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Scale 1537

Scale 1537, 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

Cardinality3 (tritonic)
Pitch Class Set{0,9,10}
Forte Number3-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 13
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes2
Prime?no
prime: 11
Deep Scaleno
Interval Vector111000
Interval Spectrumnsd
Distribution Spectra<1> = {1,2,9}
<2> = {3,10,11}
Spectra Variation5.333
Maximally Evenno
Maximal Area Setno
Interior Area0.183
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 1537 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 11
Scale 11, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2053
Scale 2053, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 11

Scale 11Scale 11, Ian Ring Music Theory

Complement

The tritonic modal family [1537, 11, 2053] (Forte: 3-2) is the complement of the nonatonic modal family [767, 2041, 2431, 3263, 3679, 3887, 3991, 4043, 4069] (Forte: 9-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1537 is 13

Scale 13Scale 13, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1537 is chiral, and its enantiomorph is scale 13

Scale 13Scale 13, Ian Ring Music Theory

Transformations:

T0 1537  T0I 13
T1 3074  T1I 26
T2 2053  T2I 52
T3 11  T3I 104
T4 22  T4I 208
T5 44  T5I 416
T6 88  T6I 832
T7 176  T7I 1664
T8 352  T8I 3328
T9 704  T9I 2561
T10 1408  T10I 1027
T11 2816  T11I 2054

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 1539Scale 1539, Ian Ring Music Theory
Scale 1541Scale 1541, Ian Ring Music Theory
Scale 1545Scale 1545, Ian Ring Music Theory
Scale 1553Scale 1553, Ian Ring Music Theory
Scale 1569Scale 1569, Ian Ring Music Theory
Scale 1601Scale 1601, Ian Ring Music Theory
Scale 1665Scale 1665, Ian Ring Music Theory
Scale 1793Scale 1793, Ian Ring Music Theory
Scale 1025Scale 1025: Warao Ditonic, Ian Ring Music TheoryWarao Ditonic
Scale 1281Scale 1281, Ian Ring Music Theory
Scale 513Scale 513, Ian Ring Music Theory
Scale 2561Scale 2561, Ian Ring Music Theory
Scale 3585Scale 3585, 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, 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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.