The Exciting Universe Of Music Theory

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Scale 3461

Scale 3461, 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

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).


Cardinality6 (hexatonic)
Pitch Class Set{0,2,7,8,10,11}
Forte Number6-Z10
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1079
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
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
Ridge Tonesnone

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{7,11,2}210.67
Minor Triadsgm{7,10,2}121
Diminished Triadsg♯°{8,11,2}121
Parsimonious Voice Leading Between Common Triads of Scale 3461. Created by Ian Ring ©2019 gm gm Parsimonious Voice Leading Between Common Triads of Scale 3461. Created by Ian Ring ©2019 G gm->G g#° g#° G->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.

Central VerticesG
Peripheral Verticesgm, g♯°


Modes are the rotational transformation of this scale. Scale 3461 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1889
Scale 1889, Ian Ring Music Theory
3rd mode:
Scale 187
Scale 187, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2141
Scale 2141, Ian Ring Music Theory
5th mode:
Scale 1559
Scale 1559, Ian Ring Music Theory
6th mode:
Scale 2827
Scale 2827, Ian Ring Music Theory


The prime form of this scale is Scale 187

Scale 187Scale 187, Ian Ring Music Theory


The hexatonic modal family [3461, 1889, 187, 2141, 1559, 2827] (Forte: 6-Z10) is the complement of the hexatonic modal family [317, 977, 1103, 2599, 3347, 3721] (Forte: 6-Z39)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3461 is 1079

Scale 1079Scale 1079, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3461 is chiral, and its enantiomorph is scale 1079

Scale 1079Scale 1079, Ian Ring Music Theory


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

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 3463Scale 3463, Ian Ring Music Theory
Scale 3457Scale 3457, Ian Ring Music Theory
Scale 3459Scale 3459, Ian Ring Music Theory
Scale 3465Scale 3465: Katathimic, Ian Ring Music TheoryKatathimic
Scale 3469Scale 3469: Monian, Ian Ring Music TheoryMonian
Scale 3477Scale 3477: Kyptian, Ian Ring Music TheoryKyptian
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 3525Scale 3525: Zocrian, Ian Ring Music TheoryZocrian
Scale 3333Scale 3333, Ian Ring Music Theory
Scale 3397Scale 3397: Sydimic, Ian Ring Music TheorySydimic
Scale 3205Scale 3205, Ian Ring Music Theory
Scale 3717Scale 3717, Ian Ring Music Theory
Scale 3973Scale 3973, Ian Ring Music Theory
Scale 2437Scale 2437, Ian Ring Music Theory
Scale 2949Scale 2949, Ian Ring Music Theory
Scale 1413Scale 1413, 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 ( 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.