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Scale 2997: "Major Bebop"

Scale 2997: Major Bebop, 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
Major Bebop
Bebop Major
Western Modern
Altered Mixolydian
Zeitler
Ionoptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,4,5,7,8,9,11}
Forte Number8-26
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes7
Prime?no
prime: 1467
Deep Scaleno
Interval Vector456562
Interval Spectrump6m5n6s5d4t2
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 Tones[4]
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 TriadsC{0,4,7}242.23
E{4,8,11}441.92
F{5,9,0}342.15
G{7,11,2}342.23
Minor Triadsdm{2,5,9}342.23
em{4,7,11}342.15
fm{5,8,0}441.92
am{9,0,4}242.23
Augmented TriadsC+{0,4,8}441.85
Diminished Triads{2,5,8}242.31
{5,8,11}242.15
g♯°{8,11,2}242.31
{11,2,5}242.31
Parsimonious Voice Leading Between Common Triads of Scale 2997. Created by Ian Ring ©2019 C C C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm am am C+->am dm dm d°->dm d°->fm F F dm->F dm->b° em->E Parsimonious Voice Leading Between Common Triads of Scale 2997. Created by Ian Ring ©2019 G em->G E->f° g#° g#° E->g#° f°->fm fm->F F->am G->g#° G->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2997 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1773
Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
3rd mode:
Scale 1467
Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish PhrygianThis is the prime mode
4th mode:
Scale 2781
Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
5th mode:
Scale 1719
Scale 1719: Lyryllic, Ian Ring Music TheoryLyryllic
6th mode:
Scale 2907
Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2
7th mode:
Scale 3501
Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
8th mode:
Scale 1899
Scale 1899: Moptyllic, Ian Ring Music TheoryMoptyllic

Prime

The prime form of this scale is Scale 1467

Scale 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian

Complement

The octatonic modal family [2997, 1773, 1467, 2781, 1719, 2907, 3501, 1899] (Forte: 8-26) is the complement of the tetratonic modal family [297, 549, 657, 1161] (Forte: 4-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2997 is 1467

Scale 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian

Transformations:

T0 2997  T0I 1467
T1 1899  T1I 2934
T2 3798  T2I 1773
T3 3501  T3I 3546
T4 2907  T4I 2997
T5 1719  T5I 1899
T6 3438  T6I 3798
T7 2781  T7I 3501
T8 1467  T8I 2907
T9 2934  T9I 1719
T10 1773  T10I 3438
T11 3546  T11I 2781

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 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
Scale 2993Scale 2993: Stythian, Ian Ring Music TheoryStythian
Scale 2995Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
Scale 3001Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
Scale 3005Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic
Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 2965Scale 2965: Darian, Ian Ring Music TheoryDarian
Scale 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 3061Scale 3061: Apinygic, Ian Ring Music TheoryApinygic
Scale 2869Scale 2869: Ionian Augmented, Ian Ring Music TheoryIonian Augmented
Scale 2933Scale 2933, Ian Ring Music Theory
Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor
Scale 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major
Scale 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
Scale 4021Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
Scale 949Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic

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.