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Scale 3805: "Moptygic"

Scale 3805: Moptygic, 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

Zeitler
Moptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,4,6,7,9,10,11}
Forte Number9-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1903
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes8
Prime?no
prime: 1775
Deep Scaleno
Interval Vector667773
Interval Spectrump7m7n7s6d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {5,6}
<5> = {6,7}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.111
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
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}342.5
D{2,6,9}342.56
D♯{3,7,10}442.17
G{7,11,2}342.39
B{11,3,6}442.17
Minor Triadscm{0,3,7}442.28
d♯m{3,6,10}442.22
em{4,7,11}342.39
gm{7,10,2}342.44
am{9,0,4}342.67
bm{11,2,6}342.44
Augmented TriadsD+{2,6,10}442.33
D♯+{3,7,11}542
Diminished Triads{0,3,6}242.56
d♯°{3,6,9}242.67
{4,7,10}242.67
f♯°{6,9,0}242.72
{9,0,3}242.72
Parsimonious Voice Leading Between Common Triads of Scale 3805. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ cm->a° em em C->em am am C->am D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m gm gm D+->gm bm bm D+->bm d#°->d#m D# D# d#m->D# d#m->B D#->D#+ D#->e° D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3805. Created by Ian Ring ©2019 G D#+->G D#+->B e°->em f#°->am gm->G G->bm a°->am 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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3805 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1975
Scale 1975: Ionocrygic, Ian Ring Music TheoryIonocrygic
3rd mode:
Scale 3035
Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
4th mode:
Scale 3565
Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
5th mode:
Scale 1915
Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
6th mode:
Scale 3005
Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic
7th mode:
Scale 1775
Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygicThis is the prime mode
8th mode:
Scale 2935
Scale 2935: Modygic, Ian Ring Music TheoryModygic
9th mode:
Scale 3515
Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian

Prime

The prime form of this scale is Scale 1775

Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic

Complement

The nonatonic modal family [3805, 1975, 3035, 3565, 1915, 3005, 1775, 2935, 3515] (Forte: 9-11) is the complement of the tritonic modal family [137, 289, 529] (Forte: 3-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3805 is 1903

Scale 1903Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3805 is chiral, and its enantiomorph is scale 1903

Scale 1903Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic

Transformations:

T0 3805  T0I 1903
T1 3515  T1I 3806
T2 2935  T2I 3517
T3 1775  T3I 2939
T4 3550  T4I 1783
T5 3005  T5I 3566
T6 1915  T6I 3037
T7 3830  T7I 1979
T8 3565  T8I 3958
T9 3035  T9I 3821
T10 1975  T10I 3547
T11 3950  T11I 2999

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 3807Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 3803Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
Scale 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
Scale 3837Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
Scale 3741Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
Scale 3773Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
Scale 3677Scale 3677, Ian Ring Music Theory
Scale 3933Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
Scale 4061Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
Scale 3293Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
Scale 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse
Scale 2781Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
Scale 1757Scale 1757, Ian Ring Music Theory

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.