The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 2179

Scale 2179, 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).



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


Forte Number

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


Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.


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.



A palindromic scale has the same pattern of intervals both ascending and descending.



A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

enantiomorph: 2083


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

2 (dihemitonic)


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

1 (uncohemitonic)


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.



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.


Prime Form

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

prime: 71


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


Deep Scale

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


Interval Structure

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

[1, 6, 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.

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

Interval Spectrum

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


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

Spectra Variation

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


Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.


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.


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.


Polygon Perimeter

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


Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.



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.


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.



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".


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.

(6, 1, 16)

Common Triads

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


Modes are the rotational transformation of this scale. Scale 2179 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 3137
Scale 3137, Ian Ring Music Theory
3rd mode:
Scale 113
Scale 113, Ian Ring Music Theory
4th mode:
Scale 263
Scale 263, Ian Ring Music Theory


The prime form of this scale is Scale 71

Scale 71Scale 71: Aloian, Ian Ring Music TheoryAloian


The tetratonic modal family [2179, 3137, 113, 263] (Forte: 4-5) is the complement of the octatonic modal family [479, 1991, 2287, 3043, 3191, 3569, 3643, 3869] (Forte: 8-5)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2179 is 2083

Scale 2083Scale 2083: Mofian, Ian Ring Music TheoryMofian


Only scales that are chiral will have an enantiomorph. Scale 2179 is chiral, and its enantiomorph is scale 2083

Scale 2083Scale 2083: Mofian, Ian Ring Music TheoryMofian


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> 2179       T0I <11,0> 2083
T1 <1,1> 263      T1I <11,1> 71
T2 <1,2> 526      T2I <11,2> 142
T3 <1,3> 1052      T3I <11,3> 284
T4 <1,4> 2104      T4I <11,4> 568
T5 <1,5> 113      T5I <11,5> 1136
T6 <1,6> 226      T6I <11,6> 2272
T7 <1,7> 452      T7I <11,7> 449
T8 <1,8> 904      T8I <11,8> 898
T9 <1,9> 1808      T9I <11,9> 1796
T10 <1,10> 3616      T10I <11,10> 3592
T11 <1,11> 3137      T11I <11,11> 3089
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2209      T0MI <7,0> 163
T1M <5,1> 323      T1MI <7,1> 326
T2M <5,2> 646      T2MI <7,2> 652
T3M <5,3> 1292      T3MI <7,3> 1304
T4M <5,4> 2584      T4MI <7,4> 2608
T5M <5,5> 1073      T5MI <7,5> 1121
T6M <5,6> 2146      T6MI <7,6> 2242
T7M <5,7> 197      T7MI <7,7> 389
T8M <5,8> 394      T8MI <7,8> 778
T9M <5,9> 788      T9MI <7,9> 1556
T10M <5,10> 1576      T10MI <7,10> 3112
T11M <5,11> 3152      T11MI <7,11> 2129

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 2177Scale 2177: Major Seventh Omit 3, Ian Ring Music TheoryMajor Seventh Omit 3
Scale 2181Scale 2181: Nemian, Ian Ring Music TheoryNemian
Scale 2183Scale 2183: Nenian, Ian Ring Music TheoryNenian
Scale 2187Scale 2187: Ionothitonic, Ian Ring Music TheoryIonothitonic
Scale 2195Scale 2195: Zalitonic, Ian Ring Music TheoryZalitonic
Scale 2211Scale 2211: Raga Gauri, Ian Ring Music TheoryRaga Gauri
Scale 2243Scale 2243: Noyian, Ian Ring Music TheoryNoyian
Scale 2051Scale 2051: Tritonic Chromatic 2, Ian Ring Music TheoryTritonic Chromatic 2
Scale 2115Scale 2115: Muyian, Ian Ring Music TheoryMuyian
Scale 2307Scale 2307: Ocoian, Ian Ring Music TheoryOcoian
Scale 2435Scale 2435: Raga Deshgaur, Ian Ring Music TheoryRaga Deshgaur
Scale 2691Scale 2691: Rahian, Ian Ring Music TheoryRahian
Scale 3203Scale 3203: Etrian, Ian Ring Music TheoryEtrian
Scale 131Scale 131: Atoian, Ian Ring Music TheoryAtoian
Scale 1155Scale 1155, Ian Ring Music Theory

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 ( 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.