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Scale 843: "Molimic"

Scale 843: Molimic, 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
Molimic
Dozenal
Fehian

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

{0,1,3,6,8,9}

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-Z29

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.

[4.5]

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.

no

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: 717

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, 2, 3, 2, 1, 3]

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, 2, 4, 2, 3, 2>

Interval Spectrum

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

p3m2n4s2d2t2

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}
<2> = {3,4,5}
<3> = {5,6,7}
<4> = {7,8,9}
<5> = {9,10,11}

Spectra Variation

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

1.667

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.

2.366

Polygon Perimeter

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

5.864

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.

[9]

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".

Proper

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.

(0, 12, 57)

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♯{8,0,3}231.5
Minor Triadsf♯m{6,9,1}231.5
Diminished Triads{0,3,6}231.5
d♯°{3,6,9}231.5
f♯°{6,9,0}231.5
{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 843. Created by Ian Ring ©2019 d#° d#° c°->d#° G# G# c°->G# f#m f#m d#°->f#m f#° f#° f#°->f#m f#°->a° G#->a°

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
Radius3
Self-Centeredyes

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.


Minor: {6, 9, 1}
Major: {8, 0, 3}

Modes

Modes are the rotational transformation of this scale. Scale 843 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2469
Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
3rd mode:
Scale 1641
Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic
4th mode:
Scale 717
Scale 717: Raga Vijayanagari, Ian Ring Music TheoryRaga VijayanagariThis is the prime mode
5th mode:
Scale 1203
Scale 1203: Pagimic, Ian Ring Music TheoryPagimic
6th mode:
Scale 2649
Scale 2649: Aeolythimic, Ian Ring Music TheoryAeolythimic

Prime

The prime form of this scale is Scale 717

Scale 717Scale 717: Raga Vijayanagari, Ian Ring Music TheoryRaga Vijayanagari

Complement

The hexatonic modal family [843, 2469, 1641, 717, 1203, 2649] (Forte: 6-Z29) is the complement of the hexatonic modal family [723, 813, 1227, 1689, 2409, 2661] (Forte: 6-Z50)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 843 is 2649

Scale 2649Scale 2649: Aeolythimic, Ian Ring Music TheoryAeolythimic

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> 843       T0I <11,0> 2649
T1 <1,1> 1686      T1I <11,1> 1203
T2 <1,2> 3372      T2I <11,2> 2406
T3 <1,3> 2649      T3I <11,3> 717
T4 <1,4> 1203      T4I <11,4> 1434
T5 <1,5> 2406      T5I <11,5> 2868
T6 <1,6> 717      T6I <11,6> 1641
T7 <1,7> 1434      T7I <11,7> 3282
T8 <1,8> 2868      T8I <11,8> 2469
T9 <1,9> 1641      T9I <11,9> 843
T10 <1,10> 3282      T10I <11,10> 1686
T11 <1,11> 2469      T11I <11,11> 3372
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 633      T0MI <7,0> 969
T1M <5,1> 1266      T1MI <7,1> 1938
T2M <5,2> 2532      T2MI <7,2> 3876
T3M <5,3> 969      T3MI <7,3> 3657
T4M <5,4> 1938      T4MI <7,4> 3219
T5M <5,5> 3876      T5MI <7,5> 2343
T6M <5,6> 3657      T6MI <7,6> 591
T7M <5,7> 3219      T7MI <7,7> 1182
T8M <5,8> 2343      T8MI <7,8> 2364
T9M <5,9> 591      T9MI <7,9> 633
T10M <5,10> 1182      T10MI <7,10> 1266
T11M <5,11> 2364      T11MI <7,11> 2532

The transformations that map this set to itself are: T0, T9I

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 841Scale 841: Phrothitonic, Ian Ring Music TheoryPhrothitonic
Scale 845Scale 845: Raga Neelangi, Ian Ring Music TheoryRaga Neelangi
Scale 847Scale 847: Ganian, Ian Ring Music TheoryGanian
Scale 835Scale 835: Fecian, Ian Ring Music TheoryFecian
Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 851Scale 851: Raga Hejjajji, Ian Ring Music TheoryRaga Hejjajji
Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian
Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
Scale 779Scale 779: Etrian, Ian Ring Music TheoryEtrian
Scale 811Scale 811: Radimic, Ian Ring Music TheoryRadimic
Scale 907Scale 907: Tholimic, Ian Ring Music TheoryTholimic
Scale 971Scale 971: Mela Gavambodhi, Ian Ring Music TheoryMela Gavambodhi
Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic
Scale 715Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi
Scale 1355Scale 1355: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 1867Scale 1867: Solian, Ian Ring Music TheorySolian
Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian

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.