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Scale 2733: "Melodic Minor Ascending"

Scale 2733: Melodic Minor Ascending, 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

Western
Melodic Minor Ascending
Melodic Minor
Unknown / Unsorted
Heptatonia Seconda
Velavali
Deshi(2)
Jazz and Blues
Jazz Minor
Western Mixed
Minor-Major
Carnatic
Mela Gaurimanohari
Raga Patdip
Schenkerian
Mischung 1
Exoticisms
Hawaiian
Zeitler
Bocrian
Dozenal
Melian
Carnatic Melakarta
Gourimanohari
Carnatic Numbered Melakarta
23rd Melakarta raga

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,3,5,7,9,11}

Forte Number

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

7-34

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.

[1]

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.

6

Prime Form

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

no
prime: 1371

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, 1, 2, 2, 2, 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.

<2, 5, 4, 4, 4, 2>

Interval Spectrum

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

p4m4n4s5d2t2

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

Spectra Variation

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

1.143

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.

yes

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.

2.665

Polygon Perimeter

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

6.035

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.

[2]

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, 10, 72)

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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 TriadsF{5,9,0}231.71
G{7,11,2}231.71
Minor Triadscm{0,3,7}231.71
dm{2,5,9}231.71
Augmented TriadsD♯+{3,7,11}231.71
Diminished Triads{9,0,3}231.71
{11,2,5}231.71
Parsimonious Voice Leading Between Common Triads of Scale 2733. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ cm->a° dm dm F F dm->F dm->b° Parsimonious Voice Leading Between Common Triads of Scale 2733. Created by Ian Ring ©2019 G D#+->G F->a° G->b°

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

Modes

Modes are the rotational transformation of this scale. Scale 2733 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1707
Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
3rd mode:
Scale 2901
Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented
4th mode:
Scale 1749
Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
5th mode:
Scale 1461
Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
6th mode:
Scale 1389
Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
7th mode:
Scale 1371
Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrianThis is the prime mode

Prime

The prime form of this scale is Scale 1371

Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian

Complement

The heptatonic modal family [2733, 1707, 2901, 1749, 1461, 1389, 1371] (Forte: 7-34) is the complement of the pentatonic modal family [597, 681, 1173, 1317, 1353] (Forte: 5-34)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2733 is 1707

Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2

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> 2733       T0I <11,0> 1707
T1 <1,1> 1371      T1I <11,1> 3414
T2 <1,2> 2742      T2I <11,2> 2733
T3 <1,3> 1389      T3I <11,3> 1371
T4 <1,4> 2778      T4I <11,4> 2742
T5 <1,5> 1461      T5I <11,5> 1389
T6 <1,6> 2922      T6I <11,6> 2778
T7 <1,7> 1749      T7I <11,7> 1461
T8 <1,8> 3498      T8I <11,8> 2922
T9 <1,9> 2901      T9I <11,9> 1749
T10 <1,10> 1707      T10I <11,10> 3498
T11 <1,11> 3414      T11I <11,11> 2901
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3723      T0MI <7,0> 2607
T1M <5,1> 3351      T1MI <7,1> 1119
T2M <5,2> 2607      T2MI <7,2> 2238
T3M <5,3> 1119      T3MI <7,3> 381
T4M <5,4> 2238      T4MI <7,4> 762
T5M <5,5> 381      T5MI <7,5> 1524
T6M <5,6> 762      T6MI <7,6> 3048
T7M <5,7> 1524      T7MI <7,7> 2001
T8M <5,8> 3048      T8MI <7,8> 4002
T9M <5,9> 2001      T9MI <7,9> 3909
T10M <5,10> 4002      T10MI <7,10> 3723
T11M <5,11> 3909      T11MI <7,11> 3351

The transformations that map this set to itself are: T0, T2I

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 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
Scale 2729Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
Scale 2731Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor
Scale 2749Scale 2749: Katagyllic, Ian Ring Music TheoryKatagyllic
Scale 2701Scale 2701: Hawaiian, Ian Ring Music TheoryHawaiian
Scale 2717Scale 2717: Epygian, Ian Ring Music TheoryEpygian
Scale 2765Scale 2765: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
Scale 2605Scale 2605: Rylimic, Ian Ring Music TheoryRylimic
Scale 2669Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode
Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 2221Scale 2221: Raga Sindhura Kafi, Ian Ring Music TheoryRaga Sindhura Kafi
Scale 2477Scale 2477: Harmonic Minor, Ian Ring Music TheoryHarmonic Minor
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala
Scale 1709Scale 1709: Dorian, Ian Ring Music TheoryDorian

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.