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Scale 1461: "Major-Minor"

Scale 1461: Major-Minor, Ian Ring Music Theory

Identical to Aeolian but for its raised third; this is named Aeolian Dominant because its 1-3-5-7 members form a dominant seventh chord.


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 Mixed
Major-Minor
Western
Aeolian Dominant
Western Modern
Melodic Major
Schenkerian
Mischung 6
Western Altered
Mixolydian Flat 6
Mixolydian Flat 13
Altered Mixolydian
Carnatic
Mela Carukesi
Raga Charukeshi
Tarangini
Exoticisms
Hindu
Hindustan
Zeitler
Stydian
Dozenal
Jusian
Carnatic Melakarta
Charukesi
Carnatic Numbered Melakarta
26th 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

{0,2,4,5,7,8,10}

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.

[0]

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

yes

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, 2, 1, 2, 1, 2, 2]

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.

[0]

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 TriadsC{0,4,7}231.71
A♯{10,2,5}231.71
Minor Triadsfm{5,8,0}231.71
gm{7,10,2}231.71
Augmented TriadsC+{0,4,8}231.71
Diminished Triads{2,5,8}231.71
{4,7,10}231.71
Parsimonious Voice Leading Between Common Triads of Scale 1461. Created by Ian Ring ©2019 C C C+ C+ C->C+ C->e° fm fm C+->fm d°->fm A# A# d°->A# gm gm e°->gm gm->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

Modes

Modes are the rotational transformation of this scale. Scale 1461 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1389
Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
3rd mode:
Scale 1371
Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrianThis is the prime mode
4th mode:
Scale 2733
Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
5th mode:
Scale 1707
Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
6th mode:
Scale 2901
Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented
7th mode:
Scale 1749
Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic

Prime

The prime form of this scale is Scale 1371

Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian

Complement

The heptatonic modal family [1461, 1389, 1371, 2733, 1707, 2901, 1749] (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 1461 is itself, because it is a palindromic scale!

Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor

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

The transformations that map this set to itself are: T0, T0I

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 1463Scale 1463: Ugrian, Ian Ring Music TheoryUgrian
Scale 1457Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari
Scale 1459Scale 1459: Phrygian Dominant, Ian Ring Music TheoryPhrygian Dominant
Scale 1465Scale 1465: Mela Ragavardhani, Ian Ring Music TheoryMela Ragavardhani
Scale 1469Scale 1469: Epiryllic, Ian Ring Music TheoryEpiryllic
Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari
Scale 1453Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
Scale 1429Scale 1429: Bythimic, Ian Ring Music TheoryBythimic
Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
Scale 1525Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic
Scale 1397Scale 1397: Major Locrian, Ian Ring Music TheoryMajor Locrian
Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
Scale 437Scale 437: Ronimic, Ian Ring Music TheoryRonimic
Scale 949Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani
Scale 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major
Scale 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic

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.