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Scale 43: "Alfian"

Scale 43: Alfian, 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.

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: 2689


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

1 (unhemitonic)


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

0 (ancohemitonic)


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.



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, 2, 2, 7]

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, 2, 1, 1, 1, 0>

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

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.

(5, 0, 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 43 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 2069
Scale 2069: Mowian, Ian Ring Music TheoryMowian
3rd mode:
Scale 1541
Scale 1541: Jilian, Ian Ring Music TheoryJilian
4th mode:
Scale 1409
Scale 1409: Imsian, Ian Ring Music TheoryImsian


This is the prime form of this scale.


The tetratonic modal family [43, 2069, 1541, 1409] (Forte: 4-11) is the complement of the octatonic modal family [703, 1529, 2021, 2399, 3247, 3671, 3883, 3989] (Forte: 8-11)


The inverse of a scale is a reflection using the root as its axis. The inverse of 43 is 2689

Scale 2689Scale 2689: Ragian, Ian Ring Music TheoryRagian


Only scales that are chiral will have an enantiomorph. Scale 43 is chiral, and its enantiomorph is scale 2689

Scale 2689Scale 2689: Ragian, Ian Ring Music TheoryRagian


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> 43       T0I <11,0> 2689
T1 <1,1> 86      T1I <11,1> 1283
T2 <1,2> 172      T2I <11,2> 2566
T3 <1,3> 344      T3I <11,3> 1037
T4 <1,4> 688      T4I <11,4> 2074
T5 <1,5> 1376      T5I <11,5> 53
T6 <1,6> 2752      T6I <11,6> 106
T7 <1,7> 1409      T7I <11,7> 212
T8 <1,8> 2818      T8I <11,8> 424
T9 <1,9> 1541      T9I <11,9> 848
T10 <1,10> 3082      T10I <11,10> 1696
T11 <1,11> 2069      T11I <11,11> 3392
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 43       T0MI <7,0> 2689
T1M <5,1> 86      T1MI <7,1> 1283
T2M <5,2> 172      T2MI <7,2> 2566
T3M <5,3> 344      T3MI <7,3> 1037
T4M <5,4> 688      T4MI <7,4> 2074
T5M <5,5> 1376      T5MI <7,5> 53
T6M <5,6> 2752      T6MI <7,6> 106
T7M <5,7> 1409      T7MI <7,7> 212
T8M <5,8> 2818      T8MI <7,8> 424
T9M <5,9> 1541      T9MI <7,9> 848
T10M <5,10> 3082      T10MI <7,10> 1696
T11M <5,11> 2069      T11MI <7,11> 3392

The transformations that map this set to itself are: T0, T0M

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 41Scale 41: Vietnamese Tritonic, Ian Ring Music TheoryVietnamese Tritonic
Scale 45Scale 45: Aprian, Ian Ring Music TheoryAprian
Scale 47Scale 47: Agoian, Ian Ring Music TheoryAgoian
Scale 35Scale 35: Abbian, Ian Ring Music TheoryAbbian
Scale 39Scale 39: Afuian, Ian Ring Music TheoryAfuian
Scale 51Scale 51: Arfian, Ian Ring Music TheoryArfian
Scale 59Scale 59: Ahuian, Ian Ring Music TheoryAhuian
Scale 11Scale 11: Ankian, Ian Ring Music TheoryAnkian
Scale 27Scale 27: Adoian, Ian Ring Music TheoryAdoian
Scale 75Scale 75: Iloian, Ian Ring Music TheoryIloian
Scale 107Scale 107: Ansian, Ian Ring Music TheoryAnsian
Scale 171Scale 171: Pruian, Ian Ring Music TheoryPruian
Scale 299Scale 299: Raga Chitthakarshini, Ian Ring Music TheoryRaga Chitthakarshini
Scale 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic
Scale 1067Scale 1067: Gopian, Ian Ring Music TheoryGopian
Scale 2091Scale 2091: Mukian, Ian Ring Music TheoryMukian

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.