The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 4055: "Dagyllian"

Scale 4055: Dagyllian, 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
Dagyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,4,6,7,8,9,10,11}
Forte Number10-2
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia7 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1535
Deep Scaleno
Interval Vector898884
Interval Spectrump8m8n8s9d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {7,8,9}
<8> = {8,9,10}
<9> = {10,11}
Spectra Variation1.6
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[8]
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}352.7
D{2,6,9}252.8
E{4,8,11}352.7
F♯{6,10,1}452.6
G{7,11,2}452.6
A{9,1,4}452.6
Minor Triadsc♯m{1,4,8}352.7
em{4,7,11}452.6
f♯m{6,9,1}452.6
gm{7,10,2}452.6
am{9,0,4}352.7
bm{11,2,6}252.8
Augmented TriadsC+{0,4,8}452.6
D+{2,6,10}452.6
Diminished Triadsc♯°{1,4,7}253
{4,7,10}252.8
f♯°{6,9,0}252.9
{7,10,1}252.8
g♯°{8,11,2}252.9
a♯°{10,1,4}252.8
Parsimonious Voice Leading Between Common Triads of Scale 4055. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E am am C+->am c#°->c#m A A c#m->A D D D+ D+ D->D+ f#m f#m D->f#m F# F# D+->F# gm gm D+->gm bm bm D+->bm e°->em e°->gm em->E Parsimonious Voice Leading Between Common Triads of Scale 4055. Created by Ian Ring ©2019 G em->G g#° g#° E->g#° f#° f#° f#°->f#m f#°->am f#m->F# f#m->A F#->g° a#° a#° F#->a#° g°->gm gm->G G->g#° G->bm am->A A->a#°

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
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 4055 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 4075
Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
3rd mode:
Scale 4085
Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
4th mode:
Scale 2045
Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
5th mode:
Scale 1535
Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllianThis is the prime mode
6th mode:
Scale 2815
Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
7th mode:
Scale 3455
Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
8th mode:
Scale 3775
Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian
9th mode:
Scale 3935
Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
10th mode:
Scale 4015
Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian

Prime

The prime form of this scale is Scale 1535

Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian

Complement

The decatonic modal family [4055, 4075, 4085, 2045, 1535, 2815, 3455, 3775, 3935, 4015] (Forte: 10-2) is the complement of the modal family [5, 1025] (Forte: 2-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4055 is 3455

Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian

Transformations:

T0 4055  T0I 3455
T1 4015  T1I 2815
T2 3935  T2I 1535
T3 3775  T3I 3070
T4 3455  T4I 2045
T5 2815  T5I 4090
T6 1535  T6I 4085
T7 3070  T7I 4075
T8 2045  T8I 4055
T9 4090  T9I 4015
T10 4085  T10I 3935
T11 4075  T11I 3775

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 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
Scale 4051Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic
Scale 4059Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
Scale 4063Scale 4063: Eptatic, Ian Ring Music TheoryEptatic
Scale 4039Scale 4039: Ionogygic, Ian Ring Music TheoryIonogygic
Scale 4047Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian
Scale 4071Scale 4071: Rygyllian, Ian Ring Music TheoryRygyllian
Scale 4087Scale 4087: Aeolatic, Ian Ring Music TheoryAeolatic
Scale 3991Scale 3991: Badygic, Ian Ring Music TheoryBadygic
Scale 4023Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic
Scale 3799Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 3031Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
Scale 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic

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.