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Scale 3635: "Katygian"

Scale 3635: Katygian, 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
Katygian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,4,5,9,10,11}
Forte Number7-6
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2447
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes6
Prime?no
prime: 415
Deep Scaleno
Interval Vector533442
Interval Spectrump4m4n3s3d5t2
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {7,8,10}
<6> = {8,9,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.183
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsF{5,9,0}231.5
A{9,1,4}321.17
Minor Triadsam{9,0,4}231.5
a♯m{10,1,5}231.5
Augmented TriadsC♯+{1,5,9}321.17
Diminished Triadsa♯°{10,1,4}231.5
Parsimonious Voice Leading Between Common Triads of Scale 3635. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F A A C#+->A a#m a#m C#+->a#m am am F->am am->A a#° a#° A->a#° a#°->a#m

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
Radius2
Self-Centeredno
Central VerticesC♯+, A
Peripheral VerticesF, am, a♯°, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3635 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3865
Scale 3865: Starian, Ian Ring Music TheoryStarian
3rd mode:
Scale 995
Scale 995: Phrathian, Ian Ring Music TheoryPhrathian
4th mode:
Scale 2545
Scale 2545: Thycrian, Ian Ring Music TheoryThycrian
5th mode:
Scale 415
Scale 415: Aeoladian, Ian Ring Music TheoryAeoladianThis is the prime mode
6th mode:
Scale 2255
Scale 2255: Dylian, Ian Ring Music TheoryDylian
7th mode:
Scale 3175
Scale 3175: Eponian, Ian Ring Music TheoryEponian

Prime

The prime form of this scale is Scale 415

Scale 415Scale 415: Aeoladian, Ian Ring Music TheoryAeoladian

Complement

The heptatonic modal family [3635, 3865, 995, 2545, 415, 2255, 3175] (Forte: 7-6) is the complement of the pentatonic modal family [103, 899, 2099, 2497, 3097] (Forte: 5-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3635 is 2447

Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3635 is chiral, and its enantiomorph is scale 2447

Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian

Transformations:

T0 3635  T0I 2447
T1 3175  T1I 799
T2 2255  T2I 1598
T3 415  T3I 3196
T4 830  T4I 2297
T5 1660  T5I 499
T6 3320  T6I 998
T7 2545  T7I 1996
T8 995  T8I 3992
T9 1990  T9I 3889
T10 3980  T10I 3683
T11 3865  T11I 3271

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 3633Scale 3633: Daptimic, Ian Ring Music TheoryDaptimic
Scale 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 3639Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
Scale 3627Scale 3627: Kalian, Ian Ring Music TheoryKalian
Scale 3603Scale 3603, Ian Ring Music Theory
Scale 3667Scale 3667: Kaptian, Ian Ring Music TheoryKaptian
Scale 3699Scale 3699: Galyllic, Ian Ring Music TheoryGalyllic
Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
Scale 3123Scale 3123, Ian Ring Music Theory
Scale 3379Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
Scale 2611Scale 2611: Raga Vasanta, Ian Ring Music TheoryRaga Vasanta
Scale 1587Scale 1587: Raga Rudra Pancama, Ian Ring Music TheoryRaga Rudra Pancama

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.