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Scale 3489

Scale 3489, 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{0,5,7,8,10,11}
Forte Number6-Z11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 183
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 183
Deep Scaleno
Interval Vector333231
Interval Spectrump3m2n3s3d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {4,5,7,8}
<4> = {5,6,9,10}
<5> = {7,10,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area1.866
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Minor Triadsfm{5,8,0}110.5
Diminished Triads{5,8,11}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3489. Created by Ian Ring ©2019 fm fm f°->fm

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3489 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 237
Scale 237, Ian Ring Music Theory
3rd mode:
Scale 1083
Scale 1083, Ian Ring Music Theory
4th mode:
Scale 2589
Scale 2589, Ian Ring Music Theory
5th mode:
Scale 1671
Scale 1671, Ian Ring Music Theory
6th mode:
Scale 2883
Scale 2883, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 183

Scale 183Scale 183, Ian Ring Music Theory

Complement

The hexatonic modal family [3489, 237, 1083, 2589, 1671, 2883] (Forte: 6-Z11) is the complement of the hexatonic modal family [303, 753, 1929, 2199, 3147, 3621] (Forte: 6-Z40)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3489 is 183

Scale 183Scale 183, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3489 is chiral, and its enantiomorph is scale 183

Scale 183Scale 183, Ian Ring Music Theory

Transformations:

T0 3489  T0I 183
T1 2883  T1I 366
T2 1671  T2I 732
T3 3342  T3I 1464
T4 2589  T4I 2928
T5 1083  T5I 1761
T6 2166  T6I 3522
T7 237  T7I 2949
T8 474  T8I 1803
T9 948  T9I 3606
T10 1896  T10I 3117
T11 3792  T11I 2139

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 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 3497Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian
Scale 3505Scale 3505: Stygian, Ian Ring Music TheoryStygian
Scale 3457Scale 3457, Ian Ring Music Theory
Scale 3473Scale 3473: Lathimic, Ian Ring Music TheoryLathimic
Scale 3521Scale 3521, Ian Ring Music Theory
Scale 3553Scale 3553, Ian Ring Music Theory
Scale 3361Scale 3361, Ian Ring Music Theory
Scale 3425Scale 3425, Ian Ring Music Theory
Scale 3233Scale 3233, Ian Ring Music Theory
Scale 3745Scale 3745, Ian Ring Music Theory
Scale 4001Scale 4001, Ian Ring Music Theory
Scale 2465Scale 2465: Raga Devaranjani, Ian Ring Music TheoryRaga Devaranjani
Scale 2977Scale 2977, Ian Ring Music Theory
Scale 1441Scale 1441, 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.