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Scale 1857

Scale 1857, 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).

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,6,8,9,10}
Forte Number5-8
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections5
Modes4
Prime?no
prime: 93
Deep Scaleno
Interval Vector232201
Interval Spectrumm2n2s3d2t
Distribution Spectra<1> = {1,2,6}
<2> = {2,3,8}
<3> = {4,9,10}
<4> = {6,10,11}
Spectra Variation4.4
Maximally Evenno
Maximal Area Setno
Interior Area1.366
Myhill Propertyno
Balancedno
Ridge Tones[6]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1857 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 93
Scale 93, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 1047
Scale 1047, Ian Ring Music Theory
4th mode:
Scale 2571
Scale 2571, Ian Ring Music Theory
5th mode:
Scale 3333
Scale 3333, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 93

Scale 93Scale 93, Ian Ring Music Theory

Complement

The pentatonic modal family [1857, 93, 1047, 2571, 3333] (Forte: 5-8) is the complement of the heptatonic modal family [381, 1119, 2001, 2607, 3351, 3723, 3909] (Forte: 7-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1857 is 93

Scale 93Scale 93, Ian Ring Music Theory

Transformations:

T0 1857  T0I 93
T1 3714  T1I 186
T2 3333  T2I 372
T3 2571  T3I 744
T4 1047  T4I 1488
T5 2094  T5I 2976
T6 93  T6I 1857
T7 186  T7I 3714
T8 372  T8I 3333
T9 744  T9I 2571
T10 1488  T10I 1047
T11 2976  T11I 2094

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 1859Scale 1859, Ian Ring Music Theory
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
Scale 1889Scale 1889, Ian Ring Music Theory
Scale 1793Scale 1793, Ian Ring Music Theory
Scale 1825Scale 1825, Ian Ring Music Theory
Scale 1921Scale 1921, Ian Ring Music Theory
Scale 1985Scale 1985, Ian Ring Music Theory
Scale 1601Scale 1601, Ian Ring Music Theory
Scale 1729Scale 1729, Ian Ring Music Theory
Scale 1345Scale 1345, Ian Ring Music Theory
Scale 833Scale 833, Ian Ring Music Theory
Scale 2881Scale 2881, Ian Ring Music Theory
Scale 3905Scale 3905, 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.