The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3027: "Rythyllic"

Scale 3027: Rythyllic, 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
Rythyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,4,6,7,8,9,11}
Forte Number8-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2427
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 TriadsC{0,4,7}341.9
E{4,8,11}242.1
A{9,1,4}341.9
Minor Triadsc♯m{1,4,8}331.7
em{4,7,11}252.5
f♯m{6,9,1}252.5
am{9,0,4}331.7
Augmented TriadsC+{0,4,8}431.5
Diminished Triadsc♯°{1,4,7}242.1
f♯°{6,9,0}242.3
Parsimonious Voice Leading Between Common Triads of Scale 3027. 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 am am C+->am c#°->c#m A A c#m->A em->E f#° f#° f#m f#m f#°->f#m f#°->am f#m->A am->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 VerticesC+, c♯m, am
Peripheral Verticesem, f♯m

Modes

Modes are the rotational transformation of this scale. Scale 3027 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3561
Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
3rd mode:
Scale 957
Scale 957: Phronyllic, Ian Ring Music TheoryPhronyllic
4th mode:
Scale 1263
Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic
5th mode:
Scale 2679
Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
6th mode:
Scale 3387
Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
7th mode:
Scale 3741
Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
8th mode:
Scale 1959
Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic

Prime

The prime form of this scale is Scale 759

Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic

Complement

The octatonic modal family [3027, 3561, 957, 1263, 2679, 3387, 3741, 1959] (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 3027 is 2427

Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3027 is chiral, and its enantiomorph is scale 2427

Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic

Transformations:

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

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 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
Scale 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 3031Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 3011Scale 3011, Ian Ring Music Theory
Scale 3019Scale 3019, Ian Ring Music Theory
Scale 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
Scale 3059Scale 3059: Madygic, Ian Ring Music TheoryMadygic
Scale 2963Scale 2963: Bygian, Ian Ring Music TheoryBygian
Scale 2995Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian
Scale 2771Scale 2771: Marva That, Ian Ring Music TheoryMarva That
Scale 2515Scale 2515: Chromatic Hypolydian, Ian Ring Music TheoryChromatic Hypolydian
Scale 3539Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 4051Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic
Scale 979Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari
Scale 2003Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.