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Scale 3221: "Bycrimic"

Scale 3221: Bycrimic, 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

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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).

Common Names

Zeitler
Bycrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,4,7,10,11}
Forte Number6-Z46
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1319
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 599
Deep Scaleno
Interval Vector233331
Interval Spectrump3m3n3s3d2t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5,6}
<3> = {4,5,7,8}
<4> = {6,7,8,9,10}
<5> = {9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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 TriadsC{0,4,7}131.6
G{7,11,2}221.2
Minor Triadsem{4,7,11}321
gm{7,10,2}231.4
Diminished Triads{4,7,10}221.2
Parsimonious Voice Leading Between Common Triads of Scale 3221. Created by Ian Ring ©2019 C C em em C->em e°->em gm gm e°->gm Parsimonious Voice Leading Between Common Triads of Scale 3221. Created by Ian Ring ©2019 G em->G gm->G

view full size

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.

Diameter3
Radius2
Self-Centeredno
Central Verticese°, em, G
Peripheral VerticesC, gm

Modes

Modes are the rotational transformation of this scale. Scale 3221 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1829
Scale 1829: Pathimic, Ian Ring Music TheoryPathimic
3rd mode:
Scale 1481
Scale 1481: Zagimic, Ian Ring Music TheoryZagimic
4th mode:
Scale 697
Scale 697: Lagimic, Ian Ring Music TheoryLagimic
5th mode:
Scale 599
Scale 599: Thyrimic, Ian Ring Music TheoryThyrimicThis is the prime mode
6th mode:
Scale 2347
Scale 2347: Raga Viyogavarali, Ian Ring Music TheoryRaga Viyogavarali

Prime

The prime form of this scale is Scale 599

Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic

Complement

The hexatonic modal family [3221, 1829, 1481, 697, 599, 2347] (Forte: 6-Z46) is the complement of the hexatonic modal family [347, 1457, 1579, 1733, 2221, 2837] (Forte: 6-Z24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3221 is 1319

Scale 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3221 is chiral, and its enantiomorph is scale 1319

Scale 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic

Transformations:

T0 3221  T0I 1319
T1 2347  T1I 2638
T2 599  T2I 1181
T3 1198  T3I 2362
T4 2396  T4I 629
T5 697  T5I 1258
T6 1394  T6I 2516
T7 2788  T7I 937
T8 1481  T8I 1874
T9 2962  T9I 3748
T10 1829  T10I 3401
T11 3658  T11I 2707

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 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3217Scale 3217: Molitonic, Ian Ring Music TheoryMolitonic
Scale 3219Scale 3219: Ionaphimic, Ian Ring Music TheoryIonaphimic
Scale 3225Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic
Scale 3229Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian
Scale 3205Scale 3205, Ian Ring Music Theory
Scale 3213Scale 3213: Eponimic, Ian Ring Music TheoryEponimic
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3253Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini
Scale 3285Scale 3285: Mela Citrambari, Ian Ring Music TheoryMela Citrambari
Scale 3093Scale 3093, Ian Ring Music Theory
Scale 3157Scale 3157: Zyptimic, Ian Ring Music TheoryZyptimic
Scale 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic
Scale 3477Scale 3477: Kyptian, Ian Ring Music TheoryKyptian
Scale 3733Scale 3733: Gycrian, Ian Ring Music TheoryGycrian
Scale 2197Scale 2197: Raga Hamsadhvani, Ian Ring Music TheoryRaga Hamsadhvani
Scale 2709Scale 2709: Raga Kumud, Ian Ring Music TheoryRaga Kumud
Scale 1173Scale 1173: Dominant Pentatonic, Ian Ring Music TheoryDominant Pentatonic

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 (http://allthescales.org) 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.