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Scale 2005: "Gygyllic"

Scale 2005: Gygyllic, 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
Gygyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,4,6,7,8,9,10}
Forte Number8-21
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 1375
Deep Scaleno
Interval Vector474643
Interval Spectrump4m6n4s7d4t3
Distribution Spectra<1> = {1,2}
<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> = {10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tones[4]
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
D{2,6,9}242
Minor Triadsgm{7,10,2}242
am{9,0,4}242
Augmented TriadsC+{0,4,8}242
D+{2,6,10}242
Diminished Triads{4,7,10}242
f♯°{6,9,0}242
Parsimonious Voice Leading Between Common Triads of Scale 2005. Created by Ian Ring ©2019 C C C+ C+ C->C+ C->e° am am C+->am D D D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm e°->gm f#°->am

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 2005 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1525
Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
3rd mode:
Scale 1405
Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
4th mode:
Scale 1375
Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllicThis is the prime mode
5th mode:
Scale 2735
Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
6th mode:
Scale 3415
Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
7th mode:
Scale 3755
Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
8th mode:
Scale 3925
Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic

Prime

The prime form of this scale is Scale 1375

Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic

Complement

The octatonic modal family [2005, 1525, 1405, 1375, 2735, 3415, 3755, 3925] (Forte: 8-21) is the complement of the tetratonic modal family [85, 1045, 1285, 1345] (Forte: 4-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2005 is 1405

Scale 1405Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic

Transformations:

T0 2005  T0I 1405
T1 4010  T1I 2810
T2 3925  T2I 1525
T3 3755  T3I 3050
T4 3415  T4I 2005
T5 2735  T5I 4010
T6 1375  T6I 3925
T7 2750  T7I 3755
T8 1405  T8I 3415
T9 2810  T9I 2735
T10 1525  T10I 1375
T11 3050  T11I 2750

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 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
Scale 2001Scale 2001: Gydian, Ian Ring Music TheoryGydian
Scale 2003Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
Scale 1989Scale 1989: Dydian, Ian Ring Music TheoryDydian
Scale 1997Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
Scale 2021Scale 2021: Katycryllic, Ian Ring Music TheoryKatycryllic
Scale 2037Scale 2037: Sythygic, Ian Ring Music TheorySythygic
Scale 1941Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani
Scale 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic

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.