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Scale 3165: "Mylian"

Scale 3165: Mylian, 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
Mylian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,4,6,10,11}
Forte Number7-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1863
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 375
Deep Scaleno
Interval Vector443532
Interval Spectrump3m5n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsB{11,3,6}321
Minor Triadsd♯m{3,6,10}221.2
bm{11,2,6}221.2
Augmented TriadsD+{2,6,10}231.4
Diminished Triads{0,3,6}131.6
Parsimonious Voice Leading Between Common Triads of Scale 3165. Created by Ian Ring ©2019 B B c°->B D+ D+ d#m d#m D+->d#m bm bm D+->bm d#m->B bm->B

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesd♯m, bm, B
Peripheral Verticesc°, D+

Modes

Modes are the rotational transformation of this scale. Scale 3165 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1815
Scale 1815: Godian, Ian Ring Music TheoryGodian
3rd mode:
Scale 2955
Scale 2955: Thorian, Ian Ring Music TheoryThorian
4th mode:
Scale 3525
Scale 3525: Zocrian, Ian Ring Music TheoryZocrian
5th mode:
Scale 1905
Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian
6th mode:
Scale 375
Scale 375: Sodian, Ian Ring Music TheorySodianThis is the prime mode
7th mode:
Scale 2235
Scale 2235: Bathian, Ian Ring Music TheoryBathian

Prime

The prime form of this scale is Scale 375

Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian

Complement

The heptatonic modal family [3165, 1815, 2955, 3525, 1905, 375, 2235] (Forte: 7-13) is the complement of the pentatonic modal family [279, 369, 1809, 2187, 3141] (Forte: 5-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3165 is 1863

Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3165 is chiral, and its enantiomorph is scale 1863

Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian

Transformations:

T0 3165  T0I 1863
T1 2235  T1I 3726
T2 375  T2I 3357
T3 750  T3I 2619
T4 1500  T4I 1143
T5 3000  T5I 2286
T6 1905  T6I 477
T7 3810  T7I 954
T8 3525  T8I 1908
T9 2955  T9I 3816
T10 1815  T10I 3537
T11 3630  T11I 2979

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 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3161Scale 3161: Kodimic, Ian Ring Music TheoryKodimic
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3157Scale 3157: Zyptimic, Ian Ring Music TheoryZyptimic
Scale 3149Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
Scale 3181Scale 3181: Rolian, Ian Ring Music TheoryRolian
Scale 3197Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic
Scale 3101Scale 3101, Ian Ring Music Theory
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 3229Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian
Scale 3293Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
Scale 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 3677Scale 3677, Ian Ring Music Theory
Scale 2141Scale 2141, Ian Ring Music Theory
Scale 2653Scale 2653: Sygian, Ian Ring Music TheorySygian
Scale 1117Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic

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.