The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3747: "Myrian"

Scale 3747: Myrian, 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
Myrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,5,7,9,10,11}
Forte Number7-9
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2223
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 351
Deep Scaleno
Interval Vector453432
Interval Spectrump3m4n3s5d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5,6}
<3> = {3,4,5,6,7,8}
<4> = {4,5,6,7,8,9}
<5> = {6,7,8,9,10}
<6> = {8,10,11}
Spectra Variation3.429
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 TriadsF{5,9,0}131.5
Minor Triadsa♯m{10,1,5}221
Augmented TriadsC♯+{1,5,9}221
Diminished Triads{7,10,1}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3747. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F a#m a#m C#+->a#m g°->a#m

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 VerticesC♯+, a♯m
Peripheral VerticesF, g°

Modes

Modes are the rotational transformation of this scale. Scale 3747 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3921
Scale 3921: Pythian, Ian Ring Music TheoryPythian
3rd mode:
Scale 501
Scale 501: Katylian, Ian Ring Music TheoryKatylian
4th mode:
Scale 1149
Scale 1149: Bydian, Ian Ring Music TheoryBydian
5th mode:
Scale 1311
Scale 1311: Bynian, Ian Ring Music TheoryBynian
6th mode:
Scale 2703
Scale 2703: Galian, Ian Ring Music TheoryGalian
7th mode:
Scale 3399
Scale 3399: Zonian, Ian Ring Music TheoryZonian

Prime

The prime form of this scale is Scale 351

Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian

Complement

The heptatonic modal family [3747, 3921, 501, 1149, 1311, 2703, 3399] (Forte: 7-9) is the complement of the pentatonic modal family [87, 1473, 1797, 2091, 3093] (Forte: 5-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3747 is 2223

Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3747 is chiral, and its enantiomorph is scale 2223

Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian

Transformations:

T0 3747  T0I 2223
T1 3399  T1I 351
T2 2703  T2I 702
T3 1311  T3I 1404
T4 2622  T4I 2808
T5 1149  T5I 1521
T6 2298  T6I 3042
T7 501  T7I 1989
T8 1002  T8I 3978
T9 2004  T9I 3861
T10 4008  T10I 3627
T11 3921  T11I 3159

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 3745Scale 3745, Ian Ring Music Theory
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
Scale 3715Scale 3715, Ian Ring Music Theory
Scale 3731Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian
Scale 3779Scale 3779, Ian Ring Music Theory
Scale 3811Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 2723Scale 2723: Raga Jivantika, Ian Ring Music TheoryRaga Jivantika
Scale 1699Scale 1699: Raga Rasavali, Ian Ring Music TheoryRaga Rasavali

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.