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Scale 2365: "Sythian"

Scale 2365: Sythian, 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

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
Sythian

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

{0,2,3,4,5,8,11}

Forte Number

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

7-16

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: 1939

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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: 623

Deep Scale

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

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[2, 1, 1, 1, 3, 3, 1]

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.

<4, 3, 5, 4, 3, 2>

Interval Spectrum

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

p3m4n5s3d4t2

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> = {2,3,4,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,8,9,10}
<6> = {9,10,11}

Spectra Variation

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

2.857

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.

2.433

Polygon Perimeter

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

5.899

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

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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 TriadsE{4,8,11}331.67
G♯{8,0,3}231.89
Minor Triadsfm{5,8,0}331.67
g♯m{8,11,3}331.67
Augmented TriadsC+{0,4,8}331.67
Diminished Triads{2,5,8}231.89
{5,8,11}231.89
g♯°{8,11,2}231.89
{11,2,5}232
Parsimonious Voice Leading Between Common Triads of Scale 2365. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm G# G# C+->G# d°->fm d°->b° E->f° g#m g#m E->g#m f°->fm g#° g#° g#°->g#m g#°->b° g#m->G#

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2365 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1615
Scale 1615: Sydian, Ian Ring Music TheorySydian
3rd mode:
Scale 2855
Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain
4th mode:
Scale 3475
Scale 3475: Kylian, Ian Ring Music TheoryKylian
5th mode:
Scale 3785
Scale 3785: Epagian, Ian Ring Music TheoryEpagian
6th mode:
Scale 985
Scale 985: Mela Sucaritra, Ian Ring Music TheoryMela Sucaritra
7th mode:
Scale 635
Scale 635: Epolian, Ian Ring Music TheoryEpolian

Prime

The prime form of this scale is Scale 623

Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian

Complement

The heptatonic modal family [2365, 1615, 2855, 3475, 3785, 985, 635] (Forte: 7-16) is the complement of the pentatonic modal family [155, 865, 1555, 2125, 2825] (Forte: 5-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2365 is 1939

Scale 1939Scale 1939: Dathian, Ian Ring Music TheoryDathian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2365 is chiral, and its enantiomorph is scale 1939

Scale 1939Scale 1939: Dathian, Ian Ring Music TheoryDathian

Transformations:

T0 2365  T0I 1939
T1 635  T1I 3878
T2 1270  T2I 3661
T3 2540  T3I 3227
T4 985  T4I 2359
T5 1970  T5I 623
T6 3940  T6I 1246
T7 3785  T7I 2492
T8 3475  T8I 889
T9 2855  T9I 1778
T10 1615  T10I 3556
T11 3230  T11I 3017

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 2367Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
Scale 2361Scale 2361: Docrimic, Ian Ring Music TheoryDocrimic
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
Scale 2349Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
Scale 2333Scale 2333: Stynimic, Ian Ring Music TheoryStynimic
Scale 2397Scale 2397: Stagian, Ian Ring Music TheoryStagian
Scale 2429Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
Scale 2493Scale 2493: Manyllic, Ian Ring Music TheoryManyllic
Scale 2109Scale 2109, Ian Ring Music Theory
Scale 2237Scale 2237: Epothian, Ian Ring Music TheoryEpothian
Scale 2621Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
Scale 2877Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic
Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic
Scale 1341Scale 1341: Madian, Ian Ring Music TheoryMadian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. 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.