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Scale 2071: "Moxian"

Scale 2071: Moxian, 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

Dozenal
Moxian

Analysis

Cardinality

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

5 (pentatonic)

Pitch Class Set

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

{0,1,2,4,11}

Forte Number

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

5-2

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: 3331

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.

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.

4

Prime Form

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

no
prime: 47

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

[1, 1, 2, 7, 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.

<3, 3, 2, 1, 1, 0>

Interval Spectrum

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

pmn2s3d3

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

Spectra Variation

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

5.2

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.

0.933

Polygon Perimeter

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

4.485

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

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(15, 6, 32)

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 2071 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3083
Scale 3083: Rehian, Ian Ring Music TheoryRehian
3rd mode:
Scale 3589
Scale 3589: Widian, Ian Ring Music TheoryWidian
4th mode:
Scale 1921
Scale 1921: Lukian, Ian Ring Music TheoryLukian
5th mode:
Scale 47
Scale 47: Agoian, Ian Ring Music TheoryAgoianThis is the prime mode

Prime

The prime form of this scale is Scale 47

Scale 47Scale 47: Agoian, Ian Ring Music TheoryAgoian

Complement

The pentatonic modal family [2071, 3083, 3589, 1921, 47] (Forte: 5-2) is the complement of the heptatonic modal family [191, 2017, 2143, 3119, 3607, 3851, 3973] (Forte: 7-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2071 is 3331

Scale 3331Scale 3331: Vabian, Ian Ring Music TheoryVabian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2071 is chiral, and its enantiomorph is scale 3331

Scale 3331Scale 3331: Vabian, Ian Ring Music TheoryVabian

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 2071       T0I <11,0> 3331
T1 <1,1> 47      T1I <11,1> 2567
T2 <1,2> 94      T2I <11,2> 1039
T3 <1,3> 188      T3I <11,3> 2078
T4 <1,4> 376      T4I <11,4> 61
T5 <1,5> 752      T5I <11,5> 122
T6 <1,6> 1504      T6I <11,6> 244
T7 <1,7> 3008      T7I <11,7> 488
T8 <1,8> 1921      T8I <11,8> 976
T9 <1,9> 3842      T9I <11,9> 1952
T10 <1,10> 3589      T10I <11,10> 3904
T11 <1,11> 3083      T11I <11,11> 3713
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1441      T0MI <7,0> 181
T1M <5,1> 2882      T1MI <7,1> 362
T2M <5,2> 1669      T2MI <7,2> 724
T3M <5,3> 3338      T3MI <7,3> 1448
T4M <5,4> 2581      T4MI <7,4> 2896
T5M <5,5> 1067      T5MI <7,5> 1697
T6M <5,6> 2134      T6MI <7,6> 3394
T7M <5,7> 173      T7MI <7,7> 2693
T8M <5,8> 346      T8MI <7,8> 1291
T9M <5,9> 692      T9MI <7,9> 2582
T10M <5,10> 1384      T10MI <7,10> 1069
T11M <5,11> 2768      T11MI <7,11> 2138

The transformations that map this set to itself are: T0

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 2069Scale 2069: Mowian, Ian Ring Music TheoryMowian
Scale 2067Scale 2067: Movian, Ian Ring Music TheoryMovian
Scale 2075Scale 2075: Mozian, Ian Ring Music TheoryMozian
Scale 2079Scale 2079: Hexatonic Chromatic 4, Ian Ring Music TheoryHexatonic Chromatic 4
Scale 2055Scale 2055: Tetratonic Chromatic 2, Ian Ring Music TheoryTetratonic Chromatic 2
Scale 2063Scale 2063: Pentatonic Chromatic 2, Ian Ring Music TheoryPentatonic Chromatic 2
Scale 2087Scale 2087: Muhian, Ian Ring Music TheoryMuhian
Scale 2103Scale 2103: Murian, Ian Ring Music TheoryMurian
Scale 2135Scale 2135: Nakian, Ian Ring Music TheoryNakian
Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic
Scale 2327Scale 2327: Epalimic, Ian Ring Music TheoryEpalimic
Scale 2583Scale 2583: Purian, Ian Ring Music TheoryPurian
Scale 3095Scale 3095: Tivian, Ian Ring Music TheoryTivian
Scale 23Scale 23: Aphian, Ian Ring Music TheoryAphian
Scale 1047Scale 1047: Gician, Ian Ring Music TheoryGician

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. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.