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Scale 693: "Arezzo Major Diatonic Hexachord"

Scale 693: Arezzo Major Diatonic Hexachord, 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

Unknown / Unsorted
Arezzo Major Diatonic Hexachord
Devarangini
Sama
Syama
Carnatic Raga
Raga Kambhoji
Exoticisms
Scottish Hexatonic
Zeitler
Mynimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,4,5,7,9}
Forte Number6-32
Rotational Symmetrynone
Reflection Axes4.5
Palindromicno
Chiralityno
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections1
Modes5
Prime?yes
Deep Scaleyes
Interval Vector143250
Interval Spectrump5m2n3s4d
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {5,7}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation1.667
Maximally Evenno
Maximal Area Setno
Interior Area2.482
Myhill Propertyno
Balancedno
Ridge Tones[9]
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}131.5
F{5,9,0}221
Minor Triadsdm{2,5,9}131.5
am{9,0,4}221
Parsimonious Voice Leading Between Common Triads of Scale 693. Created by Ian Ring ©2019 C C am am C->am dm dm F F dm->F F->am

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.

Diameter3
Radius2
Self-Centeredno
Central VerticesF, am
Peripheral VerticesC, dm

Modes

Modes are the rotational transformation of this scale. Scale 693 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1197
Scale 1197: Minor Hexatonic, Ian Ring Music TheoryMinor Hexatonic
3rd mode:
Scale 1323
Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
4th mode:
Scale 2709
Scale 2709: Raga Kumud, Ian Ring Music TheoryRaga Kumud
5th mode:
Scale 1701
Scale 1701: Dominant Seventh, Ian Ring Music TheoryDominant Seventh
6th mode:
Scale 1449
Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [693, 1197, 1323, 2709, 1701, 1449] (Forte: 6-32) is the complement of the hexatonic modal family [693, 1197, 1323, 1449, 1701, 2709] (Forte: 6-32)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 693 is 1449

Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam

Transformations:

T0 693  T0I 1449
T1 1386  T1I 2898
T2 2772  T2I 1701
T3 1449  T3I 3402
T4 2898  T4I 2709
T5 1701  T5I 1323
T6 3402  T6I 2646
T7 2709  T7I 1197
T8 1323  T8I 2394
T9 2646  T9I 693
T10 1197  T10I 1386
T11 2394  T11I 2772

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 695Scale 695: Sarian, Ian Ring Music TheorySarian
Scale 689Scale 689: Raga Nagasvaravali, Ian Ring Music TheoryRaga Nagasvaravali
Scale 691Scale 691: Raga Kalavati, Ian Ring Music TheoryRaga Kalavati
Scale 697Scale 697: Lagimic, Ian Ring Music TheoryLagimic
Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian
Scale 677Scale 677: Scottish Pentatonic, Ian Ring Music TheoryScottish Pentatonic
Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala
Scale 661Scale 661: Major Pentatonic, Ian Ring Music TheoryMajor Pentatonic
Scale 725Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani
Scale 757Scale 757: Ionyptian, Ian Ring Music TheoryIonyptian
Scale 565Scale 565: Aeolyphritonic, Ian Ring Music TheoryAeolyphritonic
Scale 629Scale 629: Aeronimic, Ian Ring Music TheoryAeronimic
Scale 821Scale 821: Aeranimic, Ian Ring Music TheoryAeranimic
Scale 949Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani
Scale 181Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari
Scale 437Scale 437: Ronimic, Ian Ring Music TheoryRonimic
Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor

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.