The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1791: "Aerygyllian"

Scale 1791: Aerygyllian, 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
Aerygyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,5,6,7,9,10}
Forte Number10-3
Rotational Symmetrynone
Reflection Axes3.5
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?yes
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[7]
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}452.83
D{2,6,9}452.67
D♯{3,7,10}452.75
F{5,9,0}352.75
F♯{6,10,1}452.58
A{9,1,4}452.67
A♯{10,2,5}352.75
Minor Triadscm{0,3,7}452.83
dm{2,5,9}352.75
d♯m{3,6,10}452.67
f♯m{6,9,1}452.58
gm{7,10,2}352.75
am{9,0,4}452.75
a♯m{10,1,5}452.67
Augmented TriadsC♯+{1,5,9}552.5
D+{2,6,10}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 1791. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# cm->a° c#° c#° C->c#° C->e° am am C->am A A c#°->A C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m C#+->A a#m a#m C#+->a#m D D dm->D A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° D->f#m D+->d#m F# F# D+->F# gm gm D+->gm D+->A# d#°->d#m d#m->D# D#->e° D#->gm f#° f#° F->f#° F->am f#°->f#m f#m->F# F#->g° F#->a#m g°->gm a°->am am->A a#° a#° A->a#° a#°->a#m a#m->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 1791 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 2943
Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian
3rd mode:
Scale 3519
Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
4th mode:
Scale 3807
Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian
5th mode:
Scale 3951
Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
6th mode:
Scale 4023
Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
7th mode:
Scale 4059
Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
8th mode:
Scale 4077
Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
9th mode:
Scale 2043
Scale 2043: Maqam Tarzanuyn, Ian Ring Music TheoryMaqam Tarzanuyn
10th mode:
Scale 3069
Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza

Prime

This is the prime form of this scale.

Complement

The decatonic modal family [1791, 2943, 3519, 3807, 3951, 4023, 4059, 4077, 2043, 3069] (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 1791 is 4077

Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian

Transformations:

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

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 1789Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II
Scale 1787Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic
Scale 1783Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 1727Scale 1727: Sydygic, Ian Ring Music TheorySydygic
Scale 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian
Scale 2047Scale 2047: Monatic, Ian Ring Music TheoryMonatic
Scale 1279Scale 1279: Sarygic, Ian Ring Music TheorySarygic
Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian
Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic
Scale 2815Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
Scale 3839Scale 3839: Mixolatic, Ian Ring Music TheoryMixolatic

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.