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Scale 3675: "Monyllic"

Scale 3675: Monyllic, 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

Zeitler
Monyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,6,9,10,11}
Forte Number8-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2895
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 735
Deep Scaleno
Interval Vector556453
Interval Spectrump5m4n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tonesnone
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♯{6,10,1}341.91
A{9,1,4}341.91
B{11,3,6}242.27
Minor Triadsd♯m{3,6,10}342
f♯m{6,9,1}441.82
am{9,0,4}342
Diminished Triads{0,3,6}242.36
d♯°{3,6,9}242.09
f♯°{6,9,0}242.09
{9,0,3}242.27
a♯°{10,1,4}242.18
Parsimonious Voice Leading Between Common Triads of Scale 3675. Created by Ian Ring ©2019 c°->a° B B c°->B d#° d#° d#m d#m d#°->d#m f#m f#m d#°->f#m F# F# d#m->F# d#m->B f#° f#° f#°->f#m am am f#°->am f#m->F# A A f#m->A a#° a#° F#->a#° a°->am am->A A->a#°

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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 3675 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3885
Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
3rd mode:
Scale 1995
Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
4th mode:
Scale 3045
Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
5th mode:
Scale 1785
Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
6th mode:
Scale 735
Scale 735: Sylyllic, Ian Ring Music TheorySylyllicThis is the prime mode
7th mode:
Scale 2415
Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
8th mode:
Scale 3255
Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic

Prime

The prime form of this scale is Scale 735

Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic

Complement

The octatonic modal family [3675, 3885, 1995, 3045, 1785, 735, 2415, 3255] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3675 is 2895

Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3675 is chiral, and its enantiomorph is scale 2895

Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic

Transformations:

T0 3675  T0I 2895
T1 3255  T1I 1695
T2 2415  T2I 3390
T3 735  T3I 2685
T4 1470  T4I 1275
T5 2940  T5I 2550
T6 1785  T6I 1005
T7 3570  T7I 2010
T8 3045  T8I 4020
T9 1995  T9I 3945
T10 3990  T10I 3795
T11 3885  T11I 3495

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 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 3677Scale 3677, Ian Ring Music Theory
Scale 3679Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
Scale 3667Scale 3667: Kaptian, Ian Ring Music TheoryKaptian
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3707Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
Scale 3611Scale 3611, Ian Ring Music Theory
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
Scale 3803Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 1627Scale 1627: Zyptian, Ian Ring Music TheoryZyptian

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.