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Scale 629: "Aeronimic"

Scale 629: Aeronimic, 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: 1481


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

2 (dihemitonic)


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

1 (uncohemitonic)


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: 599


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.

[2, 2, 1, 1, 3, 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.

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

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.

(12, 17, 65)

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 TriadsD{2,6,9}231.4
Minor Triadsdm{2,5,9}221.2
Diminished Triadsf♯°{6,9,0}221.2
Parsimonious Voice Leading Between Common Triads of Scale 629. Created by Ian Ring ©2019 dm dm D D dm->D F F dm->F f#° f#° D->f#° F->f#° am am F->am

view full size

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.

Central Verticesdm, F, f♯°
Peripheral VerticesD, am


Modes are the rotational transformation of this scale. Scale 629 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1181
Scale 1181: Katagimic, Ian Ring Music TheoryKatagimic
3rd mode:
Scale 1319
Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic
4th mode:
Scale 2707
Scale 2707: Banimic, Ian Ring Music TheoryBanimic
5th mode:
Scale 3401
Scale 3401: Palimic, Ian Ring Music TheoryPalimic
6th mode:
Scale 937
Scale 937: Stothimic, Ian Ring Music TheoryStothimic


The prime form of this scale is Scale 599

Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic


The hexatonic modal family [629, 1181, 1319, 2707, 3401, 937] (Forte: 6-Z46) is the complement of the hexatonic modal family [347, 1457, 1579, 1733, 2221, 2837] (Forte: 6-Z24)


The inverse of a scale is a reflection using the root as its axis. The inverse of 629 is 1481

Scale 1481Scale 1481: Zagimic, Ian Ring Music TheoryZagimic


Only scales that are chiral will have an enantiomorph. Scale 629 is chiral, and its enantiomorph is scale 1481

Scale 1481Scale 1481: Zagimic, Ian Ring Music TheoryZagimic


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> 629       T0I <11,0> 1481
T1 <1,1> 1258      T1I <11,1> 2962
T2 <1,2> 2516      T2I <11,2> 1829
T3 <1,3> 937      T3I <11,3> 3658
T4 <1,4> 1874      T4I <11,4> 3221
T5 <1,5> 3748      T5I <11,5> 2347
T6 <1,6> 3401      T6I <11,6> 599
T7 <1,7> 2707      T7I <11,7> 1198
T8 <1,8> 1319      T8I <11,8> 2396
T9 <1,9> 2638      T9I <11,9> 697
T10 <1,10> 1181      T10I <11,10> 1394
T11 <1,11> 2362      T11I <11,11> 2788
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1859      T0MI <7,0> 2141
T1M <5,1> 3718      T1MI <7,1> 187
T2M <5,2> 3341      T2MI <7,2> 374
T3M <5,3> 2587      T3MI <7,3> 748
T4M <5,4> 1079      T4MI <7,4> 1496
T5M <5,5> 2158      T5MI <7,5> 2992
T6M <5,6> 221      T6MI <7,6> 1889
T7M <5,7> 442      T7MI <7,7> 3778
T8M <5,8> 884      T8MI <7,8> 3461
T9M <5,9> 1768      T9MI <7,9> 2827
T10M <5,10> 3536      T10MI <7,10> 1559
T11M <5,11> 2977      T11MI <7,11> 3118

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 631Scale 631: Zygian, Ian Ring Music TheoryZygian
Scale 625Scale 625: Ionyptitonic, Ian Ring Music TheoryIonyptitonic
Scale 627Scale 627: Mogimic, Ian Ring Music TheoryMogimic
Scale 633Scale 633: Kydimic, Ian Ring Music TheoryKydimic
Scale 637Scale 637: Debussy's Heptatonic, Ian Ring Music TheoryDebussy's Heptatonic
Scale 613Scale 613: Phralitonic, Ian Ring Music TheoryPhralitonic
Scale 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic
Scale 597Scale 597: Kung, Ian Ring Music TheoryKung
Scale 565Scale 565: Aeolyphritonic, Ian Ring Music TheoryAeolyphritonic
Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord
Scale 757Scale 757: Ionyptian, Ian Ring Music TheoryIonyptian
Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian
Scale 117Scale 117: Anbian, Ian Ring Music TheoryAnbian
Scale 373Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
Scale 1141Scale 1141: Rynimic, Ian Ring Music TheoryRynimic
Scale 1653Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
Scale 2677Scale 2677: Thodian, Ian Ring Music TheoryThodian

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.