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Scale 1867: "Solian"

Scale 1867: Solian, 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
Solian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,6,8,9,10}
Forte Number7-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2653
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 733
Deep Scaleno
Interval Vector345342
Interval Spectrump4m3n5s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 1867 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2981
Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
3rd mode:
Scale 1769
Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
4th mode:
Scale 733
Scale 733: Donian, Ian Ring Music TheoryDonianThis is the prime mode
5th mode:
Scale 1207
Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
6th mode:
Scale 2651
Scale 2651: Panian, Ian Ring Music TheoryPanian
7th mode:
Scale 3373
Scale 3373: Lodian, Ian Ring Music TheoryLodian

Prime

The prime form of this scale is Scale 733

Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian

Complement

The heptatonic modal family [1867, 2981, 1769, 733, 1207, 2651, 3373] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1867 is 2653

Scale 2653Scale 2653: Sygian, Ian Ring Music TheorySygian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1867 is chiral, and its enantiomorph is scale 2653

Scale 2653Scale 2653: Sygian, Ian Ring Music TheorySygian

Transformations:

T0 1867  T0I 2653
T1 3734  T1I 1211
T2 3373  T2I 2422
T3 2651  T3I 749
T4 1207  T4I 1498
T5 2414  T5I 2996
T6 733  T6I 1897
T7 1466  T7I 3794
T8 2932  T8I 3493
T9 1769  T9I 2891
T10 3538  T10I 1687
T11 2981  T11I 3374

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 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
Scale 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
Scale 1871Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
Scale 1859Scale 1859, Ian Ring Music Theory
Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian
Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale
Scale 1883Scale 1883, Ian Ring Music Theory
Scale 1899Scale 1899: Moptyllic, Ian Ring Music TheoryMoptyllic
Scale 1803Scale 1803, Ian Ring Music Theory
Scale 1835Scale 1835: Byptian, Ian Ring Music TheoryByptian
Scale 1931Scale 1931: Stogian, Ian Ring Music TheoryStogian
Scale 1995Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
Scale 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
Scale 1739Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
Scale 1355Scale 1355: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 843Scale 843: Molimic, Ian Ring Music TheoryMolimic
Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
Scale 3915Scale 3915, Ian Ring Music Theory

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.