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Scale 1567: "JOBIAN"

Scale 1567: JOBIAN, 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).

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

{0,1,2,3,4,9,10}

Forte Number

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

7-4

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: 3853

Hemitonia

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

5 (multihemitonic)

Cohemitonia

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

3 (tricohemitonic)

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.

6

Prime Form

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

no
prime: 223

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

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.

[5, 4, 4, 3, 3, 2]

Interval Spectrum

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

p3m3n4s4d5t2

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

Spectra Variation

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

3.714

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.

1.933

Polygon Perimeter

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

5.52

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

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 TriadsA{9,1,4}221
Minor Triadsam{9,0,4}221
Diminished Triads{9,0,3}131.5
a♯°{10,1,4}131.5

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

Parsimonious Voice Leading Between Common Triads of Scale 1567. Created by Ian Ring ©2019 am am a°->am A A am->A a#° a#° A->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
Radius2
Self-Centeredno
Central Verticesam, A
Peripheral Verticesa°, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 1567 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2831
Scale 2831: RUQIAN, Ian Ring Music TheoryRUQIAN
3rd mode:
Scale 3463
Scale 3463: VOFIAN, Ian Ring Music TheoryVOFIAN
4th mode:
Scale 3779
Scale 3779: YASIAN, Ian Ring Music TheoryYASIAN
5th mode:
Scale 3937
Scale 3937: ZALIAN, Ian Ring Music TheoryZALIAN
6th mode:
Scale 251
Scale 251: BORIAN, Ian Ring Music TheoryBORIAN
7th mode:
Scale 2173
Scale 2173: NEHIAN, Ian Ring Music TheoryNEHIAN

Prime

The prime form of this scale is Scale 223

Scale 223Scale 223: BIZIAN, Ian Ring Music TheoryBIZIAN

Complement

The heptatonic modal family [1567, 2831, 3463, 3779, 3937, 251, 2173] (Forte: 7-4) is the complement of the pentatonic modal family [79, 961, 2087, 3091, 3593] (Forte: 5-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1567 is 3853

Scale 3853Scale 3853: YOMIAN, Ian Ring Music TheoryYOMIAN

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1567 is chiral, and its enantiomorph is scale 3853

Scale 3853Scale 3853: YOMIAN, Ian Ring Music TheoryYOMIAN

Transformations:

T0 1567  T0I 3853
T1 3134  T1I 3611
T2 2173  T2I 3127
T3 251  T3I 2159
T4 502  T4I 223
T5 1004  T5I 446
T6 2008  T6I 892
T7 4016  T7I 1784
T8 3937  T8I 3568
T9 3779  T9I 3041
T10 3463  T10I 1987
T11 2831  T11I 3974

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 1565Scale 1565: JOZIAN, Ian Ring Music TheoryJOZIAN
Scale 1563Scale 1563: JOYIAN, Ian Ring Music TheoryJOYIAN
Scale 1559Scale 1559: JOWIAN, Ian Ring Music TheoryJOWIAN
Scale 1551Scale 1551: JORIAN, Ian Ring Music TheoryJORIAN
Scale 1583Scale 1583: Salian, Ian Ring Music TheorySalian
Scale 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic
Scale 1823Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
Scale 1055Scale 1055: GIHIAN, Ian Ring Music TheoryGIHIAN
Scale 1311Scale 1311: Bynian, Ian Ring Music TheoryBynian
Scale 543Scale 543: DENIAN, Ian Ring Music TheoryDENIAN
Scale 2591Scale 2591: PUWIAN, Ian Ring Music TheoryPUWIAN
Scale 3615Scale 3615: Octatonic Chromatic 4, Ian Ring Music TheoryOctatonic Chromatic 4

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. Special thanks to Richard Repp for helping with technical accuracy.