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Scale 3009: "Suvian"

Scale 3009: Suvian, 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




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


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: 123


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

4 (multihemitonic)


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

2 (dicohemitonic)


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: 111


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.

[6, 1, 1, 1, 2, 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.

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

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.

(34, 9, 55)

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
Diminished Triadsf♯°{6,9,0}000

The following pitch classes are not present in any of the common triads: {7,8,11}

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.


Modes are the rotational transformation of this scale. Scale 3009 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 111
Scale 111: Aroian, Ian Ring Music TheoryAroianThis is the prime mode
3rd mode:
Scale 2103
Scale 2103: Murian, Ian Ring Music TheoryMurian
4th mode:
Scale 3099
Scale 3099: Tixian, Ian Ring Music TheoryTixian
5th mode:
Scale 3597
Scale 3597: Wijian, Ian Ring Music TheoryWijian
6th mode:
Scale 1923
Scale 1923: Lulian, Ian Ring Music TheoryLulian


The prime form of this scale is Scale 111

Scale 111Scale 111: Aroian, Ian Ring Music TheoryAroian


The hexatonic modal family [3009, 111, 2103, 3099, 3597, 1923] (Forte: 6-Z3) is the complement of the hexatonic modal family [159, 993, 2127, 3111, 3603, 3849] (Forte: 6-Z36)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3009 is 123

Scale 123Scale 123: Asuian, Ian Ring Music TheoryAsuian


Only scales that are chiral will have an enantiomorph. Scale 3009 is chiral, and its enantiomorph is scale 123

Scale 123Scale 123: Asuian, Ian Ring Music TheoryAsuian


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> 3009       T0I <11,0> 123
T1 <1,1> 1923      T1I <11,1> 246
T2 <1,2> 3846      T2I <11,2> 492
T3 <1,3> 3597      T3I <11,3> 984
T4 <1,4> 3099      T4I <11,4> 1968
T5 <1,5> 2103      T5I <11,5> 3936
T6 <1,6> 111      T6I <11,6> 3777
T7 <1,7> 222      T7I <11,7> 3459
T8 <1,8> 444      T8I <11,8> 2823
T9 <1,9> 888      T9I <11,9> 1551
T10 <1,10> 1776      T10I <11,10> 3102
T11 <1,11> 3552      T11I <11,11> 2109
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2769      T0MI <7,0> 363
T1M <5,1> 1443      T1MI <7,1> 726
T2M <5,2> 2886      T2MI <7,2> 1452
T3M <5,3> 1677      T3MI <7,3> 2904
T4M <5,4> 3354      T4MI <7,4> 1713
T5M <5,5> 2613      T5MI <7,5> 3426
T6M <5,6> 1131      T6MI <7,6> 2757
T7M <5,7> 2262      T7MI <7,7> 1419
T8M <5,8> 429      T8MI <7,8> 2838
T9M <5,9> 858      T9MI <7,9> 1581
T10M <5,10> 1716      T10MI <7,10> 3162
T11M <5,11> 3432      T11MI <7,11> 2229

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 3011Scale 3011, Ian Ring Music Theory
Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian
Scale 3017Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
Scale 3041Scale 3041: Tanian, Ian Ring Music TheoryTanian
Scale 2945Scale 2945: Sihian, Ian Ring Music TheorySihian
Scale 2977Scale 2977: Sobian, Ian Ring Music TheorySobian
Scale 2881Scale 2881: Satian, Ian Ring Music TheorySatian
Scale 2753Scale 2753: Ritian, Ian Ring Music TheoryRitian
Scale 2497Scale 2497: Peqian, Ian Ring Music TheoryPeqian
Scale 3521Scale 3521: Wanian, Ian Ring Music TheoryWanian
Scale 4033Scale 4033: Heptatonic Chromatic Descending, Ian Ring Music TheoryHeptatonic Chromatic Descending
Scale 961Scale 961: Gabian, Ian Ring Music TheoryGabian
Scale 1985Scale 1985: Mewian, Ian Ring Music TheoryMewian

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.