The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 221

Scale 221, 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{0,2,3,4,6,7}
Forte Number6-Z10
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1889
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


Modes are the rotational transformation of this scale. Scale 221 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1079
Scale 1079, Ian Ring Music Theory
3rd mode:
Scale 2587
Scale 2587, Ian Ring Music Theory
4th mode:
Scale 3341
Scale 3341, Ian Ring Music Theory
5th mode:
Scale 1859
Scale 1859, Ian Ring Music Theory
6th mode:
Scale 2977
Scale 2977, Ian Ring Music Theory


The prime form of this scale is Scale 187

Scale 187Scale 187, Ian Ring Music Theory


The hexatonic modal family [221, 1079, 2587, 3341, 1859, 2977] (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 221 is 1889

Scale 1889Scale 1889, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 221 is chiral, and its enantiomorph is scale 1889

Scale 1889Scale 1889, Ian Ring Music Theory


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

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 223Scale 223, Ian Ring Music Theory
Scale 217Scale 217, Ian Ring Music Theory
Scale 219Scale 219: Istrian, Ian Ring Music TheoryIstrian
Scale 213Scale 213, Ian Ring Music Theory
Scale 205Scale 205, Ian Ring Music Theory
Scale 237Scale 237, Ian Ring Music Theory
Scale 253Scale 253, Ian Ring Music Theory
Scale 157Scale 157, Ian Ring Music Theory
Scale 189Scale 189, Ian Ring Music Theory
Scale 93Scale 93, Ian Ring Music Theory
Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic
Scale 477Scale 477: Stacrian, Ian Ring Music TheoryStacrian
Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian
Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian
Scale 2269Scale 2269: Pygian, Ian Ring Music TheoryPygian

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler ( Peruse this Bibliography.