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Scale 2169

Scale 2169, 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

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,5,6,11}
Forte Number6-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 963
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 207
Deep Scaleno
Interval Vector422232
Interval Spectrump3m2n2s2d4t2
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6}
<3> = {3,5,7,9}
<4> = {6,8,10}
<5> = {7,9,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area1.75
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 2169 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 783
Scale 783, Ian Ring Music Theory
3rd mode:
Scale 2439
Scale 2439, Ian Ring Music Theory
4th mode:
Scale 3267
Scale 3267, Ian Ring Music Theory
5th mode:
Scale 3681
Scale 3681, Ian Ring Music Theory
6th mode:
Scale 243
Scale 243, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 207

Scale 207Scale 207, Ian Ring Music Theory

Complement

The hexatonic modal family [2169, 783, 2439, 3267, 3681, 243] (Forte: 6-5) is the complement of the hexatonic modal family [207, 963, 2151, 2529, 3123, 3609] (Forte: 6-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2169 is 963

Scale 963Scale 963, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2169 is chiral, and its enantiomorph is scale 963

Scale 963Scale 963, Ian Ring Music Theory

Transformations:

T0 2169  T0I 963
T1 243  T1I 1926
T2 486  T2I 3852
T3 972  T3I 3609
T4 1944  T4I 3123
T5 3888  T5I 2151
T6 3681  T6I 207
T7 3267  T7I 414
T8 2439  T8I 828
T9 783  T9I 1656
T10 1566  T10I 3312
T11 3132  T11I 2529

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 2171Scale 2171, Ian Ring Music Theory
Scale 2173Scale 2173, Ian Ring Music Theory
Scale 2161Scale 2161, Ian Ring Music Theory
Scale 2165Scale 2165, Ian Ring Music Theory
Scale 2153Scale 2153, Ian Ring Music Theory
Scale 2137Scale 2137, Ian Ring Music Theory
Scale 2105Scale 2105, Ian Ring Music Theory
Scale 2233Scale 2233: Donimic, Ian Ring Music TheoryDonimic
Scale 2297Scale 2297: Thylian, Ian Ring Music TheoryThylian
Scale 2425Scale 2425: Rorian, Ian Ring Music TheoryRorian
Scale 2681Scale 2681: Aerycrian, Ian Ring Music TheoryAerycrian
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian
Scale 121Scale 121, Ian Ring Music Theory
Scale 1145Scale 1145: Zygimic, Ian Ring Music TheoryZygimic

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.