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Scale 2285: "Aerogian"

Scale 2285: Aerogian, 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

Zeitler
Aerogian
Dozenal
Nuyian

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,3,5,6,7,11}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

7-Z38

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

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.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 1763

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

1 (uncohemitonic)

Imperfections

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.

3

Modes

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.

6

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 439

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

[2, 1, 2, 1, 1, 4, 1]

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.

<4, 3, 4, 4, 4, 2>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p4m4n4s3d4t2

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

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.571

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

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.

no

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.

2.299

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

5.803

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

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.

no

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.

none

Propriety

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".

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.

(27, 24, 90)

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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 TriadsG{7,11,2}231.57
B{11,3,6}321.29
Minor Triadscm{0,3,7}241.86
bm{11,2,6}331.43
Augmented TriadsD♯+{3,7,11}331.43
Diminished Triads{0,3,6}231.71
{11,2,5}142.14
Parsimonious Voice Leading Between Common Triads of Scale 2285. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ Parsimonious Voice Leading Between Common Triads of Scale 2285. Created by Ian Ring ©2019 G D#+->G D#+->B bm bm G->bm b°->bm bm->B

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.

Diameter4
Radius2
Self-Centeredno
Central VerticesB
Peripheral Verticescm, b°

Modes

Modes are the rotational transformation of this scale. Scale 2285 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1595
Scale 1595: Dacrian, Ian Ring Music TheoryDacrian
3rd mode:
Scale 2845
Scale 2845: Baptian, Ian Ring Music TheoryBaptian
4th mode:
Scale 1735
Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam
5th mode:
Scale 2915
Scale 2915: Aeolydian, Ian Ring Music TheoryAeolydian
6th mode:
Scale 3505
Scale 3505: Stygian, Ian Ring Music TheoryStygian
7th mode:
Scale 475
Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian

Prime

The prime form of this scale is Scale 439

Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian

Complement

The heptatonic modal family [2285, 1595, 2845, 1735, 2915, 3505, 475] (Forte: 7-Z38) is the complement of the pentatonic modal family [295, 625, 905, 2195, 3145] (Forte: 5-Z38)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2285 is 1763

Scale 1763Scale 1763: Katalian, Ian Ring Music TheoryKatalian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2285 is chiral, and its enantiomorph is scale 1763

Scale 1763Scale 1763: Katalian, Ian Ring Music TheoryKatalian

Transformations:

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> 2285       T0I <11,0> 1763
T1 <1,1> 475      T1I <11,1> 3526
T2 <1,2> 950      T2I <11,2> 2957
T3 <1,3> 1900      T3I <11,3> 1819
T4 <1,4> 3800      T4I <11,4> 3638
T5 <1,5> 3505      T5I <11,5> 3181
T6 <1,6> 2915      T6I <11,6> 2267
T7 <1,7> 1735      T7I <11,7> 439
T8 <1,8> 3470      T8I <11,8> 878
T9 <1,9> 2845      T9I <11,9> 1756
T10 <1,10> 1595      T10I <11,10> 3512
T11 <1,11> 3190      T11I <11,11> 2929
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3275      T0MI <7,0> 2663
T1M <5,1> 2455      T1MI <7,1> 1231
T2M <5,2> 815      T2MI <7,2> 2462
T3M <5,3> 1630      T3MI <7,3> 829
T4M <5,4> 3260      T4MI <7,4> 1658
T5M <5,5> 2425      T5MI <7,5> 3316
T6M <5,6> 755      T6MI <7,6> 2537
T7M <5,7> 1510      T7MI <7,7> 979
T8M <5,8> 3020      T8MI <7,8> 1958
T9M <5,9> 1945      T9MI <7,9> 3916
T10M <5,10> 3890      T10MI <7,10> 3737
T11M <5,11> 3685      T11MI <7,11> 3379

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 2287Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic
Scale 2281Scale 2281: Rathimic, Ian Ring Music TheoryRathimic
Scale 2283Scale 2283: Aeolyptian, Ian Ring Music TheoryAeolyptian
Scale 2277Scale 2277: Kagimic, Ian Ring Music TheoryKagimic
Scale 2293Scale 2293: Gorian, Ian Ring Music TheoryGorian
Scale 2301Scale 2301: Bydyllic, Ian Ring Music TheoryBydyllic
Scale 2253Scale 2253: Raga Amarasenapriya, Ian Ring Music TheoryRaga Amarasenapriya
Scale 2269Scale 2269: Pygian, Ian Ring Music TheoryPygian
Scale 2221Scale 2221: Raga Sindhura Kafi, Ian Ring Music TheoryRaga Sindhura Kafi
Scale 2157Scale 2157: Nexian, Ian Ring Music TheoryNexian
Scale 2413Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
Scale 2541Scale 2541: Algerian, Ian Ring Music TheoryAlgerian
Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
Scale 3309Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
Scale 237Scale 237: Bijian, Ian Ring Music TheoryBijian
Scale 1261Scale 1261: Modified Blues, Ian Ring Music TheoryModified Blues

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 (http://allthescales.org) 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.