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Scale 1135: "Katolian"

Scale 1135: Katolian, 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

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



Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,5,6,10}
Forte Number7-11
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3781
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 379
Deep Scaleno
Interval Vector444441
Interval Spectrump4m4n4s4d4t
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Myhill Propertyno
Ridge Tonesnone


Modes are the rotational transformation of this scale. Scale 1135 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2615
Scale 2615: Thoptian, Ian Ring Music TheoryThoptian
3rd mode:
Scale 3355
Scale 3355: Bagian, Ian Ring Music TheoryBagian
4th mode:
Scale 3725
Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
5th mode:
Scale 1955
Scale 1955: Sonian, Ian Ring Music TheorySonian
6th mode:
Scale 3025
Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
7th mode:
Scale 445
Scale 445: Gocrian, Ian Ring Music TheoryGocrian


The prime form of this scale is Scale 379

Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian


The heptatonic modal family [1135, 2615, 3355, 3725, 1955, 3025, 445] (Forte: 7-11) is the complement of the pentatonic modal family [157, 929, 1063, 2579, 3337] (Forte: 5-11)


The inverse of a scale is a reflection using the root as its axis. The inverse of 1135 is 3781

Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian


Only scales that are chiral will have an enantiomorph. Scale 1135 is chiral, and its enantiomorph is scale 3781

Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian


T0 1135  T0I 3781
T1 2270  T1I 3467
T2 445  T2I 2839
T3 890  T3I 1583
T4 1780  T4I 3166
T5 3560  T5I 2237
T6 3025  T6I 379
T7 1955  T7I 758
T8 3910  T8I 1516
T9 3725  T9I 3032
T10 3355  T10I 1969
T11 2615  T11I 3938

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 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form
Scale 1127Scale 1127: Eparimic, Ian Ring Music TheoryEparimic
Scale 1143Scale 1143: Styrian, Ian Ring Music TheoryStyrian
Scale 1151Scale 1151: Mythyllic, Ian Ring Music TheoryMythyllic
Scale 1103Scale 1103: Lynimic, Ian Ring Music TheoryLynimic
Scale 1119Scale 1119: Rarian, Ian Ring Music TheoryRarian
Scale 1071Scale 1071, Ian Ring Music Theory
Scale 1199Scale 1199: Magian, Ian Ring Music TheoryMagian
Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic
Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic
Scale 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
Scale 111Scale 111, Ian Ring Music Theory
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 2159Scale 2159, Ian Ring Music Theory
Scale 3183Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic

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 ( Peruse this Bibliography.