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Scale 3833: "Dycrygic"

Scale 3833: Dycrygic, 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
Dycrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,3,4,5,6,7,9,10,11}
Forte Number9-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1007
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 991
Deep Scaleno
Interval Vector766674
Interval Spectrump7m6n6s6d7t4
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation1.778
Maximally Evenno
Maximal Area Setno
Interior Area2.683
Myhill Propertyno
Balancedno
Ridge Tonesnone
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}342.14
D♯{3,7,10}342.21
F{5,9,0}242.64
B{11,3,6}342.21
Minor Triadscm{0,3,7}442.07
d♯m{3,6,10}342.29
em{4,7,11}342.21
am{9,0,4}342.36
Augmented TriadsD♯+{3,7,11}442
Diminished Triads{0,3,6}242.43
d♯°{3,6,9}242.57
{4,7,10}242.57
f♯°{6,9,0}242.71
{9,0,3}242.43
Parsimonious Voice Leading Between Common Triads of Scale 3833. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ cm->a° em em C->em am am C->am d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° D# D# d#m->D# d#m->B D#->D#+ D#->e° D#+->em D#+->B e°->em F F F->f#° F->am a°->am

view full size

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 3833 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 991
Scale 991: Aeolygic, Ian Ring Music TheoryAeolygicThis is the prime mode
3rd mode:
Scale 2543
Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
4th mode:
Scale 3319
Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
5th mode:
Scale 3707
Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
6th mode:
Scale 3901
Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
7th mode:
Scale 1999
Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
8th mode:
Scale 3047
Scale 3047: Panygic, Ian Ring Music TheoryPanygic
9th mode:
Scale 3571
Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic

Prime

The prime form of this scale is Scale 991

Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic

Complement

The nonatonic modal family [3833, 991, 2543, 3319, 3707, 3901, 1999, 3047, 3571] (Forte: 9-5) is the complement of the tritonic modal family [67, 193, 2081] (Forte: 3-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3833 is 1007

Scale 1007Scale 1007: Epitygic, Ian Ring Music TheoryEpitygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3833 is chiral, and its enantiomorph is scale 1007

Scale 1007Scale 1007: Epitygic, Ian Ring Music TheoryEpitygic

Transformations:

T0 3833  T0I 1007
T1 3571  T1I 2014
T2 3047  T2I 4028
T3 1999  T3I 3961
T4 3998  T4I 3827
T5 3901  T5I 3559
T6 3707  T6I 3023
T7 3319  T7I 1951
T8 2543  T8I 3902
T9 991  T9I 3709
T10 1982  T10I 3323
T11 3964  T11I 2551

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 3835Scale 3835, Ian Ring Music Theory
Scale 3837Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
Scale 3825Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 3769Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic
Scale 3705Scale 3705: Messiaen Mode 4 Inverse, Ian Ring Music TheoryMessiaen Mode 4 Inverse
Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 4089Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian
Scale 3321Scale 3321: Epagyllic, Ian Ring Music TheoryEpagyllic
Scale 3577Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic
Scale 2809Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
Scale 1785Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic

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.