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Scale 1119: "Rarian"

Scale 1119: Rarian, 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
Rarian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,4,6,10}
Forte Number7-8
Rotational Symmetrynone
Reflection Axes2
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[4]
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 TriadsF♯{6,10,1}231.4
Minor Triadsd♯m{3,6,10}231.4
Augmented TriadsD+{2,6,10}221.2
Diminished Triads{0,3,6}142
a♯°{10,1,4}142
Parsimonious Voice Leading Between Common Triads of Scale 1119. Created by Ian Ring ©2019 d#m d#m c°->d#m D+ D+ D+->d#m F# F# D+->F# a#° a#° F#->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.

Diameter4
Radius2
Self-Centeredno
Central VerticesD+
Peripheral Verticesc°, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 1119 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2607
Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
3rd mode:
Scale 3351
Scale 3351: Karian, Ian Ring Music TheoryKarian
4th mode:
Scale 3723
Scale 3723: Myptian, Ian Ring Music TheoryMyptian
5th mode:
Scale 3909
Scale 3909: Rydian, Ian Ring Music TheoryRydian
6th mode:
Scale 2001
Scale 2001: Gydian, Ian Ring Music TheoryGydian
7th mode:
Scale 381
Scale 381: Kogian, Ian Ring Music TheoryKogianThis is the prime mode

Prime

The prime form of this scale is Scale 381

Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian

Complement

The heptatonic modal family [1119, 2607, 3351, 3723, 3909, 2001, 381] (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 1119 is 3909

Scale 3909Scale 3909: Rydian, Ian Ring Music TheoryRydian

Transformations:

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

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 1117Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
Scale 1111Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic
Scale 1103Scale 1103: Lynimic, Ian Ring Music TheoryLynimic
Scale 1135Scale 1135: Katolian, Ian Ring Music TheoryKatolian
Scale 1151Scale 1151: Mythyllic, Ian Ring Music TheoryMythyllic
Scale 1055Scale 1055, Ian Ring Music Theory
Scale 1087Scale 1087, Ian Ring Music Theory
Scale 1183Scale 1183: Sadian, Ian Ring Music TheorySadian
Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 95Scale 95, Ian Ring Music Theory
Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 2143Scale 2143, Ian Ring Music Theory
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic

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.