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Scale 3055: "Messiaen Mode 7"

Scale 3055: Messiaen Mode 7, 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).

Common Names

Messiaen
Messiaen Mode 7
Seventh Mode Of Limited Transposition

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,5,6,7,8,9,11}
Forte Number10-6
Rotational Symmetry6 semitones
Reflection Axes1, 4
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes4
Prime?no
prime: 2015
Deep Scaleno
Interval Vector888885
Interval Spectrump8m8n8s8d8t5
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5}
<5> = {6}
<6> = {7,8}
<7> = {8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation0.8
Maximally Evenyes
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedyes
Ridge Tones[2,8]
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♯{1,5,8}352.77
D{2,6,9}452.59
F{5,9,0}452.68
G{7,11,2}352.77
G♯{8,0,3}452.59
B{11,3,6}452.68
Minor Triadscm{0,3,7}352.77
dm{2,5,9}452.68
fm{5,8,0}452.59
f♯m{6,9,1}352.77
g♯m{8,11,3}452.68
bm{11,2,6}452.59
Augmented TriadsC♯+{1,5,9}452.68
D♯+{3,7,11}452.68
Diminished Triads{0,3,6}253.05
{2,5,8}253.05
d♯°{3,6,9}252.86
{5,8,11}252.86
f♯°{6,9,0}253.05
g♯°{8,11,2}253.05
{9,0,3}252.86
{11,2,5}252.86
Parsimonious Voice Leading Between Common Triads of Scale 3055. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m d°->dm D D dm->D dm->b° d#° d#° D->d#° D->f#m bm bm D->bm d#°->B Parsimonious Voice Leading Between Common Triads of Scale 3055. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B f°->fm f°->g#m fm->F fm->G# f#° f#° F->f#° F->a° f#°->f#m g#° g#° G->g#° G->bm g#°->g#m g#m->G# G#->a° b°->bm bm->B

view full size

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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3055 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3575
Scale 3575: Symmetrical Decatonic, Ian Ring Music TheorySymmetrical Decatonic
3rd mode:
Scale 3835
Scale 3835, Ian Ring Music Theory
4th mode:
Scale 3965
Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse
5th mode:
Scale 2015
Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7This is the prime mode

Prime

The prime form of this scale is Scale 2015

Scale 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7

Complement

The decatonic modal family [3055, 3575, 3835, 3965, 2015] (Forte: 10-6) is the complement of the modal family [65] (Forte: 2-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3055 is 3835

Scale 3835Scale 3835, Ian Ring Music Theory

Transformations:

T0 3055  T0I 3835
T1 2015  T1I 3575
T2 4030  T2I 3055
T3 3965  T3I 2015
T4 3835  T4I 4030
T5 3575  T5I 3965
T6 3055  T6I 3835
T7 2015  T7I 3575
T8 4030  T8I 3055
T9 3965  T9I 2015
T10 3835  T10I 4030
T11 3575  T11I 3965

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 3053Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
Scale 3047Scale 3047: Panygic, Ian Ring Music TheoryPanygic
Scale 3063Scale 3063: Solyllian, Ian Ring Music TheorySolyllian
Scale 3071Scale 3071: Solatic, Ian Ring Music TheorySolatic
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 3039Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian
Scale 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
Scale 2927Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
Scale 2799Scale 2799: Lyryllian, Ian Ring Music TheoryLyryllian
Scale 2543Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
Scale 3567Scale 3567: Epityllian, Ian Ring Music TheoryEpityllian
Scale 4079Scale 4079: Ionatic, Ian Ring Music TheoryIonatic
Scale 1007Scale 1007: Epitygic, Ian Ring Music TheoryEpitygic
Scale 2031Scale 2031: Gadyllian, Ian Ring Music TheoryGadyllian

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.