The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 447: "Thyphyllic"

Scale 447: Thyphyllic, 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
Thyphyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,5,7,8}
Forte Number8-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 4017
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?yes
Deep Scaleno
Interval Vector655552
Interval Spectrump5m5n5s5d6t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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}341.78
C♯{1,5,8}341.89
G♯{8,0,3}242
Minor Triadscm{0,3,7}252.33
c♯m{1,4,8}331.56
fm{5,8,0}231.78
Augmented TriadsC+{0,4,8}431.44
Diminished Triadsc♯°{1,4,7}231.89
{2,5,8}152.67
Parsimonious Voice Leading Between Common Triads of Scale 447. Created by Ian Ring ©2019 cm cm C C cm->C G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m fm fm C+->fm C+->G# 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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC+, c♯°, c♯m, fm
Peripheral Verticescm, d°

Modes

Modes are the rotational transformation of this scale. Scale 447 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2271
Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
3rd mode:
Scale 3183
Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic
4th mode:
Scale 3639
Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic
5th mode:
Scale 3867
Scale 3867: Storyllic, Ian Ring Music TheoryStoryllic
6th mode:
Scale 3981
Scale 3981: Phrycryllic, Ian Ring Music TheoryPhrycryllic
7th mode:
Scale 2019
Scale 2019: Palyllic, Ian Ring Music TheoryPalyllic
8th mode:
Scale 3057
Scale 3057: Phroryllic, Ian Ring Music TheoryPhroryllic

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [447, 2271, 3183, 3639, 3867, 3981, 2019, 3057] (Forte: 8-4) is the complement of the tetratonic modal family [39, 897, 2067, 3081] (Forte: 4-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 447 is 4017

Scale 4017Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 447 is chiral, and its enantiomorph is scale 4017

Scale 4017Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic

Transformations:

T0 447  T0I 4017
T1 894  T1I 3939
T2 1788  T2I 3783
T3 3576  T3I 3471
T4 3057  T4I 2847
T5 2019  T5I 1599
T6 4038  T6I 3198
T7 3981  T7I 2301
T8 3867  T8I 507
T9 3639  T9I 1014
T10 3183  T10I 2028
T11 2271  T11I 4056

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 445Scale 445: Gocrian, Ian Ring Music TheoryGocrian
Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian
Scale 415Scale 415: Aeoladian, Ian Ring Music TheoryAeoladian
Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic
Scale 511Scale 511: Polygic, Ian Ring Music TheoryPolygic
Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic
Scale 191Scale 191, Ian Ring Music Theory
Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic
Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic
Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic

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.