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Scale 3405: "Stynian"

Scale 3405: Stynian, 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

Zeitler
Stynian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,6,8,10,11}
Forte Number7-26
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1623
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes6
Prime?no
prime: 699
Deep Scaleno
Interval Vector344532
Interval Spectrump3m5n4s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsG♯{8,0,3}242
B{11,3,6}421.25
Minor Triadsd♯m{3,6,10}231.75
g♯m{8,11,3}331.5
bm{11,2,6}331.5
Augmented TriadsD+{2,6,10}242
Diminished Triads{0,3,6}231.75
g♯°{8,11,2}231.75
Parsimonious Voice Leading Between Common Triads of Scale 3405. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B D+ D+ d#m d#m D+->d#m bm bm D+->bm d#m->B g#° g#° g#m g#m g#°->g#m g#°->bm g#m->G# g#m->B bm->B

view full size

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
Radius2
Self-Centeredno
Central VerticesB
Peripheral VerticesD+, G♯

Modes

Modes are the rotational transformation of this scale. Scale 3405 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1875
Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale
3rd mode:
Scale 2985
Scale 2985: Epacrian, Ian Ring Music TheoryEpacrian
4th mode:
Scale 885
Scale 885: Sathian, Ian Ring Music TheorySathian
5th mode:
Scale 1245
Scale 1245: Lathian, Ian Ring Music TheoryLathian
6th mode:
Scale 1335
Scale 1335: Elephant Scale, Ian Ring Music TheoryElephant Scale
7th mode:
Scale 2715
Scale 2715: Kynian, Ian Ring Music TheoryKynian

Prime

The prime form of this scale is Scale 699

Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian

Complement

The heptatonic modal family [3405, 1875, 2985, 885, 1245, 1335, 2715] (Forte: 7-26) is the complement of the pentatonic modal family [309, 849, 1101, 1299, 2697] (Forte: 5-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3405 is 1623

Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3405 is chiral, and its enantiomorph is scale 1623

Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian

Transformations:

T0 3405  T0I 1623
T1 2715  T1I 3246
T2 1335  T2I 2397
T3 2670  T3I 699
T4 1245  T4I 1398
T5 2490  T5I 2796
T6 885  T6I 1497
T7 1770  T7I 2994
T8 3540  T8I 1893
T9 2985  T9I 3786
T10 1875  T10I 3477
T11 3750  T11I 2859

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 3407Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian
Scale 3397Scale 3397: Sydimic, Ian Ring Music TheorySydimic
Scale 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
Scale 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 3437Scale 3437, Ian Ring Music Theory
Scale 3341Scale 3341, Ian Ring Music Theory
Scale 3373Scale 3373: Lodian, Ian Ring Music TheoryLodian
Scale 3469Scale 3469: Monian, Ian Ring Music TheoryMonian
Scale 3533Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
Scale 3149Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
Scale 3277Scale 3277: Mela Nitimati, Ian Ring Music TheoryMela Nitimati
Scale 3661Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
Scale 2381Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian
Scale 1357Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2

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.