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Scale 2487: "Dothyllic"

Scale 2487: Dothyllic, 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
Dothyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,7,8,11}
Forte Number8-18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3507
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 879
Deep Scaleno
Interval Vector546553
Interval Spectrump5m5n6s4d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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}342.08
C♯{1,5,8}342.15
E{4,8,11}441.92
G{7,11,2}342.23
Minor Triadsc♯m{1,4,8}342.08
em{4,7,11}342
fm{5,8,0}342.08
Augmented TriadsC+{0,4,8}441.85
Diminished Triadsc♯°{1,4,7}242.46
{2,5,8}242.38
{5,8,11}242.31
g♯°{8,11,2}242.31
{11,2,5}242.46
Parsimonious Voice Leading Between Common Triads of Scale 2487. 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 fm fm C+->fm c#°->c#m C# C# c#m->C# C#->d° C#->fm d°->b° em->E Parsimonious Voice Leading Between Common Triads of Scale 2487. Created by Ian Ring ©2019 G em->G E->f° g#° g#° E->g#° f°->fm G->g#° G->b°

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2487 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3291
Scale 3291: Lygyllic, Ian Ring Music TheoryLygyllic
3rd mode:
Scale 3693
Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
4th mode:
Scale 1947
Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic
5th mode:
Scale 3021
Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
6th mode:
Scale 1779
Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
7th mode:
Scale 2937
Scale 2937: Phragyllic, Ian Ring Music TheoryPhragyllic
8th mode:
Scale 879
Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllicThis is the prime mode

Prime

The prime form of this scale is Scale 879

Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic

Complement

The octatonic modal family [2487, 3291, 3693, 1947, 3021, 1779, 2937, 879] (Forte: 8-18) is the complement of the tetratonic modal family [147, 609, 777, 2121] (Forte: 4-18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2487 is 3507

Scale 3507Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2487 is chiral, and its enantiomorph is scale 3507

Scale 3507Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz

Transformations:

T0 2487  T0I 3507
T1 879  T1I 2919
T2 1758  T2I 1743
T3 3516  T3I 3486
T4 2937  T4I 2877
T5 1779  T5I 1659
T6 3558  T6I 3318
T7 3021  T7I 2541
T8 1947  T8I 987
T9 3894  T9I 1974
T10 3693  T10I 3948
T11 3291  T11I 3801

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 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major
Scale 2483Scale 2483: Double Harmonic, Ian Ring Music TheoryDouble Harmonic
Scale 2491Scale 2491: Layllic, Ian Ring Music TheoryLayllic
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
Scale 2471Scale 2471: Mela Ganamurti, Ian Ring Music TheoryMela Ganamurti
Scale 2479Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
Scale 2455Scale 2455: Bothian, Ian Ring Music TheoryBothian
Scale 2519Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic
Scale 2551Scale 2551: Thocrygic, Ian Ring Music TheoryThocrygic
Scale 2359Scale 2359: Gadian, Ian Ring Music TheoryGadian
Scale 2423Scale 2423, Ian Ring Music Theory
Scale 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian
Scale 2743Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic
Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
Scale 3511Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 1463Scale 1463, Ian Ring Music Theory

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.