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Scale 2993: "Stythian"

Scale 2993: Stythian, 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
Stythian
Dozenal
Sulian

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

{0,4,5,7,8,9,11}

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-Z37

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.

[2]

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.

no

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.

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.

3

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: 443

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

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

no

Interval Structure

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

[4, 1, 2, 1, 1, 2, 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, 4, 5, 4, 1>

Interval Spectrum

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

p4m5n4s3d4t

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> = {1,2,4}
<2> = {2,3,5}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {7,9,10}
<6> = {8,10,11}

Spectra Variation

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

2.571

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.

2.299

Polygon Perimeter

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

5.803

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.

[4]

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

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(34, 21, 84)

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 TriadsC{0,4,7}231.75
E{4,8,11}331.5
F{5,9,0}242
Minor Triadsem{4,7,11}242
fm{5,8,0}331.5
am{9,0,4}231.75
Augmented TriadsC+{0,4,8}421.25
Diminished Triads{5,8,11}231.75
Parsimonious Voice Leading Between Common Triads of Scale 2993. Created by Ian Ring ©2019 C C C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm am am C+->am em->E E->f° f°->fm F F fm->F F->am

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 VerticesC+
Peripheral Verticesem, F

Modes

Modes are the rotational transformation of this scale. Scale 2993 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 443
Scale 443: Kothian, Ian Ring Music TheoryKothianThis is the prime mode
3rd mode:
Scale 2269
Scale 2269: Pygian, Ian Ring Music TheoryPygian
4th mode:
Scale 1591
Scale 1591: Rodian, Ian Ring Music TheoryRodian
5th mode:
Scale 2843
Scale 2843: Sorian, Ian Ring Music TheorySorian
6th mode:
Scale 3469
Scale 3469: Monian, Ian Ring Music TheoryMonian
7th mode:
Scale 1891
Scale 1891: Thalian, Ian Ring Music TheoryThalian

Prime

The prime form of this scale is Scale 443

Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian

Complement

The heptatonic modal family [2993, 443, 2269, 1591, 2843, 3469, 1891] (Forte: 7-Z37) is the complement of the pentatonic modal family [313, 551, 913, 2323, 3209] (Forte: 5-Z37)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2993 is 443

Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 2993       T0I <11,0> 443
T1 <1,1> 1891      T1I <11,1> 886
T2 <1,2> 3782      T2I <11,2> 1772
T3 <1,3> 3469      T3I <11,3> 3544
T4 <1,4> 2843      T4I <11,4> 2993
T5 <1,5> 1591      T5I <11,5> 1891
T6 <1,6> 3182      T6I <11,6> 3782
T7 <1,7> 2269      T7I <11,7> 3469
T8 <1,8> 443      T8I <11,8> 2843
T9 <1,9> 886      T9I <11,9> 1591
T10 <1,10> 1772      T10I <11,10> 3182
T11 <1,11> 3544      T11I <11,11> 2269
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2963      T0MI <7,0> 2363
T1M <5,1> 1831      T1MI <7,1> 631
T2M <5,2> 3662      T2MI <7,2> 1262
T3M <5,3> 3229      T3MI <7,3> 2524
T4M <5,4> 2363      T4MI <7,4> 953
T5M <5,5> 631      T5MI <7,5> 1906
T6M <5,6> 1262      T6MI <7,6> 3812
T7M <5,7> 2524      T7MI <7,7> 3529
T8M <5,8> 953      T8MI <7,8> 2963
T9M <5,9> 1906      T9MI <7,9> 1831
T10M <5,10> 3812      T10MI <7,10> 3662
T11M <5,11> 3529      T11MI <7,11> 3229

The transformations that map this set to itself are: T0, T4I

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 2995Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
Scale 2997Scale 2997: Major Bebop, Ian Ring Music TheoryMajor Bebop
Scale 3001Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
Scale 2977Scale 2977: Sobian, Ian Ring Music TheorySobian
Scale 2985Scale 2985: Epacrian, Ian Ring Music TheoryEpacrian
Scale 2961Scale 2961: Bygimic, Ian Ring Music TheoryBygimic
Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
Scale 3057Scale 3057: Phroryllic, Ian Ring Music TheoryPhroryllic
Scale 2865Scale 2865: Solimic, Ian Ring Music TheorySolimic
Scale 2929Scale 2929: Aeolathian, Ian Ring Music TheoryAeolathian
Scale 2737Scale 2737: Raga Hari Nata, Ian Ring Music TheoryRaga Hari Nata
Scale 2481Scale 2481: Raga Paraju, Ian Ring Music TheoryRaga Paraju
Scale 3505Scale 3505: Stygian, Ian Ring Music TheoryStygian
Scale 4017Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic
Scale 945Scale 945: Raga Saravati, Ian Ring Music TheoryRaga Saravati
Scale 1969Scale 1969: Stylian, Ian Ring Music TheoryStylian

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. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.