The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1439: "Rolyllic"

Scale 1439: Rolyllic, 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
Rolyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,7,8,10}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3893
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 863
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {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}441.82
D♯{3,7,10}342
G♯{8,0,3}242.18
Minor Triadscm{0,3,7}341.91
c♯m{1,4,8}342
gm{7,10,2}242.27
Augmented TriadsC+{0,4,8}341.91
Diminished Triadsc♯°{1,4,7}242.09
{4,7,10}242.09
{7,10,1}242.36
a♯°{10,1,4}242.27
Parsimonious Voice Leading Between Common Triads of Scale 1439. Created by Ian Ring ©2019 cm cm C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° C->e° c#m c#m C+->c#m C+->G# c#°->c#m a#° a#° c#m->a#° D#->e° gm gm D#->gm g°->gm g°->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1439 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2767
Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic
3rd mode:
Scale 3431
Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
4th mode:
Scale 3763
Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
5th mode:
Scale 3929
Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
6th mode:
Scale 1003
Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
7th mode:
Scale 2549
Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
8th mode:
Scale 1661
Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [1439, 2767, 3431, 3763, 3929, 1003, 2549, 1661] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1439 is 3893

Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1439 is chiral, and its enantiomorph is scale 3893

Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic

Transformations:

T0 1439  T0I 3893
T1 2878  T1I 3691
T2 1661  T2I 3287
T3 3322  T3I 2479
T4 2549  T4I 863
T5 1003  T5I 1726
T6 2006  T6I 3452
T7 4012  T7I 2809
T8 3929  T8I 1523
T9 3763  T9I 3046
T10 3431  T10I 1997
T11 2767  T11I 3994

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 1437Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending
Scale 1435Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam
Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian
Scale 1423Scale 1423: Doptian, Ian Ring Music TheoryDoptian
Scale 1455Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolian
Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic
Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic
Scale 1311Scale 1311: Bynian, Ian Ring Music TheoryBynian
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic
Scale 1183Scale 1183: Sadian, Ian Ring Music TheorySadian
Scale 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic
Scale 1951Scale 1951: Marygic, Ian Ring Music TheoryMarygic
Scale 415Scale 415: Aeoladian, Ian Ring Music TheoryAeoladian
Scale 927Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllic
Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic

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.