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Scale 3381: "Katanian"

Scale 3381: Katanian, 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

41161837294116105072918310504116183
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
Katanian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,4,5,8,10,11}
Forte Number7-28
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1431
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes6
Prime?no
prime: 747
Deep Scaleno
Interval Vector344433
Interval Spectrump3m4n4s4d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 3381 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1869
Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
3rd mode:
Scale 1491
Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani
4th mode:
Scale 2793
Scale 2793: Eporian, Ian Ring Music TheoryEporian
5th mode:
Scale 861
Scale 861: Rylian, Ian Ring Music TheoryRylian
6th mode:
Scale 1239
Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
7th mode:
Scale 2667
Scale 2667: Byrian, Ian Ring Music TheoryByrian

Prime

The prime form of this scale is Scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Complement

The heptatonic modal family [3381, 1869, 1491, 2793, 861, 1239, 2667] (Forte: 7-28) is the complement of the pentatonic modal family [333, 837, 1107, 1233, 2601] (Forte: 5-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3381 is 1431

Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3381 is chiral, and its enantiomorph is scale 1431

Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian

Transformations:

T0 3381  T0I 1431
T1 2667  T1I 2862
T2 1239  T2I 1629
T3 2478  T3I 3258
T4 861  T4I 2421
T5 1722  T5I 747
T6 3444  T6I 1494
T7 2793  T7I 2988
T8 1491  T8I 1881
T9 2982  T9I 3762
T10 1869  T10I 3429
T11 3738  T11I 2763

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 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 3377Scale 3377: Phralimic, Ian Ring Music TheoryPhralimic
Scale 3379Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
Scale 3385Scale 3385: Chromatic Phrygian, Ian Ring Music TheoryChromatic Phrygian
Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3373Scale 3373: Lodian, Ian Ring Music TheoryLodian
Scale 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic
Scale 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
Scale 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse
Scale 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
Scale 3125Scale 3125, Ian Ring Music Theory
Scale 3253Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini
Scale 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
Scale 2869Scale 2869: Ionian Augmented, Ian Ring Music TheoryIonian Augmented
Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic

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 (http://allthescales.org). Peruse this Bibliography.