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Scale 3167: "Thynyllic"

Scale 3167: Thynyllic, 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
Thynyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,6,10,11}
Forte Number8-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3911
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 383
Deep Scaleno
Interval Vector665542
Interval Spectrump4m5n5s6d6t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {6,7,9,10}
<7> = {8,10,11}
Spectra Variation3.25
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3167 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3631
Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic
3rd mode:
Scale 3863
Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic
4th mode:
Scale 3979
Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
5th mode:
Scale 4037
Scale 4037: Ionyllic, Ian Ring Music TheoryIonyllic
6th mode:
Scale 2033
Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic
7th mode:
Scale 383
Scale 383: Logyllic, Ian Ring Music TheoryLogyllicThis is the prime mode
8th mode:
Scale 2239
Scale 2239: Dacryllic, Ian Ring Music TheoryDacryllic

Prime

The prime form of this scale is Scale 383

Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic

Complement

The octatonic modal family [3167, 3631, 3863, 3979, 4037, 2033, 383, 2239] (Forte: 8-2) is the complement of the tetratonic modal family [23, 1793, 2059, 3077] (Forte: 4-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3167 is 3911

Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3167 is chiral, and its enantiomorph is scale 3911

Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic

Transformations:

T0 3167  T0I 3911
T1 2239  T1I 3727
T2 383  T2I 3359
T3 766  T3I 2623
T4 1532  T4I 1151
T5 3064  T5I 2302
T6 2033  T6I 509
T7 4066  T7I 1018
T8 4037  T8I 2036
T9 3979  T9I 4072
T10 3863  T10I 4049
T11 3631  T11I 4003

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 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
Scale 3183Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic
Scale 3199Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic
Scale 3103Scale 3103, Ian Ring Music Theory
Scale 3135Scale 3135, Ian Ring Music Theory
Scale 3231Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 3679Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
Scale 2143Scale 2143, Ian Ring Music Theory
Scale 2655Scale 2655, Ian Ring Music Theory
Scale 1119Scale 1119: Rarian, Ian Ring Music TheoryRarian

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.