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Scale 3215: "Katydian"

Scale 3215: Katydian, 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
Katydian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,7,10,11}
Forte Number7-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3623
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 319
Deep Scaleno
Interval Vector544431
Interval Spectrump3m4n4s4d5t
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5,7}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {5,7,8,10}
<6> = {8,9,11}
Spectra Variation3.714
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 3215 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3655
Scale 3655: Mathian, Ian Ring Music TheoryMathian
3rd mode:
Scale 3875
Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
4th mode:
Scale 3985
Scale 3985: Thadian, Ian Ring Music TheoryThadian
5th mode:
Scale 505
Scale 505: Sanian, Ian Ring Music TheorySanian
6th mode:
Scale 575
Scale 575: Ionydian, Ian Ring Music TheoryIonydian
7th mode:
Scale 2335
Scale 2335: Epydian, Ian Ring Music TheoryEpydian

Prime

The prime form of this scale is Scale 319

Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian

Complement

The heptatonic modal family [3215, 3655, 3875, 3985, 505, 575, 2335] (Forte: 7-3) is the complement of the pentatonic modal family [55, 1795, 2075, 2945, 3085] (Forte: 5-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3215 is 3623

Scale 3623Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3215 is chiral, and its enantiomorph is scale 3623

Scale 3623Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian

Transformations:

T0 3215  T0I 3623
T1 2335  T1I 3151
T2 575  T2I 2207
T3 1150  T3I 319
T4 2300  T4I 638
T5 505  T5I 1276
T6 1010  T6I 2552
T7 2020  T7I 1009
T8 4040  T8I 2018
T9 3985  T9I 4036
T10 3875  T10I 3977
T11 3655  T11I 3859

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 3213Scale 3213: Eponimic, Ian Ring Music TheoryEponimic
Scale 3211Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic
Scale 3207Scale 3207, Ian Ring Music Theory
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3231Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
Scale 3247Scale 3247: Aeolonyllic, Ian Ring Music TheoryAeolonyllic
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
Scale 3087Scale 3087, Ian Ring Music Theory
Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
Scale 3343Scale 3343, Ian Ring Music Theory
Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
Scale 3727Scale 3727: Tholyllic, Ian Ring Music TheoryTholyllic
Scale 2191Scale 2191: Thydimic, Ian Ring Music TheoryThydimic
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 1167Scale 1167: Aerodimic, Ian Ring Music TheoryAerodimic

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.