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Scale 3705: "Messiaen Mode 4 Inverse"

Scale 3705: Messiaen Mode 4 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 4 Inverse
Named After Composers
Tcherepnin Octatonic Mode 4
Zeitler
Sydyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,4,5,6,9,10,11}
Forte Number8-9
Rotational Symmetry6 semitones
Reflection Axes1.5, 4.5
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections2
Modes3
Prime?no
prime: 975
Deep Scaleno
Interval Vector644464
Interval Spectrump6m4n4s4d6t4
Distribution Spectra<1> = {1,3}
<2> = {2,4}
<3> = {3,5}
<4> = {6}
<5> = {7,9}
<6> = {8,10}
<7> = {9,11}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setno
Interior Area2.5
Myhill Propertyno
Balancedyes
Ridge Tones[3,9]
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
Major TriadsF{5,9,0}242
B{11,3,6}242
Minor Triadsd♯m{3,6,10}242
am{9,0,4}242
Diminished Triads{0,3,6}242
d♯°{3,6,9}242
f♯°{6,9,0}242
{9,0,3}242
Parsimonious Voice Leading Between Common Triads of Scale 3705. Created by Ian Ring ©2019 c°->a° B B c°->B d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° d#m->B F F F->f#° am am F->am a°->am

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3705 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 975
Scale 975: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4This is the prime mode
3rd mode:
Scale 2535
Scale 2535: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4
4th mode:
Scale 3315
Scale 3315: Tcherepnin Octatonic Mode 1, Ian Ring Music TheoryTcherepnin Octatonic Mode 1

Prime

The prime form of this scale is Scale 975

Scale 975Scale 975: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4

Complement

The octatonic modal family [3705, 975, 2535, 3315] (Forte: 8-9) is the complement of the tetratonic modal family [195, 2145] (Forte: 4-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3705 is 975

Scale 975Scale 975: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4

Transformations:

T0 3705  T0I 975
T1 3315  T1I 1950
T2 2535  T2I 3900
T3 975  T3I 3705
T4 1950  T4I 3315
T5 3900  T5I 2535
T6 3705  T6I 975
T7 3315  T7I 1950
T8 2535  T8I 3900
T9 975  T9I 3705
T10 1950  T10I 3315
T11 3900  T11I 2535

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 3707Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic
Scale 3697Scale 3697: Ionarian, Ian Ring Music TheoryIonarian
Scale 3701Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
Scale 3689Scale 3689: Katocrian, Ian Ring Music TheoryKatocrian
Scale 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 3641Scale 3641: Thocrian, Ian Ring Music TheoryThocrian
Scale 3769Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian
Scale 3449Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
Scale 2681Scale 2681: Aerycrian, Ian Ring Music TheoryAerycrian
Scale 1657Scale 1657: Ionothian, Ian Ring Music TheoryIonothian

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.