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Scale 439: "Bythian"

Scale 439: Bythian, 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
Bythian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,5,7,8}
Forte Number7-Z38
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3505
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {8,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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 TriadsC{0,4,7}241.86
C♯{1,5,8}331.43
Minor Triadsc♯m{1,4,8}321.29
fm{5,8,0}231.57
Augmented TriadsC+{0,4,8}331.43
Diminished Triadsc♯°{1,4,7}231.71
{2,5,8}142.14
Parsimonious Voice Leading Between Common Triads of Scale 439. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m fm fm C+->fm c#°->c#m C# C# c#m->C# C#->d° C#->fm

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♯m
Peripheral VerticesC, d°

Modes

Modes are the rotational transformation of this scale. Scale 439 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2267
Scale 2267: Padian, Ian Ring Music TheoryPadian
3rd mode:
Scale 3181
Scale 3181: Rolian, Ian Ring Music TheoryRolian
4th mode:
Scale 1819
Scale 1819: Pydian, Ian Ring Music TheoryPydian
5th mode:
Scale 2957
Scale 2957: Thygian, Ian Ring Music TheoryThygian
6th mode:
Scale 1763
Scale 1763: Katalian, Ian Ring Music TheoryKatalian
7th mode:
Scale 2929
Scale 2929: Aeolathian, Ian Ring Music TheoryAeolathian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [439, 2267, 3181, 1819, 2957, 1763, 2929] (Forte: 7-Z38) is the complement of the pentatonic modal family [295, 625, 905, 2195, 3145] (Forte: 5-Z38)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 439 is 3505

Scale 3505Scale 3505: Stygian, Ian Ring Music TheoryStygian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 439 is chiral, and its enantiomorph is scale 3505

Scale 3505Scale 3505: Stygian, Ian Ring Music TheoryStygian

Transformations:

T0 439  T0I 3505
T1 878  T1I 2915
T2 1756  T2I 1735
T3 3512  T3I 3470
T4 2929  T4I 2845
T5 1763  T5I 1595
T6 3526  T6I 3190
T7 2957  T7I 2285
T8 1819  T8I 475
T9 3638  T9I 950
T10 3181  T10I 1900
T11 2267  T11I 3800

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 437Scale 437: Ronimic, Ian Ring Music TheoryRonimic
Scale 435Scale 435: Raga Purna Pancama, Ian Ring Music TheoryRaga Purna Pancama
Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian
Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic
Scale 423Scale 423: Sogimic, Ian Ring Music TheorySogimic
Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian
Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic
Scale 471Scale 471: Dodian, Ian Ring Music TheoryDodian
Scale 503Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic
Scale 311Scale 311: Stagimic, Ian Ring Music TheoryStagimic
Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian
Scale 183Scale 183, Ian Ring Music Theory
Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian
Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic
Scale 1463Scale 1463, Ian Ring Music Theory
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic

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. Special thanks to Richard Repp for helping with technical accuracy.