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Scale 3181: "Rolian"

Scale 3181: Rolian, 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
Rolian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,5,6,10,11}
Forte Number7-Z38
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1735
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 439
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {8,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 3181 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1819
Scale 1819: Pydian, Ian Ring Music TheoryPydian
3rd mode:
Scale 2957
Scale 2957: Thygian, Ian Ring Music TheoryThygian
4th mode:
Scale 1763
Scale 1763: Katalian, Ian Ring Music TheoryKatalian
5th mode:
Scale 2929
Scale 2929: Aeolathian, Ian Ring Music TheoryAeolathian
6th mode:
Scale 439
Scale 439: Bythian, Ian Ring Music TheoryBythianThis is the prime mode
7th mode:
Scale 2267
Scale 2267: Padian, Ian Ring Music TheoryPadian

Prime

The prime form of this scale is Scale 439

Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian

Complement

The heptatonic modal family [3181, 1819, 2957, 1763, 2929, 439, 2267] (Forte: 7-Z38) is the complement of the pentatonic modal family [295, 625, 905, 2195, 3145] (Forte: 5-Z38)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3181 is 1735

Scale 1735Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3181 is chiral, and its enantiomorph is scale 1735

Scale 1735Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam

Transformations:

T0 3181  T0I 1735
T1 2267  T1I 3470
T2 439  T2I 2845
T3 878  T3I 1595
T4 1756  T4I 3190
T5 3512  T5I 2285
T6 2929  T6I 475
T7 1763  T7I 950
T8 3526  T8I 1900
T9 2957  T9I 3800
T10 1819  T10I 3505
T11 3638  T11I 2915

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 3183Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic
Scale 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian
Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic
Scale 3189Scale 3189: Aeolonian, Ian Ring Music TheoryAeolonian
Scale 3197Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic
Scale 3149Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian
Scale 3117Scale 3117, Ian Ring Music Theory
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 3309Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
Scale 3437Scale 3437, Ian Ring Music Theory
Scale 3693Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
Scale 2157Scale 2157, Ian Ring Music Theory
Scale 2669Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.