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Scale 3365: "Katolimic"

Scale 3365: Katolimic, 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
Katolimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,5,8,10,11}
Forte Number6-Z45
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes5
Prime?no
prime: 605
Deep Scaleno
Interval Vector234222
Interval Spectrump2m2n4s3d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5,6}
<3> = {4,6,8}
<4> = {6,7,9,10}
<5> = {9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[10]
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsA♯{10,2,5}231.5
Minor Triadsfm{5,8,0}231.5
Diminished Triads{2,5,8}231.5
{5,8,11}231.5
g♯°{8,11,2}231.5
{11,2,5}231.5
Parsimonious Voice Leading Between Common Triads of Scale 3365. Created by Ian Ring ©2019 fm fm d°->fm A# A# d°->A# f°->fm g#° g#° f°->g#° g#°->b° A#->b°

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3365 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1865
Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
3rd mode:
Scale 745
Scale 745: Kolimic, Ian Ring Music TheoryKolimic
4th mode:
Scale 605
Scale 605: Dycrimic, Ian Ring Music TheoryDycrimicThis is the prime mode
5th mode:
Scale 1175
Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
6th mode:
Scale 2635
Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic

Prime

The prime form of this scale is Scale 605

Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic

Complement

The hexatonic modal family [3365, 1865, 745, 605, 1175, 2635] (Forte: 6-Z45) is the complement of the hexatonic modal family [365, 1115, 1675, 1745, 2605, 2885] (Forte: 6-Z23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3365 is 1175

Scale 1175Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic

Transformations:

T0 3365  T0I 1175
T1 2635  T1I 2350
T2 1175  T2I 605
T3 2350  T3I 1210
T4 605  T4I 2420
T5 1210  T5I 745
T6 2420  T6I 1490
T7 745  T7I 2980
T8 1490  T8I 1865
T9 2980  T9I 3730
T10 1865  T10I 3365
T11 3730  T11I 2635

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 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 3361Scale 3361, Ian Ring Music Theory
Scale 3363Scale 3363: Rogimic, Ian Ring Music TheoryRogimic
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 3373Scale 3373: Lodian, Ian Ring Music TheoryLodian
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian
Scale 3333Scale 3333, Ian Ring Music Theory
Scale 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic
Scale 3397Scale 3397: Sydimic, Ian Ring Music TheorySydimic
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 3109Scale 3109, Ian Ring Music Theory
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3621Scale 3621: Gylimic, Ian Ring Music TheoryGylimic
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 2341Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
Scale 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 1317Scale 1317: Chaio, Ian Ring Music TheoryChaio

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, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.