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Scale 2421: "Malian"

Scale 2421: Malian, 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

41161837294116105072918310504116183
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
Malian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,4,5,6,8,11}
Forte Number7-28
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1491
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes6
Prime?no
prime: 747
Deep Scaleno
Interval Vector344433
Interval Spectrump3m4n4s4d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsE{4,8,11}331.63
Minor Triadsfm{5,8,0}331.63
bm{11,2,6}231.88
Augmented TriadsC+{0,4,8}231.75
Diminished Triads{2,5,8}231.75
{5,8,11}231.75
g♯°{8,11,2}231.75
{11,2,5}231.88
Parsimonious Voice Leading Between Common Triads of Scale 2421. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm d°->fm d°->b° E->f° g#° g#° E->g#° f°->fm bm bm g#°->bm b°->bm

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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 2421 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1629
Scale 1629: Synian, Ian Ring Music TheorySynian
3rd mode:
Scale 1431
Scale 1431: Phragian, Ian Ring Music TheoryPhragian
4th mode:
Scale 2763
Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
5th mode:
Scale 3429
Scale 3429: Marian, Ian Ring Music TheoryMarian
6th mode:
Scale 1881
Scale 1881: Katorian, Ian Ring Music TheoryKatorian
7th mode:
Scale 747
Scale 747: Lynian, Ian Ring Music TheoryLynianThis is the prime mode

Prime

The prime form of this scale is Scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Complement

The heptatonic modal family [2421, 1629, 1431, 2763, 3429, 1881, 747] (Forte: 7-28) is the complement of the pentatonic modal family [333, 837, 1107, 1233, 2601] (Forte: 5-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2421 is 1491

Scale 1491Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2421 is chiral, and its enantiomorph is scale 1491

Scale 1491Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani

Transformations:

T0 2421  T0I 1491
T1 747  T1I 2982
T2 1494  T2I 1869
T3 2988  T3I 3738
T4 1881  T4I 3381
T5 3762  T5I 2667
T6 3429  T6I 1239
T7 2763  T7I 2478
T8 1431  T8I 861
T9 2862  T9I 1722
T10 1629  T10I 3444
T11 3258  T11I 2793

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 2423Scale 2423, Ian Ring Music Theory
Scale 2417Scale 2417: Kanimic, Ian Ring Music TheoryKanimic
Scale 2419Scale 2419: Raga Lalita, Ian Ring Music TheoryRaga Lalita
Scale 2425Scale 2425: Rorian, Ian Ring Music TheoryRorian
Scale 2429Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
Scale 2405Scale 2405: Katalimic, Ian Ring Music TheoryKatalimic
Scale 2413Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
Scale 2389Scale 2389: Eskimo Hexatonic 2, Ian Ring Music TheoryEskimo Hexatonic 2
Scale 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
Scale 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major
Scale 2549Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
Scale 2165Scale 2165, Ian Ring Music Theory
Scale 2293Scale 2293: Gorian, Ian Ring Music TheoryGorian
Scale 2677Scale 2677: Thodian, Ian Ring Music TheoryThodian
Scale 2933Scale 2933, Ian Ring Music Theory
Scale 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse
Scale 373Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
Scale 1397Scale 1397: Major Locrian, Ian Ring Music TheoryMajor Locrian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. 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.