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Scale 1893: "Ionylian"

Scale 1893: Ionylian, 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
Ionylian

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

{0,2,5,6,8,9,10}

Forte Number

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

7-26

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: 1245

Hemitonia

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

3 (trihemitonic)

Cohemitonia

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

1 (uncohemitonic)

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: 699

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.

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

Interval Spectrum

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

p3m5n4s4d3t2

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

Spectra Variation

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

2.286

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.

2.549

Polygon Perimeter

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

5.967

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

Harmonic Chords

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 TriadsD{2,6,9}331.5
F{5,9,0}331.5
A♯{10,2,5}231.75
Minor Triadsdm{2,5,9}421.25
fm{5,8,0}242
Augmented TriadsD+{2,6,10}242
Diminished Triads{2,5,8}231.75
f♯°{6,9,0}231.75
Parsimonious Voice Leading Between Common Triads of Scale 1893. Created by Ian Ring ©2019 dm dm d°->dm fm fm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° D+->A# fm->F F->f#°

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.

Diameter4
Radius2
Self-Centeredno
Central Verticesdm
Peripheral VerticesD+, fm

Modes

Modes are the rotational transformation of this scale. Scale 1893 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1497
Scale 1497: Mela Jyotisvarupini, Ian Ring Music TheoryMela Jyotisvarupini
3rd mode:
Scale 699
Scale 699: Aerothian, Ian Ring Music TheoryAerothianThis is the prime mode
4th mode:
Scale 2397
Scale 2397: Stagian, Ian Ring Music TheoryStagian
5th mode:
Scale 1623
Scale 1623: Lothian, Ian Ring Music TheoryLothian
6th mode:
Scale 2859
Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
7th mode:
Scale 3477
Scale 3477: Kyptian, Ian Ring Music TheoryKyptian

Prime

The prime form of this scale is Scale 699

Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian

Complement

The heptatonic modal family [1893, 1497, 699, 2397, 1623, 2859, 3477] (Forte: 7-26) is the complement of the pentatonic modal family [309, 849, 1101, 1299, 2697] (Forte: 5-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1893 is 1245

Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1893 is chiral, and its enantiomorph is scale 1245

Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian

Transformations:

T0 1893  T0I 1245
T1 3786  T1I 2490
T2 3477  T2I 885
T3 2859  T3I 1770
T4 1623  T4I 3540
T5 3246  T5I 2985
T6 2397  T6I 1875
T7 699  T7I 3750
T8 1398  T8I 3405
T9 2796  T9I 2715
T10 1497  T10I 1335
T11 2994  T11I 2670

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 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
Scale 1889Scale 1889, Ian Ring Music Theory
Scale 1891Scale 1891: Thalian, Ian Ring Music TheoryThalian
Scale 1897Scale 1897: Ionopian, Ian Ring Music TheoryIonopian
Scale 1901Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic
Scale 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1829Scale 1829: Pathimic, Ian Ring Music TheoryPathimic
Scale 1957Scale 1957: Pyrian, Ian Ring Music TheoryPyrian
Scale 2021Scale 2021: Katycryllic, Ian Ring Music TheoryKatycryllic
Scale 1637Scale 1637: Syptimic, Ian Ring Music TheorySyptimic
Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 869Scale 869: Kothimic, Ian Ring Music TheoryKothimic
Scale 2917Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic

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.