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Scale 509: "Ionothyllic"

Scale 509: Ionothyllic, 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
Ionothyllic

Analysis

Cardinality

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

8 (octatonic)

Pitch Class Set

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

{0,2,3,4,5,6,7,8}

Forte Number

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

8-2

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: 2033

Hemitonia

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

6 (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.

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.

7

Prime Form

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

no
prime: 383

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.

[6, 6, 5, 5, 4, 2]

Interval Spectrum

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

p4m5n5s6d6t2

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

Spectra Variation

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

3.25

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.

2.366

Polygon Perimeter

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

5.838

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}231.57
G♯{8,0,3}231.57
Minor Triadscm{0,3,7}341.71
fm{5,8,0}241.86
Augmented TriadsC+{0,4,8}331.43
Diminished Triads{0,3,6}152.43
{2,5,8}152.57
Parsimonious Voice Leading Between Common Triads of Scale 509. Created by Ian Ring ©2019 cm cm c°->cm C C cm->C G# G# cm->G# C+ C+ C->C+ fm fm C+->fm C+->G# d°->fm

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC, C+, G♯
Peripheral Verticesc°, d°

Modes

Modes are the rotational transformation of this scale. Scale 509 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1151
Scale 1151: Mythyllic, Ian Ring Music TheoryMythyllic
3rd mode:
Scale 2623
Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic
4th mode:
Scale 3359
Scale 3359: Bonyllic, Ian Ring Music TheoryBonyllic
5th mode:
Scale 3727
Scale 3727: Tholyllic, Ian Ring Music TheoryTholyllic
6th mode:
Scale 3911
Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
7th mode:
Scale 4003
Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
8th mode:
Scale 4049
Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic

Prime

The prime form of this scale is Scale 383

Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic

Complement

The octatonic modal family [509, 1151, 2623, 3359, 3727, 3911, 4003, 4049] (Forte: 8-2) is the complement of the tetratonic modal family [23, 1793, 2059, 3077] (Forte: 4-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 509 is 2033

Scale 2033Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 509 is chiral, and its enantiomorph is scale 2033

Scale 2033Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic

Transformations:

T0 509  T0I 2033
T1 1018  T1I 4066
T2 2036  T2I 4037
T3 4072  T3I 3979
T4 4049  T4I 3863
T5 4003  T5I 3631
T6 3911  T6I 3167
T7 3727  T7I 2239
T8 3359  T8I 383
T9 2623  T9I 766
T10 1151  T10I 1532
T11 2302  T11I 3064

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 511Scale 511: Chromatic Nonamode, Ian Ring Music TheoryChromatic Nonamode
Scale 505Scale 505: Sanian, Ian Ring Music TheorySanian
Scale 507Scale 507: Moryllic, Ian Ring Music TheoryMoryllic
Scale 501Scale 501: Katylian, Ian Ring Music TheoryKatylian
Scale 493Scale 493: Rygian, Ian Ring Music TheoryRygian
Scale 477Scale 477: Stacrian, Ian Ring Music TheoryStacrian
Scale 445Scale 445: Gocrian, Ian Ring Music TheoryGocrian
Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian
Scale 253Scale 253, Ian Ring Music Theory
Scale 765Scale 765, Ian Ring Music Theory
Scale 1021Scale 1021: Ladygic, Ian Ring Music TheoryLadygic
Scale 1533Scale 1533: Katycrygic, Ian Ring Music TheoryKatycrygic
Scale 2557Scale 2557: Dothygic, Ian Ring Music TheoryDothygic

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.