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Scale 2239: "Dacryllic"

Scale 2239: Dacryllic, 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.

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
Dacryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,5,7,11}
Forte Number8-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 4003
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
Coherenceno
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 2239 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3167
Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
3rd mode:
Scale 3631
Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic
4th mode:
Scale 3863
Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic
5th mode:
Scale 3979
Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
6th mode:
Scale 4037
Scale 4037: Ionyllic, Ian Ring Music TheoryIonyllic
7th mode:
Scale 2033
Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic
8th mode:
Scale 383
Scale 383: Logyllic, Ian Ring Music TheoryLogyllicThis is the prime mode

Prime

The prime form of this scale is Scale 383

Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic

Complement

The octatonic modal family [2239, 3167, 3631, 3863, 3979, 4037, 2033, 383] (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 2239 is 4003

Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2239 is chiral, and its enantiomorph is scale 4003

Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic

Transformations:

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

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 2237Scale 2237: Epothian, Ian Ring Music TheoryEpothian
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian
Scale 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian
Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian
Scale 2207Scale 2207: Mygian, Ian Ring Music TheoryMygian
Scale 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
Scale 2303Scale 2303: Stanygic, Ian Ring Music TheoryStanygic
Scale 2111Scale 2111, Ian Ring Music Theory
Scale 2175Scale 2175, Ian Ring Music Theory
Scale 2367Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
Scale 2751Scale 2751: Sylygic, Ian Ring Music TheorySylygic
Scale 3263Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
Scale 191Scale 191, Ian Ring Music Theory
Scale 1215Scale 1215, Ian Ring Music Theory

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. Bibliography