The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2009: "Stacryllic"

Scale 2009: Stacryllic, 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
Stacryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,4,6,7,8,9,10}
Forte Number8-12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 893
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 763
Deep Scaleno
Interval Vector556543
Interval Spectrump4m5n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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
D♯{3,7,10}342
G♯{8,0,3}342
Minor Triadscm{0,3,7}441.83
d♯m{3,6,10}342.17
am{9,0,4}342.17
Augmented TriadsC+{0,4,8}342
Diminished Triadsc°{0,3,6}242.17
d♯°{3,6,9}242.33
e°{4,7,10}242.33
f♯°{6,9,0}242.33
a°{9,0,3}242.33
Parsimonious Voice Leading Between Common Triads of Scale 2009. Created by Ian Ring ©2019 c° c° cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ e° e° C->e° C+->G# am am C+->am d#° d#° d#°->d#m f#° f#° d#°->f#° d#m->D# D#->e° f#°->am a° a° G#->a° 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 2009 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 763		Scale 763: Doryllic, Ian Ring Music TheoryDoryllicThis is the prime mode
3rd mode:
Scale 2429		Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
4th mode:
Scale 1631		Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
5th mode:
Scale 2863		Scale 2863: Aerogyllic, Ian Ring Music TheoryAerogyllic
6th mode:
Scale 3479		Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
7th mode:
Scale 3787		Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
8th mode:
Scale 3941		Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic

Prime

The prime form of this scale is Scale 763

Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic

Complement

The octatonic modal family [2009, 763, 2429, 1631, 2863, 3479, 3787, 3941] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2009 is 893

Scale 893Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2009 is chiral, and its enantiomorph is scale 893

Scale 893Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic

Transformations:

T0 2009  T0I 893
T1 4018  T1I 1786
T2 3941  T2I 3572
T3 3787  T3I 3049
T4 3479  T4I 2003
T5 2863  T5I 4006
T6 1631  T6I 3917
T7 3262  T7I 3739
T8 2429  T8I 3383
T9 763  T9I 2671
T10 1526  T10I 1247
T11 3052  T11I 2494

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 2011Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
Scale 2001Scale 2001: Gydian, Ian Ring Music TheoryGydian
Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
Scale 2025Scale 2025, Ian Ring Music Theory
Scale 2041Scale 2041: Aeolacrygic, Ian Ring Music TheoryAeolacrygic
Scale 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian
Scale 1977Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
Scale 1881Scale 1881: Katorian, Ian Ring Music TheoryKatorian
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1497Scale 1497: Mela Jyotisvarupini, Ian Ring Music TheoryMela Jyotisvarupini
Scale 985Scale 985: Mela Sucaritra, Ian Ring Music TheoryMela Sucaritra
Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic

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.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.