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Scale 3765: "Dominant Bebop"

Scale 3765: Dominant 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

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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
Dominant Bebop
Bebop Dominant
Western Mixed
Mixionian
Major/Mixolydian Mixed
Ionian/Mixolydian Mixed
Ancient Greek
Genus Diatonicum
Carnatic Raga
Raga Khamaj
Unknown / Unsorted
Desh Malhar
Devagandhari
Bihagara
Rast
Hindustani
Alhaiya Bilaval
Arabic
Maqam Shawq Awir
Gregorian Numbered
Gregorian Number 6
Exoticisms
Chinese Eight-Tone
Zeitler
Aerycryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,4,5,7,9,10,11}
Forte Number8-23
Rotational Symmetrynone
Reflection Axes4.5
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections1
Modes7
Prime?no
prime: 1455
Deep Scaleno
Interval Vector465472
Interval Spectrump7m4n5s6d4t2
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {5,6,7}
<5> = {7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tones[9]
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}242.1
F{5,9,0}242.3
G{7,11,2}341.9
A♯{10,2,5}341.9
Minor Triadsdm{2,5,9}242.1
em{4,7,11}341.9
gm{7,10,2}341.9
am{9,0,4}242.3
Diminished Triads{4,7,10}242.1
{11,2,5}242.1
Parsimonious Voice Leading Between Common Triads of Scale 3765. Created by Ian Ring ©2019 C C em em C->em am am C->am dm dm F F dm->F A# A# dm->A# e°->em gm gm e°->gm Parsimonious Voice Leading Between Common Triads of Scale 3765. Created by Ian Ring ©2019 G em->G F->am gm->G gm->A# G->b° A#->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 3765 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1965
Scale 1965: Raga Mukhari, Ian Ring Music TheoryRaga Mukhari
3rd mode:
Scale 1515
Scale 1515: Phrygian/Locrian Mixed, Ian Ring Music TheoryPhrygian/Locrian Mixed
4th mode:
Scale 2805
Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho
5th mode:
Scale 1725
Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
6th mode:
Scale 1455
Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolianThis is the prime mode
7th mode:
Scale 2775
Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
8th mode:
Scale 3435
Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev

Prime

The prime form of this scale is Scale 1455

Scale 1455Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolian

Complement

The octatonic modal family [3765, 1965, 1515, 2805, 1725, 1455, 2775, 3435] (Forte: 8-23) is the complement of the tetratonic modal family [165, 645, 1065, 1185] (Forte: 4-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3765 is 1455

Scale 1455Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolian

Transformations:

T0 3765  T0I 1455
T1 3435  T1I 2910
T2 2775  T2I 1725
T3 1455  T3I 3450
T4 2910  T4I 2805
T5 1725  T5I 1515
T6 3450  T6I 3030
T7 2805  T7I 1965
T8 1515  T8I 3930
T9 3030  T9I 3765
T10 1965  T10I 3435
T11 3930  T11I 2775

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 3767Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
Scale 3761Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri
Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
Scale 3769Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic
Scale 3773Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
Scale 3733Scale 3733: Gycrian, Ian Ring Music TheoryGycrian
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 3701Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 4021Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
Scale 3253Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini
Scale 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian

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.