The Exciting Universe Of Music Theory

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Scale 2821

Scale 2821, 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{0,2,8,9,11}
Forte Number5-10
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1051
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
prime: 91
Deep Scaleno
Interval Vector223111
Interval Spectrumpmn3s2d2t
Distribution Spectra<1> = {1,2,6}
<2> = {3,7,8}
<3> = {4,5,9}
<4> = {6,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.366
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
Diminished Triadsg♯°{8,11,2}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.


Modes are the rotational transformation of this scale. Scale 2821 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1729
Scale 1729, Ian Ring Music Theory
3rd mode:
Scale 91
Scale 91, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2093
Scale 2093, Ian Ring Music Theory
5th mode:
Scale 1547
Scale 1547, Ian Ring Music Theory


The prime form of this scale is Scale 91

Scale 91Scale 91, Ian Ring Music Theory


The pentatonic modal family [2821, 1729, 91, 2093, 1547] (Forte: 5-10) is the complement of the heptatonic modal family [607, 761, 1993, 2351, 3223, 3659, 3877] (Forte: 7-10)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2821 is 1051

Scale 1051Scale 1051, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 2821 is chiral, and its enantiomorph is scale 1051

Scale 1051Scale 1051, Ian Ring Music Theory


T0 2821  T0I 1051
T1 1547  T1I 2102
T2 3094  T2I 109
T3 2093  T3I 218
T4 91  T4I 436
T5 182  T5I 872
T6 364  T6I 1744
T7 728  T7I 3488
T8 1456  T8I 2881
T9 2912  T9I 1667
T10 1729  T10I 3334
T11 3458  T11I 2573

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 2823Scale 2823, Ian Ring Music Theory
Scale 2817Scale 2817, Ian Ring Music Theory
Scale 2819Scale 2819, Ian Ring Music Theory
Scale 2825Scale 2825, Ian Ring Music Theory
Scale 2829Scale 2829, Ian Ring Music Theory
Scale 2837Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
Scale 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
Scale 2949Scale 2949, Ian Ring Music Theory
Scale 2565Scale 2565, Ian Ring Music Theory
Scale 2693Scale 2693, Ian Ring Music Theory
Scale 2309Scale 2309, Ian Ring Music Theory
Scale 3333Scale 3333, Ian Ring Music Theory
Scale 3845Scale 3845, Ian Ring Music Theory
Scale 773Scale 773, Ian Ring Music Theory
Scale 1797Scale 1797, 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.