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Scale 3965: "Messiaen Mode 7 Inverse"

Scale 3965: Messiaen Mode 7 Inverse, 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 Mode 7 Inverse

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,2,3,4,5,6,8,9,10,11}
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 TriadsD{2,6,9}452.68
E{4,8,11}352.77
F{5,9,0}452.59
G♯{8,0,3}452.68
A♯{10,2,5}352.77
B{11,3,6}452.59
Minor Triadsdm{2,5,9}452.59
d♯m{3,6,10}352.77
fm{5,8,0}452.68
g♯m{8,11,3}452.59
am{9,0,4}352.77
bm{11,2,6}452.68
Augmented TriadsC+{0,4,8}452.68
D+{2,6,10}452.68
Diminished Triads{0,3,6}252.86
{2,5,8}252.86
d♯°{3,6,9}253.05
{5,8,11}253.05
f♯°{6,9,0}252.86
g♯°{8,11,2}252.86
{9,0,3}253.05
{11,2,5}253.05
Parsimonious Voice Leading Between Common Triads of Scale 3965. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ E E C+->E fm fm C+->fm C+->G# am am C+->am dm dm d°->dm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m D+->A# bm bm D+->bm d#°->d#m d#m->B E->f° g#m g#m E->g#m f°->fm fm->F F->f#° F->am g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B G#->a° a°->am A#->b° 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 3965 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2015
Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7This is the prime mode
3rd mode:
Scale 3055
Scale 3055: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
4th mode:
Scale 3575
Scale 3575: Symmetrical Decatonic, Ian Ring Music TheorySymmetrical Decatonic
5th mode:
Scale 3835
Scale 3835, Ian Ring Music Theory

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 [3965, 2015, 3055, 3575, 3835] (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 3965 is 2015

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

Transformations:

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

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 3967Scale 3967: Soratic, Ian Ring Music TheorySoratic
Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 3963Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 3933Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
Scale 3901Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
Scale 4029Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed
Scale 4093Scale 4093: Aerycratic, Ian Ring Music TheoryAerycratic
Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic
Scale 3837Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
Scale 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
Scale 2941Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
Scale 1917Scale 1917: Thydyllian, Ian Ring Music TheoryThydyllian

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.