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Scale 1441: "Jabian"

Scale 1441: Jabian, 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

Dozenal
Jabian

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

{0,5,7,8,10}

Forte Number

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

5-23

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.

none

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.

yes
enantiomorph: 181

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

1 (unhemitonic)

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.

2

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: 173

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.

[5, 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.

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

Interval Spectrum

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

p3mn2s3d

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> = {1,2,5}
<2> = {3,4,7}
<3> = {5,8,9}
<4> = {7,10,11}

Spectra Variation

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

3.2

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.

1.799

Polygon Perimeter

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

5.449

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.

none

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".

Improper

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.

(10, 4, 30)

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
Minor Triadsfm{5,8,0}000

The following pitch classes are not present in any of the common triads: {7,10}

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 1441 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 173
Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga PurnalalitaThis is the prime mode
3rd mode:
Scale 1067
Scale 1067: Gopian, Ian Ring Music TheoryGopian
4th mode:
Scale 2581
Scale 2581: Raga Neroshta, Ian Ring Music TheoryRaga Neroshta
5th mode:
Scale 1669
Scale 1669: Raga Matha Kokila, Ian Ring Music TheoryRaga Matha Kokila

Prime

The prime form of this scale is Scale 173

Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita

Complement

The pentatonic modal family [1441, 173, 1067, 2581, 1669] (Forte: 5-23) is the complement of the heptatonic modal family [701, 1199, 1513, 1957, 2647, 3371, 3733] (Forte: 7-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1441 is 181

Scale 181Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1441 is chiral, and its enantiomorph is scale 181

Scale 181Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari

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> 1441       T0I <11,0> 181
T1 <1,1> 2882      T1I <11,1> 362
T2 <1,2> 1669      T2I <11,2> 724
T3 <1,3> 3338      T3I <11,3> 1448
T4 <1,4> 2581      T4I <11,4> 2896
T5 <1,5> 1067      T5I <11,5> 1697
T6 <1,6> 2134      T6I <11,6> 3394
T7 <1,7> 173      T7I <11,7> 2693
T8 <1,8> 346      T8I <11,8> 1291
T9 <1,9> 692      T9I <11,9> 2582
T10 <1,10> 1384      T10I <11,10> 1069
T11 <1,11> 2768      T11I <11,11> 2138
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2071      T0MI <7,0> 3331
T1M <5,1> 47      T1MI <7,1> 2567
T2M <5,2> 94      T2MI <7,2> 1039
T3M <5,3> 188      T3MI <7,3> 2078
T4M <5,4> 376      T4MI <7,4> 61
T5M <5,5> 752      T5MI <7,5> 122
T6M <5,6> 1504      T6MI <7,6> 244
T7M <5,7> 3008      T7MI <7,7> 488
T8M <5,8> 1921      T8MI <7,8> 976
T9M <5,9> 3842      T9MI <7,9> 1952
T10M <5,10> 3589      T10MI <7,10> 3904
T11M <5,11> 3083      T11MI <7,11> 3713

The transformations that map this set to itself are: T0

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 1443Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti
Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari
Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 1457Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari
Scale 1409Scale 1409: Imsian, Ian Ring Music TheoryImsian
Scale 1425Scale 1425: Ryphitonic, Ian Ring Music TheoryRyphitonic
Scale 1473Scale 1473: Javian, Ian Ring Music TheoryJavian
Scale 1505Scale 1505: Jepian, Ian Ring Music TheoryJepian
Scale 1313Scale 1313: Iplian, Ian Ring Music TheoryIplian
Scale 1377Scale 1377: Insian, Ian Ring Music TheoryInsian
Scale 1185Scale 1185: Genus Primum Inverse, Ian Ring Music TheoryGenus Primum Inverse
Scale 1697Scale 1697: Raga Kuntvarali, Ian Ring Music TheoryRaga Kuntvarali
Scale 1953Scale 1953: Macian, Ian Ring Music TheoryMacian
Scale 417Scale 417: Copian, Ian Ring Music TheoryCopian
Scale 929Scale 929: Fujian, Ian Ring Music TheoryFujian
Scale 2465Scale 2465: Raga Devaranjani, Ian Ring Music TheoryRaga Devaranjani
Scale 3489Scale 3489: Vuvian, Ian Ring Music TheoryVuvian

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.