The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3807: "Bagyllian"

Scale 3807: Bagyllian, 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
Bagyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,6,7,9,10,11}
Forte Number10-3
Rotational Symmetrynone
Reflection Axes0.5
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1791
Deep Scaleno
Interval Vector889884
Interval Spectrump8m8n9s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {7,8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1.4
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[1]
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}452.75
D{2,6,9}352.75
D♯{3,7,10}452.58
F♯{6,10,1}452.67
G{7,11,2}352.75
A{9,1,4}452.83
B{11,3,6}452.67
Minor Triadscm{0,3,7}452.67
d♯m{3,6,10}452.58
em{4,7,11}352.75
f♯m{6,9,1}452.75
gm{7,10,2}452.67
am{9,0,4}452.83
bm{11,2,6}352.75
Augmented TriadsD+{2,6,10}552.5
D♯+{3,7,11}552.5
Diminished Triads{0,3,6}253
c♯°{1,4,7}253
d♯°{3,6,9}253
{4,7,10}253
f♯°{6,9,0}253
{7,10,1}253
{9,0,3}253
a♯°{10,1,4}253
Parsimonious Voice Leading Between Common Triads of Scale 3807. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ cm->a° c#° c#° C->c#° em em C->em am am C->am A A c#°->A D D D+ D+ D->D+ d#° d#° D->d#° f#m f#m D->f#m d#m d#m D+->d#m F# F# D+->F# gm gm D+->gm bm bm D+->bm d#°->d#m D# D# d#m->D# d#m->B D#->D#+ D#->e° D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3807. Created by Ian Ring ©2019 G D#+->G D#+->B e°->em f#° f#° f#°->f#m f#°->am f#m->F# f#m->A F#->g° a#° a#° F#->a#° g°->gm gm->G G->bm a°->am am->A A->a#° bm->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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3807 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3951
Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
3rd mode:
Scale 4023
Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
4th mode:
Scale 4059
Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
5th mode:
Scale 4077
Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
6th mode:
Scale 2043
Scale 2043: Maqam Tarzanuyn, Ian Ring Music TheoryMaqam Tarzanuyn
7th mode:
Scale 3069
Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza
8th mode:
Scale 1791
Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllianThis is the prime mode
9th mode:
Scale 2943
Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian
10th mode:
Scale 3519
Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi

Prime

The prime form of this scale is Scale 1791

Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian

Complement

The decatonic modal family [3807, 3951, 4023, 4059, 4077, 2043, 3069, 1791, 2943, 3519] (Forte: 10-3) is the complement of the modal family [9, 513] (Forte: 2-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3807 is 3951

Scale 3951Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian

Transformations:

T0 3807  T0I 3951
T1 3519  T1I 3807
T2 2943  T2I 3519
T3 1791  T3I 2943
T4 3582  T4I 1791
T5 3069  T5I 3582
T6 2043  T6I 3069
T7 4086  T7I 2043
T8 4077  T8I 4086
T9 4059  T9I 4077
T10 4023  T10I 4059
T11 3951  T11I 4023

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 3805Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
Scale 3803Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
Scale 3799Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
Scale 3791Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
Scale 3823Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian
Scale 3839Scale 3839: Mixolatic, Ian Ring Music TheoryMixolatic
Scale 3743Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
Scale 3775Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian
Scale 3679Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
Scale 3935Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
Scale 4063Scale 4063: Eptatic, Ian Ring Music TheoryEptatic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic

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.