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Scale 3797: "Rocryllic"

Scale 3797: Rocryllic, 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

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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
Rocryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,4,6,7,9,10,11}
Forte Number8-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1391
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 1391
Deep Scaleno
Interval Vector465562
Interval Spectrump6m5n5s6d4t2
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.75
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
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}242.1
D{2,6,9}242.1
G{7,11,2}341.9
Minor Triadsem{4,7,11}341.9
gm{7,10,2}341.9
am{9,0,4}242.3
bm{11,2,6}242.1
Augmented TriadsD+{2,6,10}341.9
Diminished Triads{4,7,10}242.1
f♯°{6,9,0}242.3
Parsimonious Voice Leading Between Common Triads of Scale 3797. Created by Ian Ring ©2019 C C em em C->em am am C->am D D D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm bm bm D+->bm e°->em e°->gm Parsimonious Voice Leading Between Common Triads of Scale 3797. Created by Ian Ring ©2019 G em->G f#°->am gm->G G->bm

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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 3797 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1973
Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
3rd mode:
Scale 1517
Scale 1517: Sagyllic, Ian Ring Music TheorySagyllic
4th mode:
Scale 1403
Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale
5th mode:
Scale 2749
Scale 2749: Katagyllic, Ian Ring Music TheoryKatagyllic
6th mode:
Scale 1711
Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh
7th mode:
Scale 2903
Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
8th mode:
Scale 3499
Scale 3499: Hamel, Ian Ring Music TheoryHamel

Prime

The prime form of this scale is Scale 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Complement

The octatonic modal family [3797, 1973, 1517, 1403, 2749, 1711, 2903, 3499] (Forte: 8-22) is the complement of the tetratonic modal family [149, 673, 1061, 1289] (Forte: 4-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3797 is 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3797 is chiral, and its enantiomorph is scale 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Transformations:

T0 3797  T0I 1391
T1 3499  T1I 2782
T2 2903  T2I 1469
T3 1711  T3I 2938
T4 3422  T4I 1781
T5 2749  T5I 3562
T6 1403  T6I 3029
T7 2806  T7I 1963
T8 1517  T8I 3926
T9 3034  T9I 3757
T10 1973  T10I 3419
T11 3946  T11I 2743

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 3799Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
Scale 3793Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 3805Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
Scale 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 3733Scale 3733: Gycrian, Ian Ring Music TheoryGycrian
Scale 3765Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
Scale 3669Scale 3669: Mothian, Ian Ring Music TheoryMothian
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
Scale 3285Scale 3285: Mela Citrambari, Ian Ring Music TheoryMela Citrambari
Scale 3541Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
Scale 2773Scale 2773: Lydian, Ian Ring Music TheoryLydian
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic

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.