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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

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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

Cardinality7 (heptatonic)
Pitch Class Set{0,2,6,8,9,10,11}
Forte Number7-8
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections5
Modes6
Prime?no
prime: 381
Deep Scaleno
Interval Vector454422
Interval Spectrump2m4n4s5d4t2
Distribution Spectra<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 Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tones[8]
ProprietyImproper
Heliotonicno

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: Karian, Ian Ring Music TheoryKarian
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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.