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Scale 987: "Aeraptyllic"

Scale 987: Aeraptyllic, 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
Aeraptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,6,7,8,9}
Forte Number8-18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2937
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 879
Deep Scaleno
Interval Vector546553
Interval Spectrump5m5n6s4d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
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}342.08
G♯{8,0,3}342.08
A{9,1,4}342
Minor Triadscm{0,3,7}342.15
c♯m{1,4,8}342.08
f♯m{6,9,1}342.23
am{9,0,4}441.92
Augmented TriadsC+{0,4,8}441.85
Diminished Triads{0,3,6}242.38
c♯°{1,4,7}242.46
d♯°{3,6,9}242.46
f♯°{6,9,0}242.31
{9,0,3}242.31
Parsimonious Voice Leading Between Common Triads of Scale 987. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° C C cm->C G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m C+->G# am am C+->am c#°->c#m A A c#m->A f#m f#m d#°->f#m f#° f#° f#°->f#m f#°->am f#m->A G#->a° a°->am am->A

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 987 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2541
Scale 2541: Algerian, Ian Ring Music TheoryAlgerian
3rd mode:
Scale 1659
Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban
4th mode:
Scale 2877
Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic
5th mode:
Scale 1743
Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
6th mode:
Scale 2919
Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
7th mode:
Scale 3507
Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz
8th mode:
Scale 3801
Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic

Prime

The prime form of this scale is Scale 879

Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic

Complement

The octatonic modal family [987, 2541, 1659, 2877, 1743, 2919, 3507, 3801] (Forte: 8-18) is the complement of the tetratonic modal family [147, 609, 777, 2121] (Forte: 4-18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 987 is 2937

Scale 2937Scale 2937: Phragyllic, Ian Ring Music TheoryPhragyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 987 is chiral, and its enantiomorph is scale 2937

Scale 2937Scale 2937: Phragyllic, Ian Ring Music TheoryPhragyllic

Transformations:

T0 987  T0I 2937
T1 1974  T1I 1779
T2 3948  T2I 3558
T3 3801  T3I 3021
T4 3507  T4I 1947
T5 2919  T5I 3894
T6 1743  T6I 3693
T7 3486  T7I 3291
T8 2877  T8I 2487
T9 1659  T9I 879
T10 3318  T10I 1758
T11 2541  T11I 3516

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 985Scale 985: Mela Sucaritra, Ian Ring Music TheoryMela Sucaritra
Scale 989Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic
Scale 979Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari
Scale 983Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic
Scale 971Scale 971: Mela Gavambodhi, Ian Ring Music TheoryMela Gavambodhi
Scale 1003Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
Scale 1019Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
Scale 923Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
Scale 955Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian
Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian
Scale 475Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian
Scale 1499Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
Scale 2011Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic

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.