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Scale 1551: "Jorian"

Scale 1551: Jorian, 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
Jorian

Analysis

Cardinality

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

6 (hexatonic)

Pitch Class Set

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

{0,1,2,3,9,10}

Forte Number

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

6-Z3

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: 3597

Hemitonia

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

4 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

2 (dicohemitonic)

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.

4

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.

5

Prime Form

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

no
prime: 111

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.

[1, 1, 1, 6, 1, 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.

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

Interval Spectrum

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

p2m2n3s3d4t

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> = {1,2,6}
<2> = {2,3,7}
<3> = {3,4,8,9}
<4> = {5,9,10}
<5> = {6,10,11}

Spectra Variation

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

4.333

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.

1.433

Polygon Perimeter

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

5.071

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.

(34, 9, 55)

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
Diminished Triads{9,0,3}000

The following pitch classes are not present in any of the common triads: {1,2,10}

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 1551 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2823
Scale 2823: Rulian, Ian Ring Music TheoryRulian
3rd mode:
Scale 3459
Scale 3459: Vocian, Ian Ring Music TheoryVocian
4th mode:
Scale 3777
Scale 3777: Yarian, Ian Ring Music TheoryYarian
5th mode:
Scale 123
Scale 123: Asuian, Ian Ring Music TheoryAsuian
6th mode:
Scale 2109
Scale 2109: Muvian, Ian Ring Music TheoryMuvian

Prime

The prime form of this scale is Scale 111

Scale 111Scale 111: Aroian, Ian Ring Music TheoryAroian

Complement

The hexatonic modal family [1551, 2823, 3459, 3777, 123, 2109] (Forte: 6-Z3) is the complement of the hexatonic modal family [159, 993, 2127, 3111, 3603, 3849] (Forte: 6-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1551 is 3597

Scale 3597Scale 3597: Wijian, Ian Ring Music TheoryWijian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1551 is chiral, and its enantiomorph is scale 3597

Scale 3597Scale 3597: Wijian, Ian Ring Music TheoryWijian

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> 1551       T0I <11,0> 3597
T1 <1,1> 3102      T1I <11,1> 3099
T2 <1,2> 2109      T2I <11,2> 2103
T3 <1,3> 123      T3I <11,3> 111
T4 <1,4> 246      T4I <11,4> 222
T5 <1,5> 492      T5I <11,5> 444
T6 <1,6> 984      T6I <11,6> 888
T7 <1,7> 1968      T7I <11,7> 1776
T8 <1,8> 3936      T8I <11,8> 3552
T9 <1,9> 3777      T9I <11,9> 3009
T10 <1,10> 3459      T10I <11,10> 1923
T11 <1,11> 2823      T11I <11,11> 3846
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1581      T0MI <7,0> 1677
T1M <5,1> 3162      T1MI <7,1> 3354
T2M <5,2> 2229      T2MI <7,2> 2613
T3M <5,3> 363      T3MI <7,3> 1131
T4M <5,4> 726      T4MI <7,4> 2262
T5M <5,5> 1452      T5MI <7,5> 429
T6M <5,6> 2904      T6MI <7,6> 858
T7M <5,7> 1713      T7MI <7,7> 1716
T8M <5,8> 3426      T8MI <7,8> 3432
T9M <5,9> 2757      T9MI <7,9> 2769
T10M <5,10> 1419      T10MI <7,10> 1443
T11M <5,11> 2838      T11MI <7,11> 2886

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 1549Scale 1549: Joqian, Ian Ring Music TheoryJoqian
Scale 1547Scale 1547: Jopian, Ian Ring Music TheoryJopian
Scale 1543Scale 1543: Jomian, Ian Ring Music TheoryJomian
Scale 1559Scale 1559: Jowian, Ian Ring Music TheoryJowian
Scale 1567Scale 1567: Jobian, Ian Ring Music TheoryJobian
Scale 1583Scale 1583: Salian, Ian Ring Music TheorySalian
Scale 1615Scale 1615: Sydian, Ian Ring Music TheorySydian
Scale 1679Scale 1679: Kydian, Ian Ring Music TheoryKydian
Scale 1807Scale 1807: Larian, Ian Ring Music TheoryLarian
Scale 1039Scale 1039: Gixian, Ian Ring Music TheoryGixian
Scale 1295Scale 1295: Huyian, Ian Ring Music TheoryHuyian
Scale 527Scale 527: Dedian, Ian Ring Music TheoryDedian
Scale 2575Scale 2575: Pumian, Ian Ring Music TheoryPumian
Scale 3599Scale 3599: Heptatonic Chromatic 4, Ian Ring Music TheoryHeptatonic Chromatic 4

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.