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Scale 1015: "Ionodygic"

Scale 1015: Ionodygic, 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

41161837294116105072918310504116183
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

Zeitler
Ionodygic

Analysis

Cardinality

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

9 (nonatonic)

Pitch Class Set

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

{0,1,2,4,5,6,7,8,9}

Forte Number

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

9-4

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: 3577

Hemitonia

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

7 (multihemitonic)

Cohemitonia

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

5 (multicohemitonic)

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.

8

Prime Form

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

no
prime: 959

Deep Scale

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

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[1, 1, 2, 1, 1, 1, 1, 1, 3]

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.

<7, 6, 6, 7, 7, 3>

Interval Spectrum

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

p7m7n6s6d7t3

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

Spectra Variation

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

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.

2.683

Polygon Perimeter

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

6.038

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 TriadsC{0,4,7}263
C♯{1,5,8}431.87
D{2,6,9}263
F{5,9,0}442
A{9,1,4}332
Minor Triadsc♯m{1,4,8}442.07
dm{2,5,9}352.4
fm{5,8,0}342.07
f♯m{6,9,1}352.4
am{9,0,4}342.2
Augmented TriadsC+{0,4,8}452.27
C♯+{1,5,9}541.8
Diminished Triadsc♯°{1,4,7}252.8
{2,5,8}242.47
f♯°{6,9,0}252.6
Parsimonious Voice Leading Between Common Triads of Scale 1015. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m fm fm C+->fm am am C+->am c#°->c#m C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m C#+->A d°->dm D D dm->D D->f#m fm->F f#° f#° F->f#° F->am f#°->f#m am->A

view full size

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.

Diameter6
Radius3
Self-Centeredno
Central VerticesC♯, A
Peripheral VerticesC, D

Modes

Modes are the rotational transformation of this scale. Scale 1015 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2555
Scale 2555: Bythygic, Ian Ring Music TheoryBythygic
3rd mode:
Scale 3325
Scale 3325: Mixolygic, Ian Ring Music TheoryMixolygic
4th mode:
Scale 1855
Scale 1855: Gaptygic, Ian Ring Music TheoryGaptygic
5th mode:
Scale 2975
Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
6th mode:
Scale 3535
Scale 3535: Mylygic, Ian Ring Music TheoryMylygic
7th mode:
Scale 3815
Scale 3815: Galygic, Ian Ring Music TheoryGalygic
8th mode:
Scale 3955
Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
9th mode:
Scale 4025
Scale 4025: Kalygic, Ian Ring Music TheoryKalygic

Prime

The prime form of this scale is Scale 959

Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic

Complement

The nonatonic modal family [1015, 2555, 3325, 1855, 2975, 3535, 3815, 3955, 4025] (Forte: 9-4) is the complement of the tritonic modal family [35, 385, 2065] (Forte: 3-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1015 is 3577

Scale 3577Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1015 is chiral, and its enantiomorph is scale 3577

Scale 3577Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic

Transformations:

T0 1015  T0I 3577
T1 2030  T1I 3059
T2 4060  T2I 2023
T3 4025  T3I 4046
T4 3955  T4I 3997
T5 3815  T5I 3899
T6 3535  T6I 3703
T7 2975  T7I 3311
T8 1855  T8I 2527
T9 3710  T9I 959
T10 3325  T10I 1918
T11 2555  T11I 3836

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 1013Scale 1013: Stydyllic, Ian Ring Music TheoryStydyllic
Scale 1011Scale 1011: Kycryllic, Ian Ring Music TheoryKycryllic
Scale 1019Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
Scale 1023Scale 1023: Chromatic Decamode, Ian Ring Music TheoryChromatic Decamode
Scale 999Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic
Scale 1007Scale 1007: Epitygic, Ian Ring Music TheoryEpitygic
Scale 983Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic
Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic
Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic
Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic
Scale 503Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic
Scale 1527Scale 1527: Aeolyrigic, Ian Ring Music TheoryAeolyrigic
Scale 2039Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian
Scale 3063Scale 3063: Solyllian, Ian Ring Music TheorySolyllian

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. 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.