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Scale 1781: "Gocryllic"

Scale 1781: Gocryllic, 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
Gocryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,4,5,6,7,9,10}
Forte Number8-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1517
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}242.3
D{2,6,9}341.9
F{5,9,0}341.9
A♯{10,2,5}242.1
Minor Triadsdm{2,5,9}341.9
gm{7,10,2}242.1
am{9,0,4}242.1
Augmented TriadsD+{2,6,10}341.9
Diminished Triads{4,7,10}242.3
f♯°{6,9,0}242.1
Parsimonious Voice Leading Between Common Triads of Scale 1781. Created by Ian Ring ©2019 C C C->e° am am C->am dm dm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm D+->A# e°->gm F->f#° F->am

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 1781 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1469
Scale 1469: Epiryllic, Ian Ring Music TheoryEpiryllic
3rd mode:
Scale 1391
Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllicThis is the prime mode
4th mode:
Scale 2743
Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic
5th mode:
Scale 3419
Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
6th mode:
Scale 3757
Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
7th mode:
Scale 1963
Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic
8th mode:
Scale 3029
Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic

Prime

The prime form of this scale is Scale 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Complement

The octatonic modal family [1781, 1469, 1391, 2743, 3419, 3757, 1963, 3029] (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 1781 is 1517

Scale 1517Scale 1517: Sagyllic, Ian Ring Music TheorySagyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1781 is chiral, and its enantiomorph is scale 1517

Scale 1517Scale 1517: Sagyllic, Ian Ring Music TheorySagyllic

Transformations:

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

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 1783Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
Scale 1777Scale 1777: Saptian, Ian Ring Music TheorySaptian
Scale 1779Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
Scale 1785Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
Scale 1789Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II
Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian
Scale 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
Scale 1653Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
Scale 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
Scale 2037Scale 2037: Sythygic, Ian Ring Music TheorySythygic
Scale 1269Scale 1269: Katythian, Ian Ring Music TheoryKatythian
Scale 1525Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
Scale 757Scale 757: Ionyptian, Ian Ring Music TheoryIonyptian
Scale 2805Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho

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.