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Scale 3351: "Karian"

Scale 3351: Karian, 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
Karian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,8,10,11}
Forte Number7-8
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections5
Modes6
Prime?no
prime: 381
Deep Scaleno
Interval Vector454422
Interval Spectrump2m4n4s5d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,6}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {6,9,10}
<6> = {8,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tones[0]
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 TriadsE{4,8,11}231.4
Minor Triadsc♯m{1,4,8}231.4
Augmented TriadsC+{0,4,8}221.2
Diminished Triadsg♯°{8,11,2}142
a♯°{10,1,4}142
Parsimonious Voice Leading Between Common Triads of Scale 3351. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E a#° a#° c#m->a#° g#° g#° E->g#°

view full size

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.

Diameter4
Radius2
Self-Centeredno
Central VerticesC+
Peripheral Verticesg♯°, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 3351 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3723
Scale 3723: Myptian, Ian Ring Music TheoryMyptian
3rd mode:
Scale 3909
Scale 3909: Rydian, Ian Ring Music TheoryRydian
4th mode:
Scale 2001
Scale 2001: Gydian, Ian Ring Music TheoryGydian
5th mode:
Scale 381
Scale 381: Kogian, Ian Ring Music TheoryKogianThis is the prime mode
6th mode:
Scale 1119
Scale 1119: Rarian, Ian Ring Music TheoryRarian
7th mode:
Scale 2607
Scale 2607: Aerolian, Ian Ring Music TheoryAerolian

Prime

The prime form of this scale is Scale 381

Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian

Complement

The heptatonic modal family [3351, 3723, 3909, 2001, 381, 1119, 2607] (Forte: 7-8) is the complement of the pentatonic modal family [93, 1047, 1857, 2571, 3333] (Forte: 5-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3351 is itself, because it is a palindromic scale!

Scale 3351Scale 3351: Karian, Ian Ring Music TheoryKarian

Transformations:

T0 3351  T0I 3351
T1 2607  T1I 2607
T2 1119  T2I 1119
T3 2238  T3I 2238
T4 381  T4I 381
T5 762  T5I 762
T6 1524  T6I 1524
T7 3048  T7I 3048
T8 2001  T8I 2001
T9 4002  T9I 4002
T10 3909  T10I 3909
T11 3723  T11I 3723

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 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic
Scale 3347Scale 3347: Synimic, Ian Ring Music TheorySynimic
Scale 3355Scale 3355: Bagian, Ian Ring Music TheoryBagian
Scale 3359Scale 3359: Bonyllic, Ian Ring Music TheoryBonyllic
Scale 3335Scale 3335, Ian Ring Music Theory
Scale 3343Scale 3343, Ian Ring Music Theory
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 3095Scale 3095, Ian Ring Music Theory
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3607Scale 3607, Ian Ring Music Theory
Scale 3863Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic
Scale 2327Scale 2327: Epalimic, Ian Ring Music TheoryEpalimic
Scale 2839Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
Scale 1303Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic

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.