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Scale 3341

Scale 3341, 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).

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,8,10,11}
Forte Number6-Z10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1559
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes5
Prime?no
prime: 187
Deep Scaleno
Interval Vector333321
Interval Spectrump2m3n3s3d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {4,8}
<4> = {5,6,9,10}
<5> = {7,10,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area1.866
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}121
Minor Triadsg♯m{8,11,3}210.67
Diminished Triadsg♯°{8,11,2}121
Parsimonious Voice Leading Between Common Triads of Scale 3341. Created by Ian Ring ©2019 g#° g#° g#m g#m g#°->g#m G# G# g#m->G#

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♯m
Peripheral Verticesg♯°, G♯

Modes

Modes are the rotational transformation of this scale. Scale 3341 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1859
Scale 1859, Ian Ring Music Theory
3rd mode:
Scale 2977
Scale 2977, Ian Ring Music Theory
4th mode:
Scale 221
Scale 221, Ian Ring Music Theory
5th mode:
Scale 1079
Scale 1079, Ian Ring Music Theory
6th mode:
Scale 2587
Scale 2587, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 187

Scale 187Scale 187, Ian Ring Music Theory

Complement

The hexatonic modal family [3341, 1859, 2977, 221, 1079, 2587] (Forte: 6-Z10) is the complement of the hexatonic modal family [317, 977, 1103, 2599, 3347, 3721] (Forte: 6-Z39)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3341 is 1559

Scale 1559Scale 1559, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3341 is chiral, and its enantiomorph is scale 1559

Scale 1559Scale 1559, Ian Ring Music Theory

Transformations:

T0 3341  T0I 1559
T1 2587  T1I 3118
T2 1079  T2I 2141
T3 2158  T3I 187
T4 221  T4I 374
T5 442  T5I 748
T6 884  T6I 1496
T7 1768  T7I 2992
T8 3536  T8I 1889
T9 2977  T9I 3778
T10 1859  T10I 3461
T11 3718  T11I 2827

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 3343Scale 3343, Ian Ring Music Theory
Scale 3337Scale 3337, Ian Ring Music Theory
Scale 3339Scale 3339, Ian Ring Music Theory
Scale 3333Scale 3333, Ian Ring Music Theory
Scale 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic
Scale 3357Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian
Scale 3373Scale 3373: Lodian, Ian Ring Music TheoryLodian
Scale 3405Scale 3405: Stynian, Ian Ring Music TheoryStynian
Scale 3469Scale 3469: Monian, Ian Ring Music TheoryMonian
Scale 3085Scale 3085, Ian Ring Music Theory
Scale 3213Scale 3213: Eponimic, Ian Ring Music TheoryEponimic
Scale 3597Scale 3597, Ian Ring Music Theory
Scale 3853Scale 3853, Ian Ring Music Theory
Scale 2317Scale 2317, Ian Ring Music Theory
Scale 2829Scale 2829, Ian Ring Music Theory
Scale 1293Scale 1293, 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.