:
Scale 2481
Scale 2481: Raga Paraju, Ian Ring Music TheoryRaga Paraju
4th mode:
Scale 411
Scale 411: Lygimic, Ian Ring Music TheoryLygimicThis is the prime mode
5th mode:
Scale 2253
Scale 2253: Raga Amarasenapriya, Ian Ring Music TheoryRaga Amarasenapriya
6th mode:
Scale 1587
Scale 1587: Raga Rudra Pancama, Ian Ring Music TheoryRaga Rudra Pancama

Prime

The prime form of this scale is Scale 411

Scale 411Scale 411: Lygimic, Ian Ring Music TheoryLygimic

Complement

The hexatonic modal family [2841, 867, 2481, 411, 2253, 1587] (Forte: 6-Z19) is the complement of the hexatonic modal family [615, 825, 915, 2355, 2505, 3225] (Forte: 6-Z44)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2841 is 795

Scale 795Scale 795: Aeologimic, Ian Ring Music TheoryAeologimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2841 is chiral, and its enantiomorph is scale 795

Scale 795Scale 795: Aeologimic, Ian Ring Music TheoryAeologimic

Transformations:

T0 2841  T0I 795
T1 1587  T1I 1590
T2 3174  T2I 3180
T3 2253  T3I 2265
T4 411  T4I 435
T5 822  T5I 870
T6 1644  T6I 1740
T7 3288  T7I 3480
T8 2481  T8I 2865
T9 867  T9I 1635
T10 1734  T10I 3270
T11 3468  T11I 2445

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 2843Scale 2843: Sorian, Ian Ring Music TheorySorian
Scale 2845Scale 2845: Baptian, Ian Ring Music TheoryBaptian
Scale 2833Scale 2833: Dolitonic, Ian Ring Music TheoryDolitonic
Scale 2837Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
Scale 2825Scale 2825, Ian Ring Music Theory
Scale 2857Scale 2857: Stythimic, Ian Ring Music TheoryStythimic
Scale 2873Scale 2873: Ionian Augmented Sharp 2, Ian Ring Music TheoryIonian Augmented Sharp 2
Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
Scale 2969Scale 2969: Tholian, Ian Ring Music TheoryTholian
Scale 2585Scale 2585, Ian Ring Music Theory
Scale 2713Scale 2713: Porimic, Ian Ring Music TheoryPorimic
Scale 2329Scale 2329: Styditonic, Ian Ring Music TheoryStyditonic
Scale 3353Scale 3353: Phraptimic, Ian Ring Music TheoryPhraptimic
Scale 3865Scale 3865: Starian, Ian Ring Music TheoryStarian
Scale 793Scale 793: Mocritonic, Ian Ring Music TheoryMocritonic
Scale 1817Scale 1817: Phrythimic, Ian Ring Music TheoryPhrythimic

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.