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Scale 3067: "Goptyllian"

Scale 3067: Goptyllian, 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
Goptyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,3,4,5,6,7,8,9,11}
Forte Number10-4
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1919
Deep Scaleno
Interval Vector888984
Interval Spectrump8m9n8s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1.2
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[0]
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}452.43
C♯{1,5,8}352.74
E{4,8,11}452.52
F{5,9,0}452.65
G♯{8,0,3}452.43
A{9,1,4}352.74
B{11,3,6}353
Minor Triadscm{0,3,7}452.65
c♯m{1,4,8}452.52
em{4,7,11}352.74
fm{5,8,0}452.43
f♯m{6,9,1}353
g♯m{8,11,3}352.74
am{9,0,4}452.43
Augmented TriadsC+{0,4,8}652.13
C♯+{1,5,9}452.78
D♯+{3,7,11}452.78
Diminished Triads{0,3,6}253.13
c♯°{1,4,7}252.91
d♯°{3,6,9}253.13
{5,8,11}252.91
f♯°{6,9,0}253.13
{9,0,3}252.83
Parsimonious Voice Leading Between Common Triads of Scale 3067. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# am am C+->am c#°->c#m C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->fm F F C#+->F f#m f#m C#+->f#m C#+->A d#° d#° d#°->f#m d#°->B D#+->em g#m g#m D#+->g#m D#+->B em->E E->f° E->g#m f°->fm fm->F f#° f#° F->f#° F->am f#°->f#m g#m->G# G#->a° a°->am am->A

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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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3067 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3581
Scale 3581: Epocryllian, Ian Ring Music TheoryEpocryllian
3rd mode:
Scale 1919
Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllianThis is the prime mode
4th mode:
Scale 3007
Scale 3007: Zyryllian, Ian Ring Music TheoryZyryllian
5th mode:
Scale 3551
Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
6th mode:
Scale 3823
Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian
7th mode:
Scale 3959
Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
8th mode:
Scale 4027
Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
9th mode:
Scale 4061
Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
10th mode:
Scale 2039
Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian

Prime

The prime form of this scale is Scale 1919

Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian

Complement

The decatonic modal family [3067, 3581, 1919, 3007, 3551, 3823, 3959, 4027, 4061, 2039] (Forte: 10-4) is the complement of the modal family [17, 257] (Forte: 2-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3067 is itself, because it is a palindromic scale!

Scale 3067Scale 3067: Goptyllian, Ian Ring Music TheoryGoptyllian

Transformations:

T0 3067  T0I 3067
T1 2039  T1I 2039
T2 4078  T2I 4078
T3 4061  T3I 4061
T4 4027  T4I 4027
T5 3959  T5I 3959
T6 3823  T6I 3823
T7 3551  T7I 3551
T8 3007  T8I 3007
T9 1919  T9I 1919
T10 3838  T10I 3838
T11 3581  T11I 3581

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 3065Scale 3065: Zothygic, Ian Ring Music TheoryZothygic
Scale 3069Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza
Scale 3071Scale 3071: Solatic, Ian Ring Music TheorySolatic
Scale 3059Scale 3059: Madygic, Ian Ring Music TheoryMadygic
Scale 3063Scale 3063: Solyllian, Ian Ring Music TheorySolyllian
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 3003Scale 3003: Genus Chromaticum, Ian Ring Music TheoryGenus Chromaticum
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 2811Scale 2811: Barygic, Ian Ring Music TheoryBarygic
Scale 2555Scale 2555: Bythygic, Ian Ring Music TheoryBythygic
Scale 3579Scale 3579: Zyphyllian, Ian Ring Music TheoryZyphyllian
Scale 4091Scale 4091: Thydatic, Ian Ring Music TheoryThydatic
Scale 1019Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
Scale 2043Scale 2043: Maqam Tarzanuyn, Ian Ring Music TheoryMaqam Tarzanuyn

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.