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Scale 1377: "Insian"

Scale 1377: Insian, 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.

5 (pentatonic)

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: 213


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: 171


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, 1, 2, 2, 2]

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

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.

(9, 3, 32)

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
Minor Triadsfm{5,8,0}000

The following pitch classes are not present in any of the common triads: {6,10}

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 1377 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 171
Scale 171: Pruian, Ian Ring Music TheoryPruianThis is the prime mode
3rd mode:
Scale 2133
Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki
4th mode:
Scale 1557
Scale 1557: Jovian, Ian Ring Music TheoryJovian
5th mode:
Scale 1413
Scale 1413: Iruian, Ian Ring Music TheoryIruian


The prime form of this scale is Scale 171

Scale 171Scale 171: Pruian, Ian Ring Music TheoryPruian


The pentatonic modal family [1377, 171, 2133, 1557, 1413] (Forte: 5-24) is the complement of the heptatonic modal family [687, 1401, 1509, 1941, 2391, 3243, 3669] (Forte: 7-24)


The inverse of a scale is a reflection using the root as its axis. The inverse of 1377 is 213

Scale 213Scale 213: Bitian, Ian Ring Music TheoryBitian


Only scales that are chiral will have an enantiomorph. Scale 1377 is chiral, and its enantiomorph is scale 213

Scale 213Scale 213: Bitian, Ian Ring Music TheoryBitian


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> 1377       T0I <11,0> 213
T1 <1,1> 2754      T1I <11,1> 426
T2 <1,2> 1413      T2I <11,2> 852
T3 <1,3> 2826      T3I <11,3> 1704
T4 <1,4> 1557      T4I <11,4> 3408
T5 <1,5> 3114      T5I <11,5> 2721
T6 <1,6> 2133      T6I <11,6> 1347
T7 <1,7> 171      T7I <11,7> 2694
T8 <1,8> 342      T8I <11,8> 1293
T9 <1,9> 684      T9I <11,9> 2586
T10 <1,10> 1368      T10I <11,10> 1077
T11 <1,11> 2736      T11I <11,11> 2154
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 87      T0MI <7,0> 3393
T1M <5,1> 174      T1MI <7,1> 2691
T2M <5,2> 348      T2MI <7,2> 1287
T3M <5,3> 696      T3MI <7,3> 2574
T4M <5,4> 1392      T4MI <7,4> 1053
T5M <5,5> 2784      T5MI <7,5> 2106
T6M <5,6> 1473      T6MI <7,6> 117
T7M <5,7> 2946      T7MI <7,7> 234
T8M <5,8> 1797      T8MI <7,8> 468
T9M <5,9> 3594      T9MI <7,9> 936
T10M <5,10> 3093      T10MI <7,10> 1872
T11M <5,11> 2091      T11MI <7,11> 3744

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 1379Scale 1379: Kycrimic, Ian Ring Music TheoryKycrimic
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 1385Scale 1385: Phracrimic, Ian Ring Music TheoryPhracrimic
Scale 1393Scale 1393: Mycrimic, Ian Ring Music TheoryMycrimic
Scale 1345Scale 1345: Iskian, Ian Ring Music TheoryIskian
Scale 1361Scale 1361: Bolitonic, Ian Ring Music TheoryBolitonic
Scale 1313Scale 1313: Iplian, Ian Ring Music TheoryIplian
Scale 1441Scale 1441: Jabian, Ian Ring Music TheoryJabian
Scale 1505Scale 1505: Jepian, Ian Ring Music TheoryJepian
Scale 1121Scale 1121: Guwian, Ian Ring Music TheoryGuwian
Scale 1249Scale 1249: Howian, Ian Ring Music TheoryHowian
Scale 1633Scale 1633: Kapian, Ian Ring Music TheoryKapian
Scale 1889Scale 1889: Loqian, Ian Ring Music TheoryLoqian
Scale 353Scale 353: Cebian, Ian Ring Music TheoryCebian
Scale 865Scale 865: Jahian, Ian Ring Music TheoryJahian
Scale 2401Scale 2401: Oroian, Ian Ring Music TheoryOroian
Scale 3425Scale 3425: Vihian, Ian Ring Music TheoryVihian

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.