The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 801: "Fahian"

Scale 801: Fahian, 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.



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.

prime: 153


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.

[5, 3, 1, 3]

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, 0, 2, 2, 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> = {1,3,5}
<2> = {4,8}
<3> = {7,9,11}

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.

(4, 0, 14)

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 TriadsF{5,9,0}110.5
Minor Triadsfm{5,8,0}110.5
Parsimonious Voice Leading Between Common Triads of Scale 801. Created by Ian Ring ©2019 fm fm F F fm->F

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.



Modes are the rotational transformation of this scale. Scale 801 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 153
Scale 153: Bajian, Ian Ring Music TheoryBajianThis is the prime mode
3rd mode:
Scale 531
Scale 531: Degian, Ian Ring Music TheoryDegian
4th mode:
Scale 2313
Scale 2313: Osrian, Ian Ring Music TheoryOsrian


The prime form of this scale is Scale 153

Scale 153Scale 153: Bajian, Ian Ring Music TheoryBajian


The tetratonic modal family [801, 153, 531, 2313] (Forte: 4-17) is the complement of the octatonic modal family [891, 1647, 1971, 2493, 2871, 3033, 3483, 3789] (Forte: 8-17)


The inverse of a scale is a reflection using the root as its axis. The inverse of 801 is 153

Scale 153Scale 153: Bajian, Ian Ring Music TheoryBajian


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> 801       T0I <11,0> 153
T1 <1,1> 1602      T1I <11,1> 306
T2 <1,2> 3204      T2I <11,2> 612
T3 <1,3> 2313      T3I <11,3> 1224
T4 <1,4> 531      T4I <11,4> 2448
T5 <1,5> 1062      T5I <11,5> 801
T6 <1,6> 2124      T6I <11,6> 1602
T7 <1,7> 153      T7I <11,7> 3204
T8 <1,8> 306      T8I <11,8> 2313
T9 <1,9> 612      T9I <11,9> 531
T10 <1,10> 1224      T10I <11,10> 1062
T11 <1,11> 2448      T11I <11,11> 2124
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 531      T0MI <7,0> 2313
T1M <5,1> 1062      T1MI <7,1> 531
T2M <5,2> 2124      T2MI <7,2> 1062
T3M <5,3> 153      T3MI <7,3> 2124
T4M <5,4> 306      T4MI <7,4> 153
T5M <5,5> 612      T5MI <7,5> 306
T6M <5,6> 1224      T6MI <7,6> 612
T7M <5,7> 2448      T7MI <7,7> 1224
T8M <5,8> 801       T8MI <7,8> 2448
T9M <5,9> 1602      T9MI <7,9> 801
T10M <5,10> 3204      T10MI <7,10> 1602
T11M <5,11> 2313      T11MI <7,11> 3204

The transformations that map this set to itself are: T0, T5I, T8M, T9MI

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 803Scale 803: Loritonic, Ian Ring Music TheoryLoritonic
Scale 805Scale 805: Rothitonic, Ian Ring Music TheoryRothitonic
Scale 809Scale 809: Dogitonic, Ian Ring Music TheoryDogitonic
Scale 817Scale 817: Zothitonic, Ian Ring Music TheoryZothitonic
Scale 769Scale 769: Enbian, Ian Ring Music TheoryEnbian
Scale 785Scale 785: Aeoloric, Ian Ring Music TheoryAeoloric
Scale 833Scale 833: Febian, Ian Ring Music TheoryFebian
Scale 865Scale 865: Jahian, Ian Ring Music TheoryJahian
Scale 929Scale 929: Fujian, Ian Ring Music TheoryFujian
Scale 545Scale 545: Dewian, Ian Ring Music TheoryDewian
Scale 673Scale 673: Estian, Ian Ring Music TheoryEstian
Scale 289Scale 289: Valian, Ian Ring Music TheoryValian
Scale 1313Scale 1313: Iplian, Ian Ring Music TheoryIplian
Scale 1825Scale 1825: Lecian, Ian Ring Music TheoryLecian
Scale 2849Scale 2849: Rubian, Ian Ring Music TheoryRubian

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.