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Scale 169: "Vietnamese Tetratonic"

Scale 169: Vietnamese Tetratonic, 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

Vietnamese Tetratonic



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: 673


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

0 (anhemitonic)


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: 149


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.

[3, 2, 2, 5]

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.

<0, 2, 1, 1, 2, 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> = {2,3,5}
<2> = {4,5,7,8}
<3> = {7,9,10}

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.

(2, 2, 16)

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 Triadscm{0,3,7}000

The following pitch classes are not present in any of the common triads: {5}

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 169 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 533
Scale 533: Dehian, Ian Ring Music TheoryDehian
3rd mode:
Scale 1157
Scale 1157: Alkian, Ian Ring Music TheoryAlkian
4th mode:
Scale 1313
Scale 1313: Iplian, Ian Ring Music TheoryIplian


The prime form of this scale is Scale 149

Scale 149Scale 149: Eskimo Tetratonic, Ian Ring Music TheoryEskimo Tetratonic


The tetratonic modal family [169, 533, 1157, 1313] (Forte: 4-22) is the complement of the octatonic modal family [1391, 1469, 1781, 1963, 2743, 3029, 3419, 3757] (Forte: 8-22)


The inverse of a scale is a reflection using the root as its axis. The inverse of 169 is 673

Scale 673Scale 673: Estian, Ian Ring Music TheoryEstian


Only scales that are chiral will have an enantiomorph. Scale 169 is chiral, and its enantiomorph is scale 673

Scale 673Scale 673: Estian, Ian Ring Music TheoryEstian


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> 169       T0I <11,0> 673
T1 <1,1> 338      T1I <11,1> 1346
T2 <1,2> 676      T2I <11,2> 2692
T3 <1,3> 1352      T3I <11,3> 1289
T4 <1,4> 2704      T4I <11,4> 2578
T5 <1,5> 1313      T5I <11,5> 1061
T6 <1,6> 2626      T6I <11,6> 2122
T7 <1,7> 1157      T7I <11,7> 149
T8 <1,8> 2314      T8I <11,8> 298
T9 <1,9> 533      T9I <11,9> 596
T10 <1,10> 1066      T10I <11,10> 1192
T11 <1,11> 2132      T11I <11,11> 2384
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2059      T0MI <7,0> 2563
T1M <5,1> 23      T1MI <7,1> 1031
T2M <5,2> 46      T2MI <7,2> 2062
T3M <5,3> 92      T3MI <7,3> 29
T4M <5,4> 184      T4MI <7,4> 58
T5M <5,5> 368      T5MI <7,5> 116
T6M <5,6> 736      T6MI <7,6> 232
T7M <5,7> 1472      T7MI <7,7> 464
T8M <5,8> 2944      T8MI <7,8> 928
T9M <5,9> 1793      T9MI <7,9> 1856
T10M <5,10> 3586      T10MI <7,10> 3712
T11M <5,11> 3077      T11MI <7,11> 3329

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 171Scale 171: Pruian, Ian Ring Music TheoryPruian
Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 161Scale 161: Raga Sarvasri, Ian Ring Music TheoryRaga Sarvasri
Scale 165Scale 165: Genus Primum, Ian Ring Music TheoryGenus Primum
Scale 177Scale 177: Bexian, Ian Ring Music TheoryBexian
Scale 185Scale 185: Becian, Ian Ring Music TheoryBecian
Scale 137Scale 137: Ute Tritonic, Ian Ring Music TheoryUte Tritonic
Scale 153Scale 153: Bajian, Ian Ring Music TheoryBajian
Scale 201Scale 201: Bemian, Ian Ring Music TheoryBemian
Scale 233Scale 233: Bigian, Ian Ring Music TheoryBigian
Scale 41Scale 41: Vietnamese Tritonic, Ian Ring Music TheoryVietnamese Tritonic
Scale 105Scale 105, Ian Ring Music Theory
Scale 297Scale 297: Mynic, Ian Ring Music TheoryMynic
Scale 425Scale 425: Raga Kokil Pancham, Ian Ring Music TheoryRaga Kokil Pancham
Scale 681Scale 681: Kyemyonjo, Ian Ring Music TheoryKyemyonjo
Scale 1193Scale 1193: Minor Pentatonic, Ian Ring Music TheoryMinor Pentatonic
Scale 2217Scale 2217: Kagitonic, Ian Ring Music TheoryKagitonic

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.