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Scale 2501: "Ralimic"

Scale 2501: Ralimic, 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
Ralimic
Dozenal
Pisian

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

{0,2,6,7,8,11}

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-Z43

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: 1139

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: 359

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

Interval Spectrum

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

p3m3n2s2d3t2

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

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.

2.116

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.

(10, 17, 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 TriadsG{7,11,2}210.67
Minor Triadsbm{11,2,6}121
Diminished Triadsg♯°{8,11,2}121

The following pitch classes are not present in any of the common triads: {0}

Parsimonious Voice Leading Between Common Triads of Scale 2501. Created by Ian Ring ©2019 Parsimonious Voice Leading Between Common Triads of Scale 2501. Created by Ian Ring ©2019 G g#° g#° G->g#° bm bm G->bm

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.

Diameter2
Radius1
Self-Centeredno
Central VerticesG
Peripheral Verticesg♯°, bm

Modes

Modes are the rotational transformation of this scale. Scale 2501 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1649
Scale 1649: Bolimic, Ian Ring Music TheoryBolimic
3rd mode:
Scale 359
Scale 359: Bothimic, Ian Ring Music TheoryBothimicThis is the prime mode
4th mode:
Scale 2227
Scale 2227: Raga Gaula, Ian Ring Music TheoryRaga Gaula
5th mode:
Scale 3161
Scale 3161: Kodimic, Ian Ring Music TheoryKodimic
6th mode:
Scale 907
Scale 907: Tholimic, Ian Ring Music TheoryTholimic

Prime

The prime form of this scale is Scale 359

Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic

Complement

The hexatonic modal family [2501, 1649, 359, 2227, 3161, 907] (Forte: 6-Z43) is the complement of the hexatonic modal family [407, 739, 1817, 2251, 2417, 3173] (Forte: 6-Z17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2501 is 1139

Scale 1139Scale 1139: Aerygimic, Ian Ring Music TheoryAerygimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2501 is chiral, and its enantiomorph is scale 1139

Scale 1139Scale 1139: Aerygimic, Ian Ring Music TheoryAerygimic

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> 2501       T0I <11,0> 1139
T1 <1,1> 907      T1I <11,1> 2278
T2 <1,2> 1814      T2I <11,2> 461
T3 <1,3> 3628      T3I <11,3> 922
T4 <1,4> 3161      T4I <11,4> 1844
T5 <1,5> 2227      T5I <11,5> 3688
T6 <1,6> 359      T6I <11,6> 3281
T7 <1,7> 718      T7I <11,7> 2467
T8 <1,8> 1436      T8I <11,8> 839
T9 <1,9> 2872      T9I <11,9> 1678
T10 <1,10> 1649      T10I <11,10> 3356
T11 <1,11> 3298      T11I <11,11> 2617
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3281      T0MI <7,0> 359
T1M <5,1> 2467      T1MI <7,1> 718
T2M <5,2> 839      T2MI <7,2> 1436
T3M <5,3> 1678      T3MI <7,3> 2872
T4M <5,4> 3356      T4MI <7,4> 1649
T5M <5,5> 2617      T5MI <7,5> 3298
T6M <5,6> 1139      T6MI <7,6> 2501
T7M <5,7> 2278      T7MI <7,7> 907
T8M <5,8> 461      T8MI <7,8> 1814
T9M <5,9> 922      T9MI <7,9> 3628
T10M <5,10> 1844      T10MI <7,10> 3161
T11M <5,11> 3688      T11MI <7,11> 2227

The transformations that map this set to itself are: T0, T6MI

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 2503Scale 2503: Mela Jhalavarali, Ian Ring Music TheoryMela Jhalavarali
Scale 2497Scale 2497: Peqian, Ian Ring Music TheoryPeqian
Scale 2499Scale 2499: Pirian, Ian Ring Music TheoryPirian
Scale 2505Scale 2505: Mydimic, Ian Ring Music TheoryMydimic
Scale 2509Scale 2509: Double Harmonic Minor, Ian Ring Music TheoryDouble Harmonic Minor
Scale 2517Scale 2517: Harmonic Lydian, Ian Ring Music TheoryHarmonic Lydian
Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian
Scale 2437Scale 2437: Pafian, Ian Ring Music TheoryPafian
Scale 2469Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
Scale 2373Scale 2373: Dyptitonic, Ian Ring Music TheoryDyptitonic
Scale 2245Scale 2245: Raga Vaijayanti, Ian Ring Music TheoryRaga Vaijayanti
Scale 2757Scale 2757: Raga Nishadi, Ian Ring Music TheoryRaga Nishadi
Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian
Scale 3525Scale 3525: Zocrian, Ian Ring Music TheoryZocrian
Scale 453Scale 453: Raditonic, Ian Ring Music TheoryRaditonic
Scale 1477Scale 1477: Raga Jaganmohanam, Ian Ring Music TheoryRaga Jaganmohanam

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.