The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 655: "Kataptimic"

Scale 655: Kataptimic, 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
Kataptimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,3,7,9}
Forte Number6-Z41
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3625
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 335
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,4,5,6}
<3> = {3,5,6,7,9}
<4> = {6,7,8,10}
<5> = {8,9,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
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
Minor Triadscm{0,3,7}110.5
Diminished Triads{9,0,3}110.5
Parsimonious Voice Leading Between Common Triads of Scale 655. Created by Ian Ring ©2019 cm cm cm->a°

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 655 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2375
Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic
3rd mode:
Scale 3235
Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
4th mode:
Scale 3665
Scale 3665: Stalimic, Ian Ring Music TheoryStalimic
5th mode:
Scale 485
Scale 485: Stoptimic, Ian Ring Music TheoryStoptimic
6th mode:
Scale 1145
Scale 1145: Zygimic, Ian Ring Music TheoryZygimic

Prime

The prime form of this scale is Scale 335

Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic

Complement

The hexatonic modal family [655, 2375, 3235, 3665, 485, 1145] (Forte: 6-Z41) is the complement of the hexatonic modal family [215, 1475, 1805, 2155, 2785, 3125] (Forte: 6-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 655 is 3625

Scale 3625Scale 3625: Podimic, Ian Ring Music TheoryPodimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 655 is chiral, and its enantiomorph is scale 3625

Scale 3625Scale 3625: Podimic, Ian Ring Music TheoryPodimic

Transformations:

T0 655  T0I 3625
T1 1310  T1I 3155
T2 2620  T2I 2215
T3 1145  T3I 335
T4 2290  T4I 670
T5 485  T5I 1340
T6 970  T6I 2680
T7 1940  T7I 1265
T8 3880  T8I 2530
T9 3665  T9I 965
T10 3235  T10I 1930
T11 2375  T11I 3860

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 653Scale 653: Dorian Pentatonic, Ian Ring Music TheoryDorian Pentatonic
Scale 651Scale 651: Golitonic, Ian Ring Music TheoryGolitonic
Scale 647Scale 647, Ian Ring Music Theory
Scale 663Scale 663: Phrynimic, Ian Ring Music TheoryPhrynimic
Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian
Scale 687Scale 687: Aeolythian, Ian Ring Music TheoryAeolythian
Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian
Scale 527Scale 527, Ian Ring Music Theory
Scale 591Scale 591: Gaptimic, Ian Ring Music TheoryGaptimic
Scale 783Scale 783, Ian Ring Music Theory
Scale 911Scale 911: Radian, Ian Ring Music TheoryRadian
Scale 143Scale 143, Ian Ring Music Theory
Scale 399Scale 399: Zynimic, Ian Ring Music TheoryZynimic
Scale 1167Scale 1167: Aerodimic, Ian Ring Music TheoryAerodimic
Scale 1679Scale 1679: Kydian, Ian Ring Music TheoryKydian
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian

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.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.