The Exciting Universe Of Music Theory

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Scale 3457

Scale 3457, 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).


Cardinality5 (pentatonic)
Pitch Class Set{0,7,8,10,11}
Forte Number5-3
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 55
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 55
Deep Scaleno
Interval Vector322210
Interval Spectrumpm2n2s2d3
Distribution Spectra<1> = {1,2,7}
<2> = {2,3,8}
<3> = {4,9,10}
<4> = {5,10,11}
Spectra Variation4.8
Maximally Evenno
Maximal Area Setno
Interior Area0.933
Myhill Propertyno
Ridge Tonesnone

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.


Modes are the rotational transformation of this scale. Scale 3457 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 59
Scale 59, Ian Ring Music Theory
3rd mode:
Scale 2077
Scale 2077, Ian Ring Music Theory
4th mode:
Scale 1543
Scale 1543, Ian Ring Music Theory
5th mode:
Scale 2819
Scale 2819, Ian Ring Music Theory


The prime form of this scale is Scale 55

Scale 55Scale 55, Ian Ring Music Theory


The pentatonic modal family [3457, 59, 2077, 1543, 2819] (Forte: 5-3) is the complement of the heptatonic modal family [319, 1009, 2207, 3151, 3623, 3859, 3977] (Forte: 7-3)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3457 is 55

Scale 55Scale 55, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3457 is chiral, and its enantiomorph is scale 55

Scale 55Scale 55, Ian Ring Music Theory


T0 3457  T0I 55
T1 2819  T1I 110
T2 1543  T2I 220
T3 3086  T3I 440
T4 2077  T4I 880
T5 59  T5I 1760
T6 118  T6I 3520
T7 236  T7I 2945
T8 472  T8I 1795
T9 944  T9I 3590
T10 1888  T10I 3085
T11 3776  T11I 2075

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 3459Scale 3459, Ian Ring Music Theory
Scale 3461Scale 3461, Ian Ring Music Theory
Scale 3465Scale 3465: Katathimic, Ian Ring Music TheoryKatathimic
Scale 3473Scale 3473: Lathimic, Ian Ring Music TheoryLathimic
Scale 3489Scale 3489, Ian Ring Music Theory
Scale 3521Scale 3521, Ian Ring Music Theory
Scale 3329Scale 3329, Ian Ring Music Theory
Scale 3393Scale 3393, Ian Ring Music Theory
Scale 3201Scale 3201, Ian Ring Music Theory
Scale 3713Scale 3713, Ian Ring Music Theory
Scale 3969Scale 3969, Ian Ring Music Theory
Scale 2433Scale 2433, Ian Ring Music Theory
Scale 2945Scale 2945, Ian Ring Music Theory
Scale 1409Scale 1409, 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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.