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Scale 2989: "Bebop Minor"

Scale 2989: Bebop Minor, 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

Jazz and Blues
Bebop Minor
Melodic Minor Bebop
Minor Bebop
Arabic
Zirafkend

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,5,7,8,9,11}
Forte Number8-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1723
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes7
Prime?no
prime: 1463
Deep Scaleno
Interval Vector456553
Interval Spectrump5m5n6s5d4t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.25
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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 TriadsF{5,9,0}342.15
G{7,11,2}342.23
G♯{8,0,3}441.85
Minor Triadscm{0,3,7}242.23
dm{2,5,9}342.23
fm{5,8,0}441.92
g♯m{8,11,3}441.92
Augmented TriadsD♯+{3,7,11}342.15
Diminished Triads{2,5,8}242.31
{5,8,11}242.15
g♯°{8,11,2}242.31
{9,0,3}242.23
{11,2,5}242.31
Parsimonious Voice Leading Between Common Triads of Scale 2989. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# dm dm d°->dm fm fm d°->fm F F dm->F dm->b° Parsimonious Voice Leading Between Common Triads of Scale 2989. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m f°->fm f°->g#m fm->F fm->G# F->a° g#° g#° G->g#° G->b° g#°->g#m g#m->G# 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 2989 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1771
Scale 1771, Ian Ring Music Theory
3rd mode:
Scale 2933
Scale 2933, Ian Ring Music Theory
4th mode:
Scale 1757
Scale 1757, Ian Ring Music Theory
5th mode:
Scale 1463
Scale 1463, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2779
Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich
7th mode:
Scale 3437
Scale 3437, Ian Ring Music Theory
8th mode:
Scale 1883
Scale 1883, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 1463

Scale 1463Scale 1463, Ian Ring Music Theory

Complement

The octatonic modal family [2989, 1771, 2933, 1757, 1463, 2779, 3437, 1883] (Forte: 8-27) is the complement of the tetratonic modal family [293, 593, 649, 1097] (Forte: 4-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2989 is 1723

Scale 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2989 is chiral, and its enantiomorph is scale 1723

Scale 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic

Transformations:

T0 2989  T0I 1723
T1 1883  T1I 3446
T2 3766  T2I 2797
T3 3437  T3I 1499
T4 2779  T4I 2998
T5 1463  T5I 1901
T6 2926  T6I 3802
T7 1757  T7I 3509
T8 3514  T8I 2923
T9 2933  T9I 1751
T10 1771  T10I 3502
T11 3542  T11I 2909

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 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
Scale 2985Scale 2985: Epacrian, Ian Ring Music TheoryEpacrian
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
Scale 2997Scale 2997: Major Bebop, Ian Ring Music TheoryMajor Bebop
Scale 3005Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic
Scale 2957Scale 2957: Thygian, Ian Ring Music TheoryThygian
Scale 2973Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
Scale 3021Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
Scale 3053Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic
Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 2925Scale 2925: Diminished, Ian Ring Music TheoryDiminished
Scale 2733Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
Scale 2477Scale 2477: Harmonic Minor, Ian Ring Music TheoryHarmonic Minor
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 941Scale 941: Mela Jhankaradhvani, Ian Ring Music TheoryMela Jhankaradhvani
Scale 1965Scale 1965: Raga Mukhari, Ian Ring Music TheoryRaga Mukhari

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.