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Scale 1621: "Scriabin's Prometheus"

Scale 1621: Scriabin's Prometheus, 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

Named After Composers
Scriabin's Prometheus
Mystic
Carnatic Raga
Raga Barbara
Zeitler
Aeolathimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,4,6,9,10}
Forte Number6-34
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1357
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 683
Deep Scaleno
Interval Vector142422
Interval Spectrump2m4n2s4dt2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {5,6,7}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation1.667
Maximally Evenno
Maximal Area Setno
Interior Area2.482
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 TriadsD{2,6,9}221
Minor Triadsam{9,0,4}131.5
Augmented TriadsD+{2,6,10}131.5
Diminished Triadsf♯°{6,9,0}221
Parsimonious Voice Leading Between Common Triads of Scale 1621. Created by Ian Ring ©2019 D D D+ D+ D->D+ f#° f#° D->f#° am am 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 VerticesD, f♯°
Peripheral VerticesD+, am

Modes

Modes are the rotational transformation of this scale. Scale 1621 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1429
Scale 1429: Bythimic, Ian Ring Music TheoryBythimic
3rd mode:
Scale 1381
Scale 1381: Padimic, Ian Ring Music TheoryPadimic
4th mode:
Scale 1369
Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
5th mode:
Scale 683
Scale 683: Stogimic, Ian Ring Music TheoryStogimicThis is the prime mode
6th mode:
Scale 2389
Scale 2389: Eskimo Hexatonic 2, Ian Ring Music TheoryEskimo Hexatonic 2

Prime

The prime form of this scale is Scale 683

Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic

Complement

The hexatonic modal family [1621, 1429, 1381, 1369, 683, 2389] (Forte: 6-34) is the complement of the hexatonic modal family [683, 1369, 1381, 1429, 1621, 2389] (Forte: 6-34)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1621 is 1357

Scale 1357Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1621 is chiral, and its enantiomorph is scale 1357

Scale 1357Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2

Transformations:

T0 1621  T0I 1357
T1 3242  T1I 2714
T2 2389  T2I 1333
T3 683  T3I 2666
T4 1366  T4I 1237
T5 2732  T5I 2474
T6 1369  T6I 853
T7 2738  T7I 1706
T8 1381  T8I 3412
T9 2762  T9I 2729
T10 1429  T10I 1363
T11 2858  T11I 2726

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 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian
Scale 1617Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic
Scale 1619Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan
Scale 1625Scale 1625: Lythimic, Ian Ring Music TheoryLythimic
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1605Scale 1605: Zanitonic, Ian Ring Music TheoryZanitonic
Scale 1613Scale 1613: Thylimic, Ian Ring Music TheoryThylimic
Scale 1637Scale 1637: Syptimic, Ian Ring Music TheorySyptimic
Scale 1653Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
Scale 1557Scale 1557, Ian Ring Music Theory
Scale 1589Scale 1589: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 1685Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1109Scale 1109: Kataditonic, Ian Ring Music TheoryKataditonic
Scale 1365Scale 1365: Whole Tone, Ian Ring Music TheoryWhole Tone
Scale 597Scale 597: Kung, Ian Ring Music TheoryKung
Scale 2645Scale 2645: Raga Mruganandana, Ian Ring Music TheoryRaga Mruganandana
Scale 3669Scale 3669: Mothian, Ian Ring Music TheoryMothian

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.