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Scale 1767: "Dyryllic"

Scale 1767: Dyryllic, 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

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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
Dyryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,5,6,7,9,10}
Forte Number8-20
Rotational Symmetrynone
Reflection Axes3.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 951
Deep Scaleno
Interval Vector545662
Interval Spectrump6m6n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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 TriadsD{2,6,9}331.83
F{5,9,0}252.5
F♯{6,10,1}431.67
A♯{10,2,5}342
Minor Triadsdm{2,5,9}342
f♯m{6,9,1}431.67
gm{7,10,2}252.5
a♯m{10,1,5}331.83
Augmented TriadsC♯+{1,5,9}441.83
D+{2,6,10}441.83
Diminished Triadsf♯°{6,9,0}242.33
{7,10,1}242.33
Parsimonious Voice Leading Between Common Triads of Scale 1767. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m D D dm->D A# A# dm->A# D+ D+ D->D+ D->f#m F# F# D+->F# gm gm D+->gm D+->A# f#° f#° F->f#° f#°->f#m f#m->F# F#->g° F#->a#m g°->gm 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
Radius3
Self-Centeredno
Central VerticesD, f♯m, F♯, a♯m
Peripheral VerticesF, gm

Modes

Modes are the rotational transformation of this scale. Scale 1767 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2931
Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic
3rd mode:
Scale 3513
Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
4th mode:
Scale 951
Scale 951: Thogyllic, Ian Ring Music TheoryThogyllicThis is the prime mode
5th mode:
Scale 2523
Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale
6th mode:
Scale 3309
Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
7th mode:
Scale 1851
Scale 1851: Zacryllic, Ian Ring Music TheoryZacryllic
8th mode:
Scale 2973
Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic

Prime

The prime form of this scale is Scale 951

Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic

Complement

The octatonic modal family [1767, 2931, 3513, 951, 2523, 3309, 1851, 2973] (Forte: 8-20) is the complement of the tetratonic modal family [291, 393, 561, 2193] (Forte: 4-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1767 is 3309

Scale 3309Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic

Transformations:

T0 1767  T0I 3309
T1 3534  T1I 2523
T2 2973  T2I 951
T3 1851  T3I 1902
T4 3702  T4I 3804
T5 3309  T5I 3513
T6 2523  T6I 2931
T7 951  T7I 1767
T8 1902  T8I 3534
T9 3804  T9I 2973
T10 3513  T10I 1851
T11 2931  T11I 3702

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 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian
Scale 1763Scale 1763: Katalian, Ian Ring Music TheoryKatalian
Scale 1771Scale 1771, Ian Ring Music Theory
Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic
Scale 1783Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
Scale 1735Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam
Scale 1751Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic
Scale 1703Scale 1703: Mela Vanaspati, Ian Ring Music TheoryMela Vanaspati
Scale 1639Scale 1639: Aeolothian, Ian Ring Music TheoryAeolothian
Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
Scale 2023Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
Scale 1255Scale 1255: Chromatic Mixolydian, Ian Ring Music TheoryChromatic Mixolydian
Scale 1511Scale 1511: Styptyllic, Ian Ring Music TheoryStyptyllic
Scale 743Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian Inverse
Scale 2791Scale 2791: Mixothyllic, Ian Ring Music TheoryMixothyllic
Scale 3815Scale 3815: Galygic, Ian Ring Music TheoryGalygic

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.