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Scale 3231: "Kataptyllic"

Scale 3231: Kataptyllic, 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
Kataptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,7,10,11}
Forte Number8-3
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 639
Deep Scaleno
Interval Vector656542
Interval Spectrump4m5n6s5d6t2
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {3,5,7}
<4> = {4,6,8}
<5> = {5,7,9}
<6> = {6,8,10}
<7> = {9,11}
Spectra Variation3
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tones[2]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3231 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3663
Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
3rd mode:
Scale 3879
Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
4th mode:
Scale 3987
Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic
5th mode:
Scale 4041
Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
6th mode:
Scale 1017
Scale 1017: Dythyllic, Ian Ring Music TheoryDythyllic
7th mode:
Scale 639
Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllicThis is the prime mode
8th mode:
Scale 2367
Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic

Prime

The prime form of this scale is Scale 639

Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic

Complement

The octatonic modal family [3231, 3663, 3879, 3987, 4041, 1017, 639, 2367] (Forte: 8-3) is the complement of the tetratonic modal family [27, 1539, 2061, 2817] (Forte: 4-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3231 is 3879

Scale 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic

Transformations:

T0 3231  T0I 3879
T1 2367  T1I 3663
T2 639  T2I 3231
T3 1278  T3I 2367
T4 2556  T4I 639
T5 1017  T5I 1278
T6 2034  T6I 2556
T7 4068  T7I 1017
T8 4041  T8I 2034
T9 3987  T9I 4068
T10 3879  T10I 4041
T11 3663  T11I 3987

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 3229Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian
Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian
Scale 3247Scale 3247: Aeolonyllic, Ian Ring Music TheoryAeolonyllic
Scale 3263Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3103Scale 3103, Ian Ring Music Theory
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3359Scale 3359: Bonyllic, Ian Ring Music TheoryBonyllic
Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
Scale 3743Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
Scale 2207Scale 2207: Mygian, Ian Ring Music TheoryMygian
Scale 2719Scale 2719: Zocryllic, Ian Ring Music TheoryZocryllic
Scale 1183Scale 1183: Sadian, Ian Ring Music TheorySadian

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.