The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2679: "Rathyllic"

Scale 2679: Rathyllic, 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
Rathyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,6,9,11}
Forte Number8-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3531
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes7
Prime?no
prime: 759
Deep Scaleno
Interval Vector555562
Interval Spectrump6m5n5s5d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
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 TriadsD{2,6,9}341.9
F{5,9,0}341.9
A{9,1,4}242.1
Minor Triadsdm{2,5,9}331.7
f♯m{6,9,1}331.7
am{9,0,4}252.5
bm{11,2,6}252.5
Augmented TriadsC♯+{1,5,9}431.5
Diminished Triadsf♯°{6,9,0}242.1
{11,2,5}242.3
Parsimonious Voice Leading Between Common Triads of Scale 2679. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m A A C#+->A D D dm->D dm->b° D->f#m bm bm D->bm f#° f#° F->f#° am am F->am f#°->f#m am->A b°->bm

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 VerticesC♯+, dm, f♯m
Peripheral Verticesam, bm

Modes

Modes are the rotational transformation of this scale. Scale 2679 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3387
Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
3rd mode:
Scale 3741
Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
4th mode:
Scale 1959
Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic
5th mode:
Scale 3027
Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
6th mode:
Scale 3561
Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
7th mode:
Scale 957
Scale 957: Phronyllic, Ian Ring Music TheoryPhronyllic
8th mode:
Scale 1263
Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic

Prime

The prime form of this scale is Scale 759

Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic

Complement

The octatonic modal family [2679, 3387, 3741, 1959, 3027, 3561, 957, 1263] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2679 is 3531

Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2679 is chiral, and its enantiomorph is scale 3531

Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri

Transformations:

T0 2679  T0I 3531
T1 1263  T1I 2967
T2 2526  T2I 1839
T3 957  T3I 3678
T4 1914  T4I 3261
T5 3828  T5I 2427
T6 3561  T6I 759
T7 3027  T7I 1518
T8 1959  T8I 3036
T9 3918  T9I 1977
T10 3741  T10I 3954
T11 3387  T11I 3813

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 2677Scale 2677: Thodian, Ian Ring Music TheoryThodian
Scale 2675Scale 2675: Chromatic Lydian, Ian Ring Music TheoryChromatic Lydian
Scale 2683Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic
Scale 2687Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
Scale 2663Scale 2663: Lalian, Ian Ring Music TheoryLalian
Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
Scale 2647Scale 2647: Dadian, Ian Ring Music TheoryDadian
Scale 2615Scale 2615: Thoptian, Ian Ring Music TheoryThoptian
Scale 2743Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic
Scale 2807Scale 2807: Zylygic, Ian Ring Music TheoryZylygic
Scale 2935Scale 2935: Modygic, Ian Ring Music TheoryModygic
Scale 2167Scale 2167, Ian Ring Music Theory
Scale 2423Scale 2423, Ian Ring Music Theory
Scale 3191Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
Scale 631Scale 631: Zygian, Ian Ring Music TheoryZygian
Scale 1655Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic

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. Special thanks to Richard Repp for helping with technical accuracy.