The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3641: "Thocrian"

Scale 3641: Thocrian, 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
Thocrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,4,5,9,10,11}
Forte Number7-7
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 911
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes6
Prime?no
prime: 463
Deep Scaleno
Interval Vector532353
Interval Spectrump5m3n2s3d5t3
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5}
<3> = {3,5,6}
<4> = {6,7,9}
<5> = {7,8,10}
<6> = {8,9,11}
Spectra Variation2.571
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}121
Minor Triadsam{9,0,4}210.67
Diminished Triads{9,0,3}121
Parsimonious Voice Leading Between Common Triads of Scale 3641. Created by Ian Ring ©2019 F F am am F->am a°->am

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.

Diameter2
Radius1
Self-Centeredno
Central Verticesam
Peripheral VerticesF, a°

Modes

Modes are the rotational transformation of this scale. Scale 3641 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 967
Scale 967: Mela Salaga, Ian Ring Music TheoryMela Salaga
3rd mode:
Scale 2531
Scale 2531: Danian, Ian Ring Music TheoryDanian
4th mode:
Scale 3313
Scale 3313: Aeolacrian, Ian Ring Music TheoryAeolacrian
5th mode:
Scale 463
Scale 463: Zythian, Ian Ring Music TheoryZythianThis is the prime mode
6th mode:
Scale 2279
Scale 2279: Dyrian, Ian Ring Music TheoryDyrian
7th mode:
Scale 3187
Scale 3187: Koptian, Ian Ring Music TheoryKoptian

Prime

The prime form of this scale is Scale 463

Scale 463Scale 463: Zythian, Ian Ring Music TheoryZythian

Complement

The heptatonic modal family [3641, 967, 2531, 3313, 463, 2279, 3187] (Forte: 7-7) is the complement of the pentatonic modal family [199, 451, 2147, 2273, 3121] (Forte: 5-7)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3641 is 911

Scale 911Scale 911: Radian, Ian Ring Music TheoryRadian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3641 is chiral, and its enantiomorph is scale 911

Scale 911Scale 911: Radian, Ian Ring Music TheoryRadian

Transformations:

T0 3641  T0I 911
T1 3187  T1I 1822
T2 2279  T2I 3644
T3 463  T3I 3193
T4 926  T4I 2291
T5 1852  T5I 487
T6 3704  T6I 974
T7 3313  T7I 1948
T8 2531  T8I 3896
T9 967  T9I 3697
T10 1934  T10I 3299
T11 3868  T11I 2503

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 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3645Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic
Scale 3633Scale 3633: Daptimic, Ian Ring Music TheoryDaptimic
Scale 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 3625Scale 3625: Podimic, Ian Ring Music TheoryPodimic
Scale 3609Scale 3609, Ian Ring Music Theory
Scale 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 3705Scale 3705: Messiaen Mode 4 Inverse, Ian Ring Music TheoryMessiaen Mode 4 Inverse
Scale 3769Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic
Scale 3897Scale 3897: Kalyllic, Ian Ring Music TheoryKalyllic
Scale 3129Scale 3129, Ian Ring Music Theory
Scale 3385Scale 3385: Chromatic Phrygian, Ian Ring Music TheoryChromatic Phrygian
Scale 2617Scale 2617: Pylimic, Ian Ring Music TheoryPylimic
Scale 1593Scale 1593: Zogimic, Ian Ring Music TheoryZogimic

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.