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Scale 4061: "Staptyllian"

Scale 4061: Staptyllian, 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
Staptyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,2,3,4,6,7,8,9,10,11}
Forte Number10-4
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1919
Deep Scaleno
Interval Vector888984
Interval Spectrump8m9n8s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1.2
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[6]
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}352.74
D{2,6,9}353
D♯{3,7,10}452.43
E{4,8,11}352.74
G{7,11,2}452.52
G♯{8,0,3}452.65
B{11,3,6}452.43
Minor Triadscm{0,3,7}452.43
d♯m{3,6,10}452.65
em{4,7,11}452.52
gm{7,10,2}352.74
g♯m{8,11,3}452.43
am{9,0,4}353
bm{11,2,6}352.74
Augmented TriadsC+{0,4,8}452.78
D+{2,6,10}452.78
D♯+{3,7,11}652.13
Diminished Triads{0,3,6}252.83
d♯°{3,6,9}253.13
{4,7,10}252.91
f♯°{6,9,0}253.13
g♯°{8,11,2}252.91
{9,0,3}253.13
Parsimonious Voice Leading Between Common Triads of Scale 4061. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E C+->G# am am C+->am D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m gm gm D+->gm bm bm D+->bm d#°->d#m D# D# d#m->D# d#m->B D#->D#+ D#->e° D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 4061. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B e°->em em->E E->g#m f#°->am gm->G g#° g#° G->g#° G->bm g#°->g#m g#m->G# G#->a° a°->am bm->B

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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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 4061 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 2039
Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian
3rd mode:
Scale 3067
Scale 3067: Goptyllian, Ian Ring Music TheoryGoptyllian
4th mode:
Scale 3581
Scale 3581: Epocryllian, Ian Ring Music TheoryEpocryllian
5th mode:
Scale 1919
Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllianThis is the prime mode
6th mode:
Scale 3007
Scale 3007: Zyryllian, Ian Ring Music TheoryZyryllian
7th mode:
Scale 3551
Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
8th mode:
Scale 3823
Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian
9th mode:
Scale 3959
Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
10th mode:
Scale 4027
Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian

Prime

The prime form of this scale is Scale 1919

Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian

Complement

The decatonic modal family [4061, 2039, 3067, 3581, 1919, 3007, 3551, 3823, 3959, 4027] (Forte: 10-4) is the complement of the modal family [17, 257] (Forte: 2-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4061 is 1919

Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian

Transformations:

T0 4061  T0I 1919
T1 4027  T1I 3838
T2 3959  T2I 3581
T3 3823  T3I 3067
T4 3551  T4I 2039
T5 3007  T5I 4078
T6 1919  T6I 4061
T7 3838  T7I 4027
T8 3581  T8I 3959
T9 3067  T9I 3823
T10 2039  T10I 3551
T11 4078  T11I 3007

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 4063Scale 4063: Eptatic, Ian Ring Music TheoryEptatic
Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
Scale 4059Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
Scale 4045Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 4093Scale 4093: Aerycratic, Ian Ring Music TheoryAerycratic
Scale 3997Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
Scale 4029Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed
Scale 3933Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
Scale 3805Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
Scale 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse
Scale 3037Scale 3037: Nine Tone Scale, Ian Ring Music TheoryNine Tone Scale
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic

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.