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Scale 3471: "Gyryllic"

Scale 3471: Gyryllic, 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
Gyryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,7,8,10,11}
Forte Number8-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3639
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 447
Deep Scaleno
Interval Vector655552
Interval Spectrump5m5n5s5d6t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation3
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3471 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3783
Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
3rd mode:
Scale 3939
Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
4th mode:
Scale 4017
Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic
5th mode:
Scale 507
Scale 507: Moryllic, Ian Ring Music TheoryMoryllic
6th mode:
Scale 2301
Scale 2301: Bydyllic, Ian Ring Music TheoryBydyllic
7th mode:
Scale 1599
Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
8th mode:
Scale 2847
Scale 2847: Phracryllic, Ian Ring Music TheoryPhracryllic

Prime

The prime form of this scale is Scale 447

Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic

Complement

The octatonic modal family [3471, 3783, 3939, 4017, 507, 2301, 1599, 2847] (Forte: 8-4) is the complement of the tetratonic modal family [39, 897, 2067, 3081] (Forte: 4-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3471 is 3639

Scale 3639Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3471 is chiral, and its enantiomorph is scale 3639

Scale 3639Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic

Transformations:

T0 3471  T0I 3639
T1 2847  T1I 3183
T2 1599  T2I 2271
T3 3198  T3I 447
T4 2301  T4I 894
T5 507  T5I 1788
T6 1014  T6I 3576
T7 2028  T7I 3057
T8 4056  T8I 2019
T9 4017  T9I 4038
T10 3939  T10I 3981
T11 3783  T11I 3867

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 3469Scale 3469: Monian, Ian Ring Music TheoryMonian
Scale 3467Scale 3467: Katonian, Ian Ring Music TheoryKatonian
Scale 3463Scale 3463, Ian Ring Music Theory
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
Scale 3503Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
Scale 3535Scale 3535: Mylygic, Ian Ring Music TheoryMylygic
Scale 3343Scale 3343, Ian Ring Music Theory
Scale 3407Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian
Scale 3727Scale 3727: Tholyllic, Ian Ring Music TheoryTholyllic
Scale 3983Scale 3983: Thyptygic, Ian Ring Music TheoryThyptygic
Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian
Scale 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
Scale 1423Scale 1423: Doptian, Ian Ring Music TheoryDoptian

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.