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Scale 3433: "Thonian"

Scale 3433: Thonian, 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
Thonian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,5,6,8,10,11}
Forte Number7-29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 727
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes6
Prime?no
prime: 727
Deep Scaleno
Interval Vector344352
Interval Spectrump5m3n4s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.549
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 TriadsG♯{8,0,3}331.43
B{11,3,6}331.43
Minor Triadsd♯m{3,6,10}142.14
fm{5,8,0}241.86
g♯m{8,11,3}321.29
Diminished Triads{0,3,6}231.57
{5,8,11}231.71
Parsimonious Voice Leading Between Common Triads of Scale 3433. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B d#m d#m d#m->B fm fm f°->fm g#m g#m f°->g#m fm->G# g#m->G# g#m->B

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 Verticesg♯m
Peripheral Verticesd♯m, fm

Modes

Modes are the rotational transformation of this scale. Scale 3433 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 941
Scale 941: Mela Jhankaradhvani, Ian Ring Music TheoryMela Jhankaradhvani
3rd mode:
Scale 1259
Scale 1259: Stadian, Ian Ring Music TheoryStadian
4th mode:
Scale 2677
Scale 2677: Thodian, Ian Ring Music TheoryThodian
5th mode:
Scale 1693
Scale 1693: Dogian, Ian Ring Music TheoryDogian
6th mode:
Scale 1447
Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
7th mode:
Scale 2771
Scale 2771: Marva That, Ian Ring Music TheoryMarva That

Prime

The prime form of this scale is Scale 727

Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian

Complement

The heptatonic modal family [3433, 941, 1259, 2677, 1693, 1447, 2771] (Forte: 7-29) is the complement of the pentatonic modal family [331, 709, 1201, 1577, 2213] (Forte: 5-29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3433 is 727

Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3433 is chiral, and its enantiomorph is scale 727

Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian

Transformations:

T0 3433  T0I 727
T1 2771  T1I 1454
T2 1447  T2I 2908
T3 2894  T3I 1721
T4 1693  T4I 3442
T5 3386  T5I 2789
T6 2677  T6I 1483
T7 1259  T7I 2966
T8 2518  T8I 1837
T9 941  T9I 3674
T10 1882  T10I 3253
T11 3764  T11I 2411

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 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 3437Scale 3437, Ian Ring Music Theory
Scale 3425Scale 3425, Ian Ring Music Theory
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3441Scale 3441: Thacrian, Ian Ring Music TheoryThacrian
Scale 3449Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 3417Scale 3417: Golian, Ian Ring Music TheoryGolian
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 3497Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian
Scale 3561Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
Scale 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
Scale 3305Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
Scale 3689Scale 3689: Katocrian, Ian Ring Music TheoryKatocrian
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 2409Scale 2409: Zacrimic, Ian Ring Music TheoryZacrimic
Scale 2921Scale 2921: Pogian, Ian Ring Music TheoryPogian
Scale 1385Scale 1385: Phracrimic, Ian Ring Music TheoryPhracrimic

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.