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Scale 3407: "Katocryllic"

Scale 3407: Katocryllic, 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
Katocryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,6,8,10,11}
Forte Number8-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3671
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 703
Deep Scaleno
Interval Vector565552
Interval Spectrump5m5n5s6d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {4,5,6,7,8}
<5> = {5,6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.75
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3407 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3751
Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
3rd mode:
Scale 3923
Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic
4th mode:
Scale 4009
Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic
5th mode:
Scale 1013
Scale 1013: Stydyllic, Ian Ring Music TheoryStydyllic
6th mode:
Scale 1277
Scale 1277: Zadyllic, Ian Ring Music TheoryZadyllic
7th mode:
Scale 1343
Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic
8th mode:
Scale 2719
Scale 2719: Zocryllic, Ian Ring Music TheoryZocryllic

Prime

The prime form of this scale is Scale 703

Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic

Complement

The octatonic modal family [3407, 3751, 3923, 4009, 1013, 1277, 1343, 2719] (Forte: 8-11) is the complement of the tetratonic modal family [43, 1409, 1541, 2069] (Forte: 4-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3407 is 3671

Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3407 is chiral, and its enantiomorph is scale 3671

Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic

Transformations:

T0 3407  T0I 3671
T1 2719  T1I 3247
T2 1343  T2I 2399
T3 2686  T3I 703
T4 1277  T4I 1406
T5 2554  T5I 2812
T6 1013  T6I 1529
T7 2026  T7I 3058
T8 4052  T8I 2021
T9 4009  T9I 4042
T10 3923  T10I 3989
T11 3751  T11I 3883

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 3405Scale 3405: Stynian, Ian Ring Music TheoryStynian
Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian
Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 3439Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
Scale 3343Scale 3343, Ian Ring Music Theory
Scale 3375Scale 3375, Ian Ring Music Theory
Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
Scale 3535Scale 3535: Mylygic, Ian Ring Music TheoryMylygic
Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
Scale 3663Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
Scale 3919Scale 3919: Lynygic, Ian Ring Music TheoryLynygic
Scale 2383Scale 2383: Katorian, Ian Ring Music TheoryKatorian
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 1359Scale 1359: Aerygian, Ian Ring Music TheoryAerygian

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.