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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

41161837294116105072918310504116183
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

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,3,6,8,10,11}

Forte Number

A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

7-26

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 1623

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

3 (trihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

1 (uncohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

4

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

6

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 699

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

[3, 4, 4, 5, 3, 2]

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.

p3m5n4s4d3t2

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<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 Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.286

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.549

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

5.967

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

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. Special thanks to Richard Repp for helping with technical accuracy.