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Scale 2835: "Ionygimic"

Scale 2835: Ionygimic, 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
Ionygimic
Dozenal
Rusian

Analysis

Cardinality

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

{0,1,4,8,9,11}

Forte Number

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

6-14

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: 2331

Hemitonia

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

3 (trihemitonic)

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.

5

Prime Form

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

no
prime: 315

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.

[1, 3, 4, 1, 2, 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.

<3, 2, 3, 4, 3, 0>

Interval Spectrum

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

p3m4n3s2d3

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

Spectra Variation

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

3.333

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.

2.116

Polygon Perimeter

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

5.699

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.

(19, 22, 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 TriadsE{4,8,11}131.6
A{9,1,4}231.4
Minor Triadsc♯m{1,4,8}221.2
am{9,0,4}221.2
Augmented TriadsC+{0,4,8}321
Parsimonious Voice Leading Between Common Triads of Scale 2835. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E am am C+->am A A c#m->A am->A

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.

Diameter3
Radius2
Self-Centeredno
Central VerticesC+, c♯m, am
Peripheral VerticesE, A

Modes

Modes are the rotational transformation of this scale. Scale 2835 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3465
Scale 3465: Katathimic, Ian Ring Music TheoryKatathimic
3rd mode:
Scale 945
Scale 945: Raga Saravati, Ian Ring Music TheoryRaga Saravati
4th mode:
Scale 315
Scale 315: Stodimic, Ian Ring Music TheoryStodimicThis is the prime mode
5th mode:
Scale 2205
Scale 2205: Ionocrimic, Ian Ring Music TheoryIonocrimic
6th mode:
Scale 1575
Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic

Prime

The prime form of this scale is Scale 315

Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic

Complement

The hexatonic modal family [2835, 3465, 945, 315, 2205, 1575] (Forte: 6-14) is the complement of the hexatonic modal family [315, 945, 1575, 2205, 2835, 3465] (Forte: 6-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2835 is 2331

Scale 2331Scale 2331: Dylimic, Ian Ring Music TheoryDylimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2835 is chiral, and its enantiomorph is scale 2331

Scale 2331Scale 2331: Dylimic, Ian Ring Music TheoryDylimic

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> 2835       T0I <11,0> 2331
T1 <1,1> 1575      T1I <11,1> 567
T2 <1,2> 3150      T2I <11,2> 1134
T3 <1,3> 2205      T3I <11,3> 2268
T4 <1,4> 315      T4I <11,4> 441
T5 <1,5> 630      T5I <11,5> 882
T6 <1,6> 1260      T6I <11,6> 1764
T7 <1,7> 2520      T7I <11,7> 3528
T8 <1,8> 945      T8I <11,8> 2961
T9 <1,9> 1890      T9I <11,9> 1827
T10 <1,10> 3780      T10I <11,10> 3654
T11 <1,11> 3465      T11I <11,11> 3213
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 945      T0MI <7,0> 441
T1M <5,1> 1890      T1MI <7,1> 882
T2M <5,2> 3780      T2MI <7,2> 1764
T3M <5,3> 3465      T3MI <7,3> 3528
T4M <5,4> 2835       T4MI <7,4> 2961
T5M <5,5> 1575      T5MI <7,5> 1827
T6M <5,6> 3150      T6MI <7,6> 3654
T7M <5,7> 2205      T7MI <7,7> 3213
T8M <5,8> 315      T8MI <7,8> 2331
T9M <5,9> 630      T9MI <7,9> 567
T10M <5,10> 1260      T10MI <7,10> 1134
T11M <5,11> 2520      T11MI <7,11> 2268

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 2833Scale 2833: Dolitonic, Ian Ring Music TheoryDolitonic
Scale 2837Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
Scale 2839Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
Scale 2843Scale 2843: Sorian, Ian Ring Music TheorySorian
Scale 2819Scale 2819: Rujian, Ian Ring Music TheoryRujian
Scale 2827Scale 2827: Runian, Ian Ring Music TheoryRunian
Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
Scale 2867Scale 2867: Socrian, Ian Ring Music TheorySocrian
Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian
Scale 2963Scale 2963: Bygian, Ian Ring Music TheoryBygian
Scale 2579Scale 2579: Pupian, Ian Ring Music TheoryPupian
Scale 2707Scale 2707: Banimic, Ian Ring Music TheoryBanimic
Scale 2323Scale 2323: Doptitonic, Ian Ring Music TheoryDoptitonic
Scale 3347Scale 3347: Synimic, Ian Ring Music TheorySynimic
Scale 3859Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
Scale 787Scale 787: Aeolapritonic, Ian Ring Music TheoryAeolapritonic
Scale 1811Scale 1811: Kyptimic, Ian Ring Music TheoryKyptimic

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.