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Scale 1999: "Zacrygic"

Scale 1999: Zacrygic, 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
Zacrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,6,7,8,9,10}
Forte Number9-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3709
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 TriadsD{2,6,9}342.21
D♯{3,7,10}342.14
F♯{6,10,1}342.21
G♯{8,0,3}242.64
Minor Triadscm{0,3,7}342.36
d♯m{3,6,10}442.07
f♯m{6,9,1}342.29
gm{7,10,2}342.21
Augmented TriadsD+{2,6,10}442
Diminished Triads{0,3,6}242.43
d♯°{3,6,9}242.43
f♯°{6,9,0}242.57
{7,10,1}242.57
{9,0,3}242.71
Parsimonious Voice Leading Between Common Triads of Scale 1999. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# G# G# cm->G# D D D+ D+ D->D+ d#° d#° D->d#° f#m f#m D->f#m D+->d#m F# F# D+->F# gm gm D+->gm d#°->d#m d#m->D# D#->gm f#° f#° f#°->f#m f#°->a° f#m->F# F#->g° g°->gm G#->a°

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 1999 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3047
Scale 3047: Panygic, Ian Ring Music TheoryPanygic
3rd mode:
Scale 3571
Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
4th mode:
Scale 3833
Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
5th mode:
Scale 991
Scale 991: Aeolygic, Ian Ring Music TheoryAeolygicThis is the prime mode
6th mode:
Scale 2543
Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
7th mode:
Scale 3319
Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
8th mode:
Scale 3707
Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
9th mode:
Scale 3901
Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic

Prime

The prime form of this scale is Scale 991

Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic

Complement

The nonatonic modal family [1999, 3047, 3571, 3833, 991, 2543, 3319, 3707, 3901] (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 1999 is 3709

Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1999 is chiral, and its enantiomorph is scale 3709

Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic

Transformations:

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

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 1997Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
Scale 1995Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
Scale 1991Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic
Scale 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
Scale 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 2031Scale 2031: Gadyllian, Ian Ring Music TheoryGadyllian
Scale 1935Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic
Scale 1967Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed
Scale 1871Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
Scale 1487Scale 1487: Mothyllic, Ian Ring Music TheoryMothyllic
Scale 975Scale 975: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 4047Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian

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.