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Scale 3363: "Rogimic"

Scale 3363: Rogimic, 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
Rogimic
Dozenal
Vavian

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

{0,1,5,8,10,11}

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-Z40

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: 2199

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.

2 (dicohemitonic)

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: 303

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, 4, 3, 2, 1, 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, 3, 3, 2, 3, 1>

Interval Spectrum

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

p3m2n3s3d3t

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

3.667

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.

2.116

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.

(29, 16, 64)

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♯{1,5,8}221
Minor Triadsfm{5,8,0}221
a♯m{10,1,5}131.5
Diminished Triads{5,8,11}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3363. Created by Ian Ring ©2019 C# C# fm fm C#->fm a#m a#m C#->a#m f°->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 Verticesf°, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3363 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3729
Scale 3729: Starimic, Ian Ring Music TheoryStarimic
3rd mode:
Scale 489
Scale 489: Phrathimic, Ian Ring Music TheoryPhrathimic
4th mode:
Scale 573
Scale 573: Saptimic, Ian Ring Music TheorySaptimic
5th mode:
Scale 1167
Scale 1167: Aerodimic, Ian Ring Music TheoryAerodimic
6th mode:
Scale 2631
Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic

Prime

The prime form of this scale is Scale 303

Scale 303Scale 303: Golimic, Ian Ring Music TheoryGolimic

Complement

The hexatonic modal family [3363, 3729, 489, 573, 1167, 2631] (Forte: 6-Z40) is the complement of the hexatonic modal family [183, 1761, 1803, 2139, 2949, 3117] (Forte: 6-Z11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3363 is 2199

Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3363 is chiral, and its enantiomorph is scale 2199

Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic

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> 3363       T0I <11,0> 2199
T1 <1,1> 2631      T1I <11,1> 303
T2 <1,2> 1167      T2I <11,2> 606
T3 <1,3> 2334      T3I <11,3> 1212
T4 <1,4> 573      T4I <11,4> 2424
T5 <1,5> 1146      T5I <11,5> 753
T6 <1,6> 2292      T6I <11,6> 1506
T7 <1,7> 489      T7I <11,7> 3012
T8 <1,8> 978      T8I <11,8> 1929
T9 <1,9> 1956      T9I <11,9> 3858
T10 <1,10> 3912      T10I <11,10> 3621
T11 <1,11> 3729      T11I <11,11> 3147
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 183      T0MI <7,0> 3489
T1M <5,1> 366      T1MI <7,1> 2883
T2M <5,2> 732      T2MI <7,2> 1671
T3M <5,3> 1464      T3MI <7,3> 3342
T4M <5,4> 2928      T4MI <7,4> 2589
T5M <5,5> 1761      T5MI <7,5> 1083
T6M <5,6> 3522      T6MI <7,6> 2166
T7M <5,7> 2949      T7MI <7,7> 237
T8M <5,8> 1803      T8MI <7,8> 474
T9M <5,9> 3606      T9MI <7,9> 948
T10M <5,10> 3117      T10MI <7,10> 1896
T11M <5,11> 2139      T11MI <7,11> 3792

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 3361Scale 3361: Vatian, Ian Ring Music TheoryVatian
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 3371Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
Scale 3379Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
Scale 3331Scale 3331: Vabian, Ian Ring Music TheoryVabian
Scale 3347Scale 3347: Synimic, Ian Ring Music TheorySynimic
Scale 3395Scale 3395: Vepian, Ian Ring Music TheoryVepian
Scale 3427Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 3107Scale 3107: Tician, Ian Ring Music TheoryTician
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 2339Scale 2339: Raga Kshanika, Ian Ring Music TheoryRaga Kshanika
Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
Scale 1315Scale 1315: Pyritonic, Ian Ring Music TheoryPyritonic

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.