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Scale 3909: "Rydian"

Scale 3909: Rydian, 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
Rydian

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

{0,2,6,8,9,10,11}

Forte Number

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

7-8

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.

[4]

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.

no

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.

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.

5

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: 381

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.

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

Interval Spectrum

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

p2m4n4s5d4t2

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

Spectra Variation

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

3.429

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.

2.299

Polygon Perimeter

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

5.803

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.

[8]

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 TriadsD{2,6,9}231.4
Minor Triadsbm{11,2,6}231.4
Augmented TriadsD+{2,6,10}221.2
Diminished Triadsf♯°{6,9,0}142
g♯°{8,11,2}142
Parsimonious Voice Leading Between Common Triads of Scale 3909. Created by Ian Ring ©2019 D D D+ D+ D->D+ f#° f#° D->f#° bm bm D+->bm g#° g#° g#°->bm

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 VerticesD+
Peripheral Verticesf♯°, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 3909 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2001
Scale 2001: Gydian, Ian Ring Music TheoryGydian
3rd mode:
Scale 381
Scale 381: Kogian, Ian Ring Music TheoryKogianThis is the prime mode
4th mode:
Scale 1119
Scale 1119: Rarian, Ian Ring Music TheoryRarian
5th mode:
Scale 2607
Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
6th mode:
Scale 3351
Scale 3351: Crater Scale, Ian Ring Music TheoryCrater Scale
7th mode:
Scale 3723
Scale 3723: Myptian, Ian Ring Music TheoryMyptian

Prime

The prime form of this scale is Scale 381

Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian

Complement

The heptatonic modal family [3909, 2001, 381, 1119, 2607, 3351, 3723] (Forte: 7-8) is the complement of the pentatonic modal family [93, 1047, 1857, 2571, 3333] (Forte: 5-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3909 is 1119

Scale 1119Scale 1119: Rarian, Ian Ring Music TheoryRarian

Transformations:

T0 3909  T0I 1119
T1 3723  T1I 2238
T2 3351  T2I 381
T3 2607  T3I 762
T4 1119  T4I 1524
T5 2238  T5I 3048
T6 381  T6I 2001
T7 762  T7I 4002
T8 1524  T8I 3909
T9 3048  T9I 3723
T10 2001  T10I 3351
T11 4002  T11I 2607

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 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
Scale 3905Scale 3905, Ian Ring Music Theory
Scale 3907Scale 3907, Ian Ring Music Theory
Scale 3913Scale 3913: Bonian, Ian Ring Music TheoryBonian
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 3845Scale 3845, Ian Ring Music Theory
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 3973Scale 3973, Ian Ring Music Theory
Scale 4037Scale 4037: Ionyllic, Ian Ring Music TheoryIonyllic
Scale 3653Scale 3653: Sathimic, Ian Ring Music TheorySathimic
Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
Scale 3397Scale 3397: Sydimic, Ian Ring Music TheorySydimic
Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic

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.