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Scale 3479: "Rothyllic"

Scale 3479: Rothyllic, 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
Rothyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,7,8,10,11}
Forte Number8-12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3383
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 763
Deep Scaleno
Interval Vector556543
Interval Spectrump4m5n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
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
E{4,8,11}342
G{7,11,2}342
Minor Triadsc♯m{1,4,8}342.17
em{4,7,11}441.83
gm{7,10,2}342.17
Augmented TriadsC+{0,4,8}342
Diminished Triadsc♯°{1,4,7}242.33
{4,7,10}242.17
{7,10,1}242.33
g♯°{8,11,2}242.33
a♯°{10,1,4}242.33
Parsimonious Voice Leading Between Common Triads of Scale 3479. 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 c#°->c#m a#° a#° c#m->a#° e°->em gm gm e°->gm em->E Parsimonious Voice Leading Between Common Triads of Scale 3479. Created by Ian Ring ©2019 G em->G g#° g#° E->g#° g°->gm g°->a#° gm->G G->g#°

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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 3479 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3787
Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
3rd mode:
Scale 3941
Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
4th mode:
Scale 2009
Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
5th mode:
Scale 763
Scale 763: Doryllic, Ian Ring Music TheoryDoryllicThis is the prime mode
6th mode:
Scale 2429
Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
7th mode:
Scale 1631
Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
8th mode:
Scale 2863
Scale 2863: Aerogyllic, Ian Ring Music TheoryAerogyllic

Prime

The prime form of this scale is Scale 763

Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic

Complement

The octatonic modal family [3479, 3787, 3941, 2009, 763, 2429, 1631, 2863] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3479 is 3383

Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3479 is chiral, and its enantiomorph is scale 3383

Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic

Transformations:

T0 3479  T0I 3383
T1 2863  T1I 2671
T2 1631  T2I 1247
T3 3262  T3I 2494
T4 2429  T4I 893
T5 763  T5I 1786
T6 1526  T6I 3572
T7 3052  T7I 3049
T8 2009  T8I 2003
T9 4018  T9I 4006
T10 3941  T10I 3917
T11 3787  T11I 3739

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 3477Scale 3477: Kyptian, Ian Ring Music TheoryKyptian
Scale 3475Scale 3475: Kylian, Ian Ring Music TheoryKylian
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
Scale 3463Scale 3463, Ian Ring Music Theory
Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
Scale 3495Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
Scale 3511Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 3351Scale 3351: Karian, Ian Ring Music TheoryKarian
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3735Scale 3735, Ian Ring Music Theory
Scale 3991Scale 3991: Badygic, Ian Ring Music TheoryBadygic
Scale 2455Scale 2455: Bothian, Ian Ring Music TheoryBothian
Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian

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.