The Exciting Universe Of Music Theory

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Scale 3105

Scale 3105, 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).


Cardinality4 (tetratonic)
Pitch Class Set{0,5,10,11}
Forte Number4-6
Rotational Symmetrynone
Reflection Axes5
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 135
Deep Scaleno
Interval Vector210021
Interval Spectrump2sd2t
Distribution Spectra<1> = {1,5}
<2> = {2,6,10}
<3> = {7,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1
Myhill Propertyno
Ridge Tones[10]

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 3105 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 225
Scale 225, Ian Ring Music Theory
3rd mode:
Scale 135
Scale 135, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2115
Scale 2115, Ian Ring Music Theory


The prime form of this scale is Scale 135

Scale 135Scale 135, Ian Ring Music Theory


The tetratonic modal family [3105, 225, 135, 2115] (Forte: 4-6) is the complement of the octatonic modal family [495, 1935, 2295, 3015, 3195, 3555, 3645, 3825] (Forte: 8-6)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3105 is 135

Scale 135Scale 135, Ian Ring Music Theory


T0 3105  T0I 135
T1 2115  T1I 270
T2 135  T2I 540
T3 270  T3I 1080
T4 540  T4I 2160
T5 1080  T5I 225
T6 2160  T6I 450
T7 225  T7I 900
T8 450  T8I 1800
T9 900  T9I 3600
T10 1800  T10I 3105
T11 3600  T11I 2115

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 3107Scale 3107, Ian Ring Music Theory
Scale 3109Scale 3109, Ian Ring Music Theory
Scale 3113Scale 3113, Ian Ring Music Theory
Scale 3121Scale 3121, Ian Ring Music Theory
Scale 3073Scale 3073, Ian Ring Music Theory
Scale 3089Scale 3089, Ian Ring Music Theory
Scale 3137Scale 3137, Ian Ring Music Theory
Scale 3169Scale 3169, Ian Ring Music Theory
Scale 3233Scale 3233, Ian Ring Music Theory
Scale 3361Scale 3361, Ian Ring Music Theory
Scale 3617Scale 3617, Ian Ring Music Theory
Scale 2081Scale 2081, Ian Ring Music Theory
Scale 2593Scale 2593, Ian Ring Music Theory
Scale 1057Scale 1057: Sansagari, Ian Ring Music TheorySansagari

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.