The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3399: "Zonian"

Scale 3399: Zonian, 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
Zonian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,6,8,10,11}
Forte Number7-9
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3159
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 351
Deep Scaleno
Interval Vector453432
Interval Spectrump3m4n3s5d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5,6}
<3> = {3,4,5,6,7,8}
<4> = {4,5,6,7,8,9}
<5> = {6,7,8,9,10}
<6> = {8,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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♯{6,10,1}131.5
Minor Triadsbm{11,2,6}221
Augmented TriadsD+{2,6,10}221
Diminished Triadsg♯°{8,11,2}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3399. Created by Ian Ring ©2019 D+ D+ F# F# D+->F# bm bm D+->bm g#° g#° g#°->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
Radius2
Self-Centeredno
Central VerticesD+, bm
Peripheral VerticesF♯, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 3399 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3747
Scale 3747: Myrian, Ian Ring Music TheoryMyrian
3rd mode:
Scale 3921
Scale 3921: Pythian, Ian Ring Music TheoryPythian
4th mode:
Scale 501
Scale 501: Katylian, Ian Ring Music TheoryKatylian
5th mode:
Scale 1149
Scale 1149: Bydian, Ian Ring Music TheoryBydian
6th mode:
Scale 1311
Scale 1311: Bynian, Ian Ring Music TheoryBynian
7th mode:
Scale 2703
Scale 2703: Galian, Ian Ring Music TheoryGalian

Prime

The prime form of this scale is Scale 351

Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian

Complement

The heptatonic modal family [3399, 3747, 3921, 501, 1149, 1311, 2703] (Forte: 7-9) is the complement of the pentatonic modal family [87, 1473, 1797, 2091, 3093] (Forte: 5-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3399 is 3159

Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3399 is chiral, and its enantiomorph is scale 3159

Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian

Transformations:

T0 3399  T0I 3159
T1 2703  T1I 2223
T2 1311  T2I 351
T3 2622  T3I 702
T4 1149  T4I 1404
T5 2298  T5I 2808
T6 501  T6I 1521
T7 1002  T7I 3042
T8 2004  T8I 1989
T9 4008  T9I 3978
T10 3921  T10I 3861
T11 3747  T11I 3627

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 3397Scale 3397: Sydimic, Ian Ring Music TheorySydimic
Scale 3395Scale 3395, Ian Ring Music Theory
Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian
Scale 3407Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3431Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
Scale 3335Scale 3335, Ian Ring Music Theory
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 3463Scale 3463, Ian Ring Music Theory
Scale 3527Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 3271Scale 3271: Mela Raghupriya, Ian Ring Music TheoryMela Raghupriya
Scale 3655Scale 3655: Mathian, Ian Ring Music TheoryMathian
Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
Scale 2375Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic
Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
Scale 1351Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic

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.