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Scale 1475

Scale 1475, 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{0,1,6,7,8,10}
Forte Number6-Z12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2165
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 215
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {7,10,11}
Spectra Variation3.333
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
Major TriadsF♯{6,10,1}110.5
Diminished Triads{7,10,1}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1475. Created by Ian Ring ©2019 F# F# F#->g°

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 1475 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2785
Scale 2785, Ian Ring Music Theory
3rd mode:
Scale 215
Scale 215, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2155
Scale 2155, Ian Ring Music Theory
5th mode:
Scale 3125
Scale 3125, Ian Ring Music Theory
6th mode:
Scale 1805
Scale 1805, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 215

Scale 215Scale 215, Ian Ring Music Theory

Complement

The hexatonic modal family [1475, 2785, 215, 2155, 3125, 1805] (Forte: 6-Z12) is the complement of the hexatonic modal family [335, 965, 1265, 2215, 3155, 3625] (Forte: 6-Z41)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1475 is 2165

Scale 2165Scale 2165, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1475 is chiral, and its enantiomorph is scale 2165

Scale 2165Scale 2165, Ian Ring Music Theory

Transformations:

T0 1475  T0I 2165
T1 2950  T1I 235
T2 1805  T2I 470
T3 3610  T3I 940
T4 3125  T4I 1880
T5 2155  T5I 3760
T6 215  T6I 3425
T7 430  T7I 2755
T8 860  T8I 1415
T9 1720  T9I 2830
T10 3440  T10I 1565
T11 2785  T11I 3130

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 1473Scale 1473, Ian Ring Music Theory
Scale 1477Scale 1477: Raga Jaganmohanam, Ian Ring Music TheoryRaga Jaganmohanam
Scale 1479Scale 1479: Mela Jalarnava, Ian Ring Music TheoryMela Jalarnava
Scale 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
Scale 1491Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani
Scale 1507Scale 1507: Zynian, Ian Ring Music TheoryZynian
Scale 1411Scale 1411, Ian Ring Music Theory
Scale 1443Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti
Scale 1347Scale 1347, Ian Ring Music Theory
Scale 1219Scale 1219, Ian Ring Music Theory
Scale 1731Scale 1731, Ian Ring Music Theory
Scale 1987Scale 1987, Ian Ring Music Theory
Scale 451Scale 451: Raga Saugandhini, Ian Ring Music TheoryRaga Saugandhini
Scale 963Scale 963, Ian Ring Music Theory
Scale 2499Scale 2499, Ian Ring Music Theory
Scale 3523Scale 3523, 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.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.