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Scale 437: "Ronimic"

Scale 437: Ronimic, 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
Ronimic
Dozenal
Cobian

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

{0,2,4,5,7,8}

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-Z24

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: 1457

Hemitonia

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

2 (dihemitonic)

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.

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: 347

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, 2, 1, 2, 1, 4]

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.

p3m3n3s3d2t

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

Spectra Variation

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

2.667

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.

2.232

Polygon Perimeter

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

5.767

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.

(14, 11, 59)

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 TriadsC{0,4,7}131.5
Minor Triadsfm{5,8,0}221
Augmented TriadsC+{0,4,8}221
Diminished Triads{2,5,8}131.5
Parsimonious Voice Leading Between Common Triads of Scale 437. Created by Ian Ring ©2019 C C C+ C+ C->C+ fm fm C+->fm d°->fm

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+, fm
Peripheral VerticesC, d°

Triad Polychords

Also known as Bi-Triadic Hexatonics (a term coined by mDecks), and related to Generic Modality Compression (a method for guitar by Mick Goodrick and Tim Miller), these are two common triads that when combined use all the tones in this scale.

There is 1 way that this hexatonic scale can be split into two common triads.


Major: {0, 4, 7}
Diminished: {2, 5, 8}

Modes

Modes are the rotational transformation of this scale. Scale 437 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1133
Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
3rd mode:
Scale 1307
Scale 1307: Katorimic, Ian Ring Music TheoryKatorimic
4th mode:
Scale 2701
Scale 2701: Hawaiian, Ian Ring Music TheoryHawaiian
5th mode:
Scale 1699
Scale 1699: Raga Rasavali, Ian Ring Music TheoryRaga Rasavali
6th mode:
Scale 2897
Scale 2897: Rycrimic, Ian Ring Music TheoryRycrimic

Prime

The prime form of this scale is Scale 347

Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic

Complement

The hexatonic modal family [437, 1133, 1307, 2701, 1699, 2897] (Forte: 6-Z24) is the complement of the hexatonic modal family [599, 697, 1481, 1829, 2347, 3221] (Forte: 6-Z46)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 437 is 1457

Scale 1457Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 437 is chiral, and its enantiomorph is scale 1457

Scale 1457Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari

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> 437       T0I <11,0> 1457
T1 <1,1> 874      T1I <11,1> 2914
T2 <1,2> 1748      T2I <11,2> 1733
T3 <1,3> 3496      T3I <11,3> 3466
T4 <1,4> 2897      T4I <11,4> 2837
T5 <1,5> 1699      T5I <11,5> 1579
T6 <1,6> 3398      T6I <11,6> 3158
T7 <1,7> 2701      T7I <11,7> 2221
T8 <1,8> 1307      T8I <11,8> 347
T9 <1,9> 2614      T9I <11,9> 694
T10 <1,10> 1133      T10I <11,10> 1388
T11 <1,11> 2266      T11I <11,11> 2776
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3347      T0MI <7,0> 2327
T1M <5,1> 2599      T1MI <7,1> 559
T2M <5,2> 1103      T2MI <7,2> 1118
T3M <5,3> 2206      T3MI <7,3> 2236
T4M <5,4> 317      T4MI <7,4> 377
T5M <5,5> 634      T5MI <7,5> 754
T6M <5,6> 1268      T6MI <7,6> 1508
T7M <5,7> 2536      T7MI <7,7> 3016
T8M <5,8> 977      T8MI <7,8> 1937
T9M <5,9> 1954      T9MI <7,9> 3874
T10M <5,10> 3908      T10MI <7,10> 3653
T11M <5,11> 3721      T11MI <7,11> 3211

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 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 433Scale 433: Raga Zilaf, Ian Ring Music TheoryRaga Zilaf
Scale 435Scale 435: Raga Purna Pancama, Ian Ring Music TheoryRaga Purna Pancama
Scale 441Scale 441: Thycrimic, Ian Ring Music TheoryThycrimic
Scale 445Scale 445: Gocrian, Ian Ring Music TheoryGocrian
Scale 421Scale 421: Han-kumoi, Ian Ring Music TheoryHan-kumoi
Scale 429Scale 429: Koptimic, Ian Ring Music TheoryKoptimic
Scale 405Scale 405: Raga Bhupeshwari, Ian Ring Music TheoryRaga Bhupeshwari
Scale 469Scale 469: Katyrimic, Ian Ring Music TheoryKatyrimic
Scale 501Scale 501: Katylian, Ian Ring Music TheoryKatylian
Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 373Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
Scale 181Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari
Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord
Scale 949Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
Scale 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major

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.