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Scale 887: "Sathyllic"

Scale 887: Sathyllic, 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
Sathyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,6,8,9}
Forte Number8-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3545
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?yes
Deep Scaleno
Interval Vector545752
Interval Spectrump5m7n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.75
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♯{1,5,8}431.77
D{2,6,9}252.62
F{5,9,0}431.77
A{9,1,4}331.92
Minor Triadsc♯m{1,4,8}342.15
dm{2,5,9}342.08
fm{5,8,0}342
f♯m{6,9,1}342.08
am{9,0,4}342.15
Augmented TriadsC+{0,4,8}352.38
C♯+{1,5,9}531.54
Diminished Triads{2,5,8}242.31
f♯°{6,9,0}242.31
Parsimonious Voice Leading Between Common Triads of Scale 887. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m C#+->A d°->dm D D dm->D D->f#m fm->F f#° f#° F->f#° F->am f#°->f#m am->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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC♯, C♯+, F, A
Peripheral VerticesC+, D

Modes

Modes are the rotational transformation of this scale. Scale 887 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2491
Scale 2491: Layllic, Ian Ring Music TheoryLayllic
3rd mode:
Scale 3293
Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
4th mode:
Scale 1847
Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
5th mode:
Scale 2971
Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
6th mode:
Scale 3533
Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
7th mode:
Scale 1907
Scale 1907: Lynyllic, Ian Ring Music TheoryLynyllic
8th mode:
Scale 3001
Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [887, 2491, 3293, 1847, 2971, 3533, 1907, 3001] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 887 is 3545

Scale 3545Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 887 is chiral, and its enantiomorph is scale 3545

Scale 3545Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic

Transformations:

T0 887  T0I 3545
T1 1774  T1I 2995
T2 3548  T2I 1895
T3 3001  T3I 3790
T4 1907  T4I 3485
T5 3814  T5I 2875
T6 3533  T6I 1655
T7 2971  T7I 3310
T8 1847  T8I 2525
T9 3694  T9I 955
T10 3293  T10I 1910
T11 2491  T11I 3820

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 885Scale 885: Sathian, Ian Ring Music TheorySathian
Scale 883Scale 883: Ralian, Ian Ring Music TheoryRalian
Scale 891Scale 891: Ionilyllic, Ian Ring Music TheoryIonilyllic
Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic
Scale 871Scale 871: Locrian Double-flat 3 Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 3 Double-flat 7
Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic
Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian
Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian
Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic
Scale 1015Scale 1015: Ionodygic, Ian Ring Music TheoryIonodygic
Scale 631Scale 631: Zygian, Ian Ring Music TheoryZygian
Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic
Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian
Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic
Scale 1911Scale 1911: Messiaen Mode 3, Ian Ring Music TheoryMessiaen Mode 3
Scale 2935Scale 2935: Modygic, Ian Ring Music TheoryModygic

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.