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Scale 2181: "Nemian"

Scale 2181: Nemian, 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
Nemian

Analysis

Cardinality

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

4 (tetratonic)

Pitch Class Set

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

{0,2,7,11}

Forte Number

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

4-14

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: 1059

Hemitonia

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

1 (unhemitonic)

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.

2

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.

3

Prime Form

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

no
prime: 141

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.

[2, 5, 4, 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.

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

Interval Spectrum

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

p2mnsd

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

Spectra Variation

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

3.5

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.

1.366

Polygon Perimeter

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

5.182

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.

(4, 2, 18)

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}

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 2181 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 1569
Scale 1569: Jocian, Ian Ring Music TheoryJocian
3rd mode:
Scale 177
Scale 177: Bexian, Ian Ring Music TheoryBexian
4th mode:
Scale 267
Scale 267: Bobian, Ian Ring Music TheoryBobian

Prime

The prime form of this scale is Scale 141

Scale 141Scale 141: Babian, Ian Ring Music TheoryBabian

Complement

The tetratonic modal family [2181, 1569, 177, 267] (Forte: 4-14) is the complement of the octatonic modal family [759, 1839, 1977, 2427, 2967, 3261, 3531, 3813] (Forte: 8-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2181 is 1059

Scale 1059Scale 1059: Gikian, Ian Ring Music TheoryGikian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2181 is chiral, and its enantiomorph is scale 1059

Scale 1059Scale 1059: Gikian, Ian Ring Music TheoryGikian

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> 2181       T0I <11,0> 1059
T1 <1,1> 267      T1I <11,1> 2118
T2 <1,2> 534      T2I <11,2> 141
T3 <1,3> 1068      T3I <11,3> 282
T4 <1,4> 2136      T4I <11,4> 564
T5 <1,5> 177      T5I <11,5> 1128
T6 <1,6> 354      T6I <11,6> 2256
T7 <1,7> 708      T7I <11,7> 417
T8 <1,8> 1416      T8I <11,8> 834
T9 <1,9> 2832      T9I <11,9> 1668
T10 <1,10> 1569      T10I <11,10> 3336
T11 <1,11> 3138      T11I <11,11> 2577
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3201      T0MI <7,0> 39
T1M <5,1> 2307      T1MI <7,1> 78
T2M <5,2> 519      T2MI <7,2> 156
T3M <5,3> 1038      T3MI <7,3> 312
T4M <5,4> 2076      T4MI <7,4> 624
T5M <5,5> 57      T5MI <7,5> 1248
T6M <5,6> 114      T6MI <7,6> 2496
T7M <5,7> 228      T7MI <7,7> 897
T8M <5,8> 456      T8MI <7,8> 1794
T9M <5,9> 912      T9MI <7,9> 3588
T10M <5,10> 1824      T10MI <7,10> 3081
T11M <5,11> 3648      T11MI <7,11> 2067

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 2183Scale 2183: Nenian, Ian Ring Music TheoryNenian
Scale 2177Scale 2177: Major Seventh Omit 3, Ian Ring Music TheoryMajor Seventh Omit 3
Scale 2179Scale 2179, Ian Ring Music Theory
Scale 2185Scale 2185: Dygic, Ian Ring Music TheoryDygic
Scale 2189Scale 2189: Zagitonic, Ian Ring Music TheoryZagitonic
Scale 2197Scale 2197: Raga Hamsadhvani, Ian Ring Music TheoryRaga Hamsadhvani
Scale 2213Scale 2213: Raga Desh, Ian Ring Music TheoryRaga Desh
Scale 2245Scale 2245: Raga Vaijayanti, Ian Ring Music TheoryRaga Vaijayanti
Scale 2053Scale 2053: Powian, Ian Ring Music TheoryPowian
Scale 2117Scale 2117: Raga Sumukam, Ian Ring Music TheoryRaga Sumukam
Scale 2309Scale 2309: Ocuian, Ian Ring Music TheoryOcuian
Scale 2437Scale 2437: Pafian, Ian Ring Music TheoryPafian
Scale 2693Scale 2693: Rajian, Ian Ring Music TheoryRajian
Scale 3205Scale 3205: Utwian, Ian Ring Music TheoryUtwian
Scale 133Scale 133: Suspended Second Triad, Ian Ring Music TheorySuspended Second Triad
Scale 1157Scale 1157: Alkian, Ian Ring Music TheoryAlkian

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.