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Scale 621: "Pyramid Hexatonic"

Scale 621: Pyramid Hexatonic, 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

Western Modern
Pyramid Hexatonic
Zeitler
Kyrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,5,6,9}
Forte Number6-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1737
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 603
Deep Scaleno
Interval Vector225222
Interval Spectrump2m2n5s2d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5,6}
<3> = {4,5,6,7,8}
<4> = {6,7,8,9}
<5> = {9,10,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsD{2,6,9}331.43
F{5,9,0}331.43
Minor Triadsdm{2,5,9}231.57
Diminished Triads{0,3,6}231.71
d♯°{3,6,9}231.57
f♯°{6,9,0}231.57
{9,0,3}231.57
Parsimonious Voice Leading Between Common Triads of Scale 621. Created by Ian Ring ©2019 d#° d#° c°->d#° c°->a° dm dm D D dm->D F F dm->F D->d#° f#° f#° D->f#° F->f#° F->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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 621 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1179
Scale 1179: Sonimic, Ian Ring Music TheorySonimic
3rd mode:
Scale 2637
Scale 2637: Raga Ranjani, Ian Ring Music TheoryRaga Ranjani
4th mode:
Scale 1683
Scale 1683: Raga Malayamarutam, Ian Ring Music TheoryRaga Malayamarutam
5th mode:
Scale 2889
Scale 2889: Thoptimic, Ian Ring Music TheoryThoptimic
6th mode:
Scale 873
Scale 873: Bagimic, Ian Ring Music TheoryBagimic

Prime

The prime form of this scale is Scale 603

Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic

Complement

The hexatonic modal family [621, 1179, 2637, 1683, 2889, 873] (Forte: 6-27) is the complement of the hexatonic modal family [603, 729, 1611, 1737, 2349, 2853] (Forte: 6-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 621 is 1737

Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 621 is chiral, and its enantiomorph is scale 1737

Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns

Transformations:

T0 621  T0I 1737
T1 1242  T1I 3474
T2 2484  T2I 2853
T3 873  T3I 1611
T4 1746  T4I 3222
T5 3492  T5I 2349
T6 2889  T6I 603
T7 1683  T7I 1206
T8 3366  T8I 2412
T9 2637  T9I 729
T10 1179  T10I 1458
T11 2358  T11I 2916

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 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 617Scale 617: Katycritonic, Ian Ring Music TheoryKatycritonic
Scale 619Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian Hexatonic
Scale 613Scale 613: Phralitonic, Ian Ring Music TheoryPhralitonic
Scale 629Scale 629: Aeronimic, Ian Ring Music TheoryAeronimic
Scale 637Scale 637: Debussy's Heptatonic, Ian Ring Music TheoryDebussy's Heptatonic
Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic
Scale 557Scale 557: Raga Abhogi, Ian Ring Music TheoryRaga Abhogi
Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala
Scale 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian
Scale 877Scale 877: Moravian Pistalkova, Ian Ring Music TheoryMoravian Pistalkova
Scale 109Scale 109, Ian Ring Music Theory
Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 1645Scale 1645: Dorian Flat 5, Ian Ring Music TheoryDorian Flat 5
Scale 2669Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode

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.