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Scale 1235: "Messiaen Truncated Mode 2"

Scale 1235: 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
Carnatic Raga
Raga Indupriya
Western Modern
Tritone Scale
Zeitler
Stylimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,4,6,7,10}
Forte Number6-30
Rotational Symmetry6 semitones
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2405
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes2
Prime?no
prime: 715
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
Major TriadsC{0,4,7}231.5
F♯{6,10,1}231.5
Diminished Triadsc♯°{1,4,7}231.5
{4,7,10}231.5
{7,10,1}231.5
a♯°{10,1,4}231.5
Parsimonious Voice Leading Between Common Triads of Scale 1235. Created by Ian Ring ©2019 C C c#° c#° C->c#° C->e° a#° a#° c#°->a#° e°->g° F# F# F#->g° 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 1235 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 2665
Scale 2665: Aeradimic, Ian Ring Music TheoryAeradimic
3rd mode:
Scale 845
Scale 845: Raga Neelangi, Ian Ring Music TheoryRaga Neelangi

Prime

The prime form of this scale is Scale 715

Scale 715Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2

Complement

The hexatonic modal family [1235, 2665, 845] (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 1235 is 2405

Scale 2405Scale 2405: Katalimic, Ian Ring Music TheoryKatalimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1235 is chiral, and its enantiomorph is scale 2405

Scale 2405Scale 2405: Katalimic, Ian Ring Music TheoryKatalimic

Transformations:

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

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 1233Scale 1233: Ionoditonic, Ian Ring Music TheoryIonoditonic
Scale 1237Scale 1237: Salimic, Ian Ring Music TheorySalimic
Scale 1239Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
Scale 1243Scale 1243: Epylian, Ian Ring Music TheoryEpylian
Scale 1219Scale 1219, Ian Ring Music Theory
Scale 1227Scale 1227: Thacrimic, Ian Ring Music TheoryThacrimic
Scale 1251Scale 1251: Sylimic, Ian Ring Music TheorySylimic
Scale 1267Scale 1267: Katynian, Ian Ring Music TheoryKatynian
Scale 1171Scale 1171: Raga Manaranjani I, Ian Ring Music TheoryRaga Manaranjani I
Scale 1203Scale 1203: Pagimic, Ian Ring Music TheoryPagimic
Scale 1107Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic
Scale 1363Scale 1363: Gygimic, Ian Ring Music TheoryGygimic
Scale 1491Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani
Scale 1747Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya
Scale 211Scale 211, Ian Ring Music Theory
Scale 723Scale 723: Ionadimic, Ian Ring Music TheoryIonadimic
Scale 2259Scale 2259: Raga Mandari, Ian Ring Music TheoryRaga Mandari
Scale 3283Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari

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.