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Scale 715: "Messiaen Truncated Mode 2"

Scale 715: Messiaen Truncated Mode 2, 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).

Common Names

Messiaen
Messiaen Truncated Mode 2
Zeitler
Dodimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,6,7,9}
Forte Number6-30
Rotational Symmetry6 semitones
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2665
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes2
Prime?yes
Deep Scaleno
Interval Vector224223
Interval Spectrump2m2n4s2d2t3
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {6}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedyes
Ridge Tonesnone
ProprietyProper
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 Triadscm{0,3,7}231.5
f♯m{6,9,1}231.5
Diminished Triads{0,3,6}231.5
d♯°{3,6,9}231.5
f♯°{6,9,0}231.5
{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 715. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° cm->a° f#m f#m d#°->f#m f#° f#° f#°->f#m f#°->a°

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 715 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 2405
Scale 2405: Katalimic, Ian Ring Music TheoryKatalimic
3rd mode:
Scale 1625
Scale 1625: Lythimic, Ian Ring Music TheoryLythimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [715, 2405, 1625] (Forte: 6-30) is the complement of the hexatonic modal family [715, 1625, 2405] (Forte: 6-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 715 is 2665

Scale 2665Scale 2665: Aeradimic, Ian Ring Music TheoryAeradimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 715 is chiral, and its enantiomorph is scale 2665

Scale 2665Scale 2665: Aeradimic, Ian Ring Music TheoryAeradimic

Transformations:

T0 715  T0I 2665
T1 1430  T1I 1235
T2 2860  T2I 2470
T3 1625  T3I 845
T4 3250  T4I 1690
T5 2405  T5I 3380
T6 715  T6I 2665
T7 1430  T7I 1235
T8 2860  T8I 2470
T9 1625  T9I 845
T10 3250  T10I 1690
T11 2405  T11I 3380

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 713Scale 713: Thoptitonic, Ian Ring Music TheoryThoptitonic
Scale 717Scale 717: Raga Vijayanagari, Ian Ring Music TheoryRaga Vijayanagari
Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian
Scale 707Scale 707, Ian Ring Music Theory
Scale 711Scale 711: Raga Chandrajyoti, Ian Ring Music TheoryRaga Chandrajyoti
Scale 723Scale 723: Ionadimic, Ian Ring Music TheoryIonadimic
Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian
Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian
Scale 651Scale 651: Golitonic, Ian Ring Music TheoryGolitonic
Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic
Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic
Scale 843Scale 843: Molimic, Ian Ring Music TheoryMolimic
Scale 971Scale 971: Mela Gavambodhi, Ian Ring Music TheoryMela Gavambodhi
Scale 203Scale 203, Ian Ring Music Theory
Scale 459Scale 459: Zaptimic, Ian Ring Music TheoryZaptimic
Scale 1227Scale 1227: Thacrimic, Ian Ring Music TheoryThacrimic
Scale 1739Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi

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.