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Scale 1321: "Blues Minor"

Scale 1321: Blues Minor, 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

Jazz and Blues
Blues Minor
Chinese
Jue
Juédiào
Màn Gong
Unknown / Unsorted
Quan Ming
Yi Ze
Jiao
Ethiopian
Shegaye
Zeitler
Epathitonic
Dozenal
Benian
Western Modern
Phrygian Pentatonic
Carnatic
Raga Malkauns
Raga Malakosh
Raga Hindola

Analysis

Cardinality

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

5 (pentatonic)

Pitch Class Set

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

{0,3,5,8,10}

Forte Number

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

5-35

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]

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.

0 (anhemitonic)

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.

1

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.

4

Prime Form

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

no
prime: 661

Generator

Indicates if the scale can be constructed using a generator, and an origin.

generator: 5
origin: 0

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.

[3, 2, 3, 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.

<0, 3, 2, 1, 4, 0>

Interval Spectrum

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

p4mn2s3

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

Spectra Variation

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

0.8

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

yes

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.

2.299

Polygon Perimeter

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

5.828

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

yes

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.

[8]

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".

Strictly 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, 0, 20)

Generator

This scale has a generator of 5, originating on 0.

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}110.5
Minor Triadsfm{5,8,0}110.5

The following pitch classes are not present in any of the common triads: {10}

Parsimonious Voice Leading Between Common Triads of Scale 1321. Created by Ian Ring ©2019 fm fm G# G# fm->G#

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1321 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 677
Scale 677: Scottish Pentatonic, Ian Ring Music TheoryScottish Pentatonic
3rd mode:
Scale 1193
Scale 1193: Minor Pentatonic, Ian Ring Music TheoryMinor Pentatonic
4th mode:
Scale 661
Scale 661: Major Pentatonic, Ian Ring Music TheoryMajor PentatonicThis is the prime mode
5th mode:
Scale 1189
Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic

Prime

The prime form of this scale is Scale 661

Scale 661Scale 661: Major Pentatonic, Ian Ring Music TheoryMajor Pentatonic

Complement

The pentatonic modal family [1321, 677, 1193, 661, 1189] (Forte: 5-35) is the complement of the heptatonic modal family [1387, 1451, 1453, 1709, 1717, 2741, 2773] (Forte: 7-35)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1321 is 661

Scale 661Scale 661: Major Pentatonic, Ian Ring Music TheoryMajor Pentatonic

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> 1321       T0I <11,0> 661
T1 <1,1> 2642      T1I <11,1> 1322
T2 <1,2> 1189      T2I <11,2> 2644
T3 <1,3> 2378      T3I <11,3> 1193
T4 <1,4> 661      T4I <11,4> 2386
T5 <1,5> 1322      T5I <11,5> 677
T6 <1,6> 2644      T6I <11,6> 1354
T7 <1,7> 1193      T7I <11,7> 2708
T8 <1,8> 2386      T8I <11,8> 1321
T9 <1,9> 677      T9I <11,9> 2642
T10 <1,10> 1354      T10I <11,10> 1189
T11 <1,11> 2708      T11I <11,11> 2378
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 31      T0MI <7,0> 3841
T1M <5,1> 62      T1MI <7,1> 3587
T2M <5,2> 124      T2MI <7,2> 3079
T3M <5,3> 248      T3MI <7,3> 2063
T4M <5,4> 496      T4MI <7,4> 31
T5M <5,5> 992      T5MI <7,5> 62
T6M <5,6> 1984      T6MI <7,6> 124
T7M <5,7> 3968      T7MI <7,7> 248
T8M <5,8> 3841      T8MI <7,8> 496
T9M <5,9> 3587      T9MI <7,9> 992
T10M <5,10> 3079      T10MI <7,10> 1984
T11M <5,11> 2063      T11MI <7,11> 3968

The transformations that map this set to itself are: T0, T8I

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 1323Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
Scale 1325Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic
Scale 1313Scale 1313: Iplian, Ian Ring Music TheoryIplian
Scale 1317Scale 1317: Chaio, Ian Ring Music TheoryChaio
Scale 1329Scale 1329: Epygitonic, Ian Ring Music TheoryEpygitonic
Scale 1337Scale 1337: Epogimic, Ian Ring Music TheoryEpogimic
Scale 1289Scale 1289: Huvian, Ian Ring Music TheoryHuvian
Scale 1305Scale 1305: Dynitonic, Ian Ring Music TheoryDynitonic
Scale 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 1385Scale 1385: Phracrimic, Ian Ring Music TheoryPhracrimic
Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 1065Scale 1065: Gonian, Ian Ring Music TheoryGonian
Scale 1193Scale 1193: Minor Pentatonic, Ian Ring Music TheoryMinor Pentatonic
Scale 1577Scale 1577: Raga Chandrakauns (Kafi), Ian Ring Music TheoryRaga Chandrakauns (Kafi)
Scale 1833Scale 1833: Ionacrimic, Ian Ring Music TheoryIonacrimic
Scale 297Scale 297: Mynic, Ian Ring Music TheoryMynic
Scale 809Scale 809: Dogitonic, Ian Ring Music TheoryDogitonic
Scale 2345Scale 2345: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic

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.