The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3899: "Katorygic"

Scale 3899: Katorygic, 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
Katorygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,4,5,8,9,10,11}
Forte Number9-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2975
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 959
Deep Scaleno
Interval Vector766773
Interval Spectrump7m7n6s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3899 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3997
Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
3rd mode:
Scale 2023
Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
4th mode:
Scale 3059
Scale 3059: Madygic, Ian Ring Music TheoryMadygic
5th mode:
Scale 3577
Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic
6th mode:
Scale 959
Scale 959: Katylygic, Ian Ring Music TheoryKatylygicThis is the prime mode
7th mode:
Scale 2527
Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
8th mode:
Scale 3311
Scale 3311: Mixodygic, Ian Ring Music TheoryMixodygic
9th mode:
Scale 3703
Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic

Prime

The prime form of this scale is Scale 959

Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic

Complement

The nonatonic modal family [3899, 3997, 2023, 3059, 3577, 959, 2527, 3311, 3703] (Forte: 9-4) is the complement of the tritonic modal family [35, 385, 2065] (Forte: 3-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3899 is 2975

Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3899 is chiral, and its enantiomorph is scale 2975

Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic

Transformations:

T0 3899  T0I 2975
T1 3703  T1I 1855
T2 3311  T2I 3710
T3 2527  T3I 3325
T4 959  T4I 2555
T5 1918  T5I 1015
T6 3836  T6I 2030
T7 3577  T7I 4060
T8 3059  T8I 4025
T9 2023  T9I 3955
T10 4046  T10I 3815
T11 3997  T11I 3535

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 3897Scale 3897: Kalyllic, Ian Ring Music TheoryKalyllic
Scale 3901Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
Scale 3903Scale 3903: Aeogyllian, Ian Ring Music TheoryAeogyllian
Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
Scale 3895Scale 3895: Eparygic, Ian Ring Music TheoryEparygic
Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
Scale 3867Scale 3867: Storyllic, Ian Ring Music TheoryStoryllic
Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 3963Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
Scale 4027Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3771Scale 3771: Katodyllian, Ian Ring Music TheoryKatodyllian
Scale 3387Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
Scale 2875Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic
Scale 1851Scale 1851: Zacryllic, Ian Ring Music TheoryZacryllic

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.