The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3465: "Katathimic"

Scale 3465: Katathimic, 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.

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
Katathimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,7,8,10,11}
Forte Number6-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 567
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 315
Deep Scaleno
Interval Vector323430
Interval Spectrump3m4n3s2d3
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5,7}
<3> = {4,5,7,8}
<4> = {5,7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation3.333
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
Coherenceno
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3465 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 945
Scale 945: Raga Saravati, Ian Ring Music TheoryRaga Saravati
3rd mode:
Scale 315
Scale 315: Stodimic, Ian Ring Music TheoryStodimicThis is the prime mode
4th mode:
Scale 2205
Scale 2205: Ionocrimic, Ian Ring Music TheoryIonocrimic
5th mode:
Scale 1575
Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic
6th mode:
Scale 2835
Scale 2835: Ionygimic, Ian Ring Music TheoryIonygimic

Prime

The prime form of this scale is Scale 315

Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic

Complement

The hexatonic modal family [3465, 945, 315, 2205, 1575, 2835] (Forte: 6-14) is the complement of the hexatonic modal family [315, 945, 1575, 2205, 2835, 3465] (Forte: 6-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3465 is 567

Scale 567Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3465 is chiral, and its enantiomorph is scale 567

Scale 567Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic

Transformations:

T0 3465  T0I 567
T1 2835  T1I 1134
T2 1575  T2I 2268
T3 3150  T3I 441
T4 2205  T4I 882
T5 315  T5I 1764
T6 630  T6I 3528
T7 1260  T7I 2961
T8 2520  T8I 1827
T9 945  T9I 3654
T10 1890  T10I 3213
T11 3780  T11I 2331

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 3467Scale 3467: Katonian, Ian Ring Music TheoryKatonian
Scale 3469Scale 3469: Monian, Ian Ring Music TheoryMonian
Scale 3457Scale 3457, Ian Ring Music Theory
Scale 3461Scale 3461, Ian Ring Music Theory
Scale 3473Scale 3473: Lathimic, Ian Ring Music TheoryLathimic
Scale 3481Scale 3481: Katathian, Ian Ring Music TheoryKatathian
Scale 3497Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian
Scale 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian
Scale 3337Scale 3337, Ian Ring Music Theory
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3721Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic
Scale 3977Scale 3977: Kythian, Ian Ring Music TheoryKythian
Scale 2441Scale 2441: Kyritonic, Ian Ring Music TheoryKyritonic
Scale 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
Scale 1417Scale 1417: Raga Shailaja, Ian Ring Music TheoryRaga Shailaja

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. Bibliography