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Scale 49: "Aguian"

Scale 49: Aguian, 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

Dozenal
Aguian

Analysis

Cardinality

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

3 (tritonic)

Pitch Class Set

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

{0,4,5}

Forte Number

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

3-4

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: 385

Hemitonia

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

1 (unhemitonic)

Cohemitonia

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

0 (ancohemitonic)

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.

2

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.

2

Prime Form

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

no
prime: 35

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.

[4, 1, 7]

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, 0, 1, 1, 0>

Interval Spectrum

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

pmd

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

Spectra Variation

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

4

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.

0.433

Polygon Perimeter

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

4.182

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.

(1, 0, 6)

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 49 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 259
Scale 259: Gijian, Ian Ring Music TheoryGijian
3rd mode:
Scale 2177
Scale 2177: Major Seventh Omit 3, Ian Ring Music TheoryMajor Seventh Omit 3

Prime

The prime form of this scale is Scale 35

Scale 35Scale 35: Abbian, Ian Ring Music TheoryAbbian

Complement

The tritonic modal family [49, 259, 2177] (Forte: 3-4) is the complement of the enneatonic modal family [959, 2023, 2527, 3059, 3311, 3577, 3703, 3899, 3997] (Forte: 9-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 49 is 385

Scale 385Scale 385: Civian, Ian Ring Music TheoryCivian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 49 is chiral, and its enantiomorph is scale 385

Scale 385Scale 385: Civian, Ian Ring Music TheoryCivian

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> 49       T0I <11,0> 385
T1 <1,1> 98      T1I <11,1> 770
T2 <1,2> 196      T2I <11,2> 1540
T3 <1,3> 392      T3I <11,3> 3080
T4 <1,4> 784      T4I <11,4> 2065
T5 <1,5> 1568      T5I <11,5> 35
T6 <1,6> 3136      T6I <11,6> 70
T7 <1,7> 2177      T7I <11,7> 140
T8 <1,8> 259      T8I <11,8> 280
T9 <1,9> 518      T9I <11,9> 560
T10 <1,10> 1036      T10I <11,10> 1120
T11 <1,11> 2072      T11I <11,11> 2240
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 259      T0MI <7,0> 2065
T1M <5,1> 518      T1MI <7,1> 35
T2M <5,2> 1036      T2MI <7,2> 70
T3M <5,3> 2072      T3MI <7,3> 140
T4M <5,4> 49       T4MI <7,4> 280
T5M <5,5> 98      T5MI <7,5> 560
T6M <5,6> 196      T6MI <7,6> 1120
T7M <5,7> 392      T7MI <7,7> 2240
T8M <5,8> 784      T8MI <7,8> 385
T9M <5,9> 1568      T9MI <7,9> 770
T10M <5,10> 3136      T10MI <7,10> 1540
T11M <5,11> 2177      T11MI <7,11> 3080

The transformations that map this set to itself are: T0, T4M

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 51Scale 51: Arfian, Ian Ring Music TheoryArfian
Scale 53Scale 53: Absian, Ian Ring Music TheoryAbsian
Scale 57Scale 57: Ahoian, Ian Ring Music TheoryAhoian
Scale 33Scale 33: Honchoshi, Ian Ring Music TheoryHonchoshi
Scale 41Scale 41: Vietnamese Tritonic, Ian Ring Music TheoryVietnamese Tritonic
Scale 17Scale 17: Major Third Ditone, Ian Ring Music TheoryMajor Third Ditone
Scale 81Scale 81: Disian, Ian Ring Music TheoryDisian
Scale 113Scale 113, Ian Ring Music Theory
Scale 177Scale 177: Bexian, Ian Ring Music TheoryBexian
Scale 305Scale 305: Gonic, Ian Ring Music TheoryGonic
Scale 561Scale 561: Phratic, Ian Ring Music TheoryPhratic
Scale 1073Scale 1073: Gosian, Ian Ring Music TheoryGosian
Scale 2097Scale 2097: Munian, Ian Ring Music TheoryMunian

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.