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Scale 2405: "Katalimic"

Scale 2405: Katalimic, 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
Katalimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,5,6,8,11}
Forte Number6-30
Rotational Symmetry6 semitones
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1235
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes2
Prime?no
prime: 715
Deep Scaleno
Interval Vector224223
Interval Spectrump2m2n4s2d2t3
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {6}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedyes
Ridge Tonesnone
ProprietyProper
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
Minor Triadsfm{5,8,0}231.5
bm{11,2,6}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 2405. Created by Ian Ring ©2019 fm fm d°->fm d°->b° f°->fm g#° g#° f°->g#° bm bm g#°->bm b°->bm

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 2405 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 1625
Scale 1625: Lythimic, Ian Ring Music TheoryLythimic
3rd mode:
Scale 715
Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2This is the prime mode

Prime

The prime form of this scale is Scale 715

Scale 715Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2

Complement

The hexatonic modal family [2405, 1625, 715] (Forte: 6-30) is the complement of the hexatonic modal family [715, 1625, 2405] (Forte: 6-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2405 is 1235

Scale 1235Scale 1235: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2405 is chiral, and its enantiomorph is scale 1235

Scale 1235Scale 1235: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2

Transformations:

T0 2405  T0I 1235
T1 715  T1I 2470
T2 1430  T2I 845
T3 2860  T3I 1690
T4 1625  T4I 3380
T5 3250  T5I 2665
T6 2405  T6I 1235
T7 715  T7I 2470
T8 1430  T8I 845
T9 2860  T9I 1690
T10 1625  T10I 3380
T11 3250  T11I 2665

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 2407Scale 2407: Zylian, Ian Ring Music TheoryZylian
Scale 2401Scale 2401, Ian Ring Music Theory
Scale 2403Scale 2403: Lycrimic, Ian Ring Music TheoryLycrimic
Scale 2409Scale 2409: Zacrimic, Ian Ring Music TheoryZacrimic
Scale 2413Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
Scale 2421Scale 2421: Malian, Ian Ring Music TheoryMalian
Scale 2373Scale 2373: Dyptitonic, Ian Ring Music TheoryDyptitonic
Scale 2389Scale 2389: Eskimo Hexatonic 2, Ian Ring Music TheoryEskimo Hexatonic 2
Scale 2341Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
Scale 2469Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian
Scale 2149Scale 2149, Ian Ring Music Theory
Scale 2277Scale 2277: Kagimic, Ian Ring Music TheoryKagimic
Scale 2661Scale 2661: Stydimic, Ian Ring Music TheoryStydimic
Scale 2917Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 357Scale 357: Banitonic, Ian Ring Music TheoryBanitonic
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic

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.