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Scale 1415

Scale 1415, 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

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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{0,1,2,7,8,10}
Forte Number6-Z12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3125
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
Minor Triadsgm{7,10,2}110.5
Diminished Triads{7,10,1}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1415. Created by Ian Ring ©2019 gm gm g°->gm

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 1415 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2755
Scale 2755, Ian Ring Music Theory
3rd mode:
Scale 3425
Scale 3425, Ian Ring Music Theory
4th mode:
Scale 235
Scale 235, Ian Ring Music Theory
5th mode:
Scale 2165
Scale 2165, Ian Ring Music Theory
6th mode:
Scale 1565
Scale 1565, 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 [1415, 2755, 3425, 235, 2165, 1565] (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 1415 is 3125

Scale 3125Scale 3125, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1415 is chiral, and its enantiomorph is scale 3125

Scale 3125Scale 3125, Ian Ring Music Theory

Transformations:

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

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 1413Scale 1413, Ian Ring Music Theory
Scale 1411Scale 1411, Ian Ring Music Theory
Scale 1419Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi
Scale 1423Scale 1423: Doptian, Ian Ring Music TheoryDoptian
Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian
Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
Scale 1479Scale 1479: Mela Jalarnava, Ian Ring Music TheoryMela Jalarnava
Scale 1287Scale 1287, Ian Ring Music Theory
Scale 1351Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic
Scale 1159Scale 1159, Ian Ring Music Theory
Scale 1671Scale 1671, Ian Ring Music Theory
Scale 1927Scale 1927, Ian Ring Music Theory
Scale 391Scale 391, Ian Ring Music Theory
Scale 903Scale 903, Ian Ring Music Theory
Scale 2439Scale 2439, Ian Ring Music Theory
Scale 3463Scale 3463, 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.