The Exciting Universe Of Music Theory

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Scale 2785

Scale 2785, 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{0,5,6,7,9,11}
Forte Number6-Z12
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 235
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 215
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {7,10,11}
Spectra Variation3.333
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 TriadsF{5,9,0}110.5
Diminished Triadsf♯°{6,9,0}110.5
Parsimonious Voice Leading Between Common Triads of Scale 2785. Created by Ian Ring ©2019 F F f#° f#° F->f#°

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.



Modes are the rotational transformation of this scale. Scale 2785 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 215
Scale 215, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2155
Scale 2155, Ian Ring Music Theory
4th mode:
Scale 3125
Scale 3125, Ian Ring Music Theory
5th mode:
Scale 1805
Scale 1805, Ian Ring Music Theory
6th mode:
Scale 1475
Scale 1475, Ian Ring Music Theory


The prime form of this scale is Scale 215

Scale 215Scale 215, Ian Ring Music Theory


The hexatonic modal family [2785, 215, 2155, 3125, 1805, 1475] (Forte: 6-Z12) is the complement of the hexatonic modal family [335, 965, 1265, 2215, 3155, 3625] (Forte: 6-Z41)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2785 is 235

Scale 235Scale 235, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 2785 is chiral, and its enantiomorph is scale 235

Scale 235Scale 235, Ian Ring Music Theory


T0 2785  T0I 235
T1 1475  T1I 470
T2 2950  T2I 940
T3 1805  T3I 1880
T4 3610  T4I 3760
T5 3125  T5I 3425
T6 2155  T6I 2755
T7 215  T7I 1415
T8 430  T8I 2830
T9 860  T9I 1565
T10 1720  T10I 3130
T11 3440  T11I 2165

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 2787Scale 2787: Zyrian, Ian Ring Music TheoryZyrian
Scale 2789Scale 2789: Zolian, Ian Ring Music TheoryZolian
Scale 2793Scale 2793: Eporian, Ian Ring Music TheoryEporian
Scale 2801Scale 2801: Zogian, Ian Ring Music TheoryZogian
Scale 2753Scale 2753, Ian Ring Music Theory
Scale 2769Scale 2769: Dyrimic, Ian Ring Music TheoryDyrimic
Scale 2721Scale 2721: Raga Puruhutika, Ian Ring Music TheoryRaga Puruhutika
Scale 2657Scale 2657, Ian Ring Music Theory
Scale 2913Scale 2913, Ian Ring Music Theory
Scale 3041Scale 3041, Ian Ring Music Theory
Scale 2273Scale 2273, Ian Ring Music Theory
Scale 2529Scale 2529, Ian Ring Music Theory
Scale 3297Scale 3297, Ian Ring Music Theory
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 737Scale 737, Ian Ring Music Theory
Scale 1761Scale 1761, 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.