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Scale 2281: "Rathimic"

Scale 2281: Rathimic, 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
Rathimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,5,6,7,11}
Forte Number6-Z17
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 739
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 407
Deep Scaleno
Interval Vector322332
Interval Spectrump3m3n2s2d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5}
<3> = {4,6,8}
<4> = {7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsB{11,3,6}221
Minor Triadscm{0,3,7}221
Augmented TriadsD♯+{3,7,11}221
Diminished Triads{0,3,6}221
Parsimonious Voice Leading Between Common Triads of Scale 2281. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ D#+->B

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.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2281 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 797
Scale 797: Katocrimic, Ian Ring Music TheoryKatocrimic
3rd mode:
Scale 1223
Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic
4th mode:
Scale 2659
Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic
5th mode:
Scale 3377
Scale 3377: Phralimic, Ian Ring Music TheoryPhralimic
6th mode:
Scale 467
Scale 467: Raga Dhavalangam, Ian Ring Music TheoryRaga Dhavalangam

Prime

The prime form of this scale is Scale 407

Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic

Complement

The hexatonic modal family [2281, 797, 1223, 2659, 3377, 467] (Forte: 6-Z17) is the complement of the hexatonic modal family [359, 907, 1649, 2227, 2501, 3161] (Forte: 6-Z43)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2281 is 739

Scale 739Scale 739: Rorimic, Ian Ring Music TheoryRorimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2281 is chiral, and its enantiomorph is scale 739

Scale 739Scale 739: Rorimic, Ian Ring Music TheoryRorimic

Transformations:

T0 2281  T0I 739
T1 467  T1I 1478
T2 934  T2I 2956
T3 1868  T3I 1817
T4 3736  T4I 3634
T5 3377  T5I 3173
T6 2659  T6I 2251
T7 1223  T7I 407
T8 2446  T8I 814
T9 797  T9I 1628
T10 1594  T10I 3256
T11 3188  T11I 2417

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 2283Scale 2283: Aeolyptian, Ian Ring Music TheoryAeolyptian
Scale 2285Scale 2285: Aerogian, Ian Ring Music TheoryAerogian
Scale 2273Scale 2273, Ian Ring Music Theory
Scale 2277Scale 2277: Kagimic, Ian Ring Music TheoryKagimic
Scale 2289Scale 2289: Mocrimic, Ian Ring Music TheoryMocrimic
Scale 2297Scale 2297: Thylian, Ian Ring Music TheoryThylian
Scale 2249Scale 2249: Raga Multani, Ian Ring Music TheoryRaga Multani
Scale 2265Scale 2265: Raga Rasamanjari, Ian Ring Music TheoryRaga Rasamanjari
Scale 2217Scale 2217: Kagitonic, Ian Ring Music TheoryKagitonic
Scale 2153Scale 2153, Ian Ring Music Theory
Scale 2409Scale 2409: Zacrimic, Ian Ring Music TheoryZacrimic
Scale 2537Scale 2537: Laptian, Ian Ring Music TheoryLaptian
Scale 2793Scale 2793: Eporian, Ian Ring Music TheoryEporian
Scale 3305Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
Scale 233Scale 233, Ian Ring Music Theory
Scale 1257Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale

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.