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Scale 2171

Scale 2171, 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

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,5,6,11}
Forte Number7-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3011
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes6
Prime?no
prime: 239
Deep Scaleno
Interval Vector543342
Interval Spectrump4m3n3s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area1.933
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
Major TriadsB{11,3,6}110.5
Diminished Triads{0,3,6}110.5
Parsimonious Voice Leading Between Common Triads of Scale 2171. Created by Ian Ring ©2019 B B c°->B

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 2171 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3133
Scale 3133, Ian Ring Music Theory
3rd mode:
Scale 1807
Scale 1807, Ian Ring Music Theory
4th mode:
Scale 2951
Scale 2951, Ian Ring Music Theory
5th mode:
Scale 3523
Scale 3523, Ian Ring Music Theory
6th mode:
Scale 3809
Scale 3809, Ian Ring Music Theory
7th mode:
Scale 247
Scale 247, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 239

Scale 239Scale 239, Ian Ring Music Theory

Complement

The heptatonic modal family [2171, 3133, 1807, 2951, 3523, 3809, 247] (Forte: 7-5) is the complement of the pentatonic modal family [143, 481, 2119, 3107, 3601] (Forte: 5-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2171 is 3011

Scale 3011Scale 3011, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2171 is chiral, and its enantiomorph is scale 3011

Scale 3011Scale 3011, Ian Ring Music Theory

Transformations:

T0 2171  T0I 3011
T1 247  T1I 1927
T2 494  T2I 3854
T3 988  T3I 3613
T4 1976  T4I 3131
T5 3952  T5I 2167
T6 3809  T6I 239
T7 3523  T7I 478
T8 2951  T8I 956
T9 1807  T9I 1912
T10 3614  T10I 3824
T11 3133  T11I 3553

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 2169Scale 2169, Ian Ring Music Theory
Scale 2173Scale 2173, Ian Ring Music Theory
Scale 2175Scale 2175, Ian Ring Music Theory
Scale 2163Scale 2163, Ian Ring Music Theory
Scale 2167Scale 2167, Ian Ring Music Theory
Scale 2155Scale 2155, Ian Ring Music Theory
Scale 2139Scale 2139, Ian Ring Music Theory
Scale 2107Scale 2107, Ian Ring Music Theory
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian
Scale 2299Scale 2299: Phraptyllic, Ian Ring Music TheoryPhraptyllic
Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
Scale 2683Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 123Scale 123, Ian Ring Music Theory
Scale 1147Scale 1147: Epynian, Ian Ring Music TheoryEpynian

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.