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Scale 3851

Scale 3851, 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).

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,8,9,10,11}
Forte Number7-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2591
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 191
Deep Scaleno
Interval Vector554331
Interval Spectrump3m3n4s5d5t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {5,6,9,10}
<6> = {7,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.933
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 TriadsG♯{8,0,3}210.67
Minor Triadsg♯m{8,11,3}121
Diminished Triads{9,0,3}121
Parsimonious Voice Leading Between Common Triads of Scale 3851. Created by Ian Ring ©2019 g#m g#m G# G# g#m->G# G#->a°

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.

Diameter2
Radius1
Self-Centeredno
Central VerticesG♯
Peripheral Verticesg♯m, a°

Modes

Modes are the rotational transformation of this scale. Scale 3851 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3973
Scale 3973, Ian Ring Music Theory
3rd mode:
Scale 2017
Scale 2017, Ian Ring Music Theory
4th mode:
Scale 191
Scale 191, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2143
Scale 2143, Ian Ring Music Theory
6th mode:
Scale 3119
Scale 3119, Ian Ring Music Theory
7th mode:
Scale 3607
Scale 3607, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 191

Scale 191Scale 191, Ian Ring Music Theory

Complement

The heptatonic modal family [3851, 3973, 2017, 191, 2143, 3119, 3607] (Forte: 7-2) is the complement of the pentatonic modal family [47, 1921, 2071, 3083, 3589] (Forte: 5-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3851 is 2591

Scale 2591Scale 2591, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3851 is chiral, and its enantiomorph is scale 2591

Scale 2591Scale 2591, Ian Ring Music Theory

Transformations:

T0 3851  T0I 2591
T1 3607  T1I 1087
T2 3119  T2I 2174
T3 2143  T3I 253
T4 191  T4I 506
T5 382  T5I 1012
T6 764  T6I 2024
T7 1528  T7I 4048
T8 3056  T8I 4001
T9 2017  T9I 3907
T10 4034  T10I 3719
T11 3973  T11I 3343

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 3849Scale 3849, Ian Ring Music Theory
Scale 3853Scale 3853, Ian Ring Music Theory
Scale 3855Scale 3855, Ian Ring Music Theory
Scale 3843Scale 3843, Ian Ring Music Theory
Scale 3847Scale 3847, Ian Ring Music Theory
Scale 3859Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
Scale 3867Scale 3867: Storyllic, Ian Ring Music TheoryStoryllic
Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
Scale 3915Scale 3915, Ian Ring Music Theory
Scale 3979Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
Scale 3595Scale 3595, Ian Ring Music Theory
Scale 3723Scale 3723: Myptian, Ian Ring Music TheoryMyptian
Scale 3339Scale 3339, Ian Ring Music Theory
Scale 2827Scale 2827, Ian Ring Music Theory
Scale 1803Scale 1803, 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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.