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Scale 2001: "Gydian"

Scale 2001: Gydian, 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
Gydian

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

{0,4,6,7,8,9,10}

Forte Number

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

7-8

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.

3 (tricohemitonic)

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.

5

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: 381

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.

[4, 2, 1, 1, 1, 1, 2] 9

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, 5, 4, 4, 2, 2>

Interval Spectrum

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

p2m4n4s5d4t2

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

Spectra Variation

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

3.429

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

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}231.4
Minor Triadsam{9,0,4}231.4
Augmented TriadsC+{0,4,8}221.2
Diminished Triads{4,7,10}142
f♯°{6,9,0}142
Parsimonious Voice Leading Between Common Triads of Scale 2001. Created by Ian Ring ©2019 C C C+ C+ C->C+ C->e° am am C+->am f#° 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 Verticese°, f♯°

Triadic Polychords

There is 1 way that this hexatonic scale can be split into two common triads.


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Modes

Modes are the rotational transformation of this scale. Scale 2001 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 381
Scale 381: Kogian, Ian Ring Music TheoryKogianThis is the prime mode
3rd mode:
Scale 1119
Scale 1119: Rarian, Ian Ring Music TheoryRarian
4th mode:
Scale 2607
Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
5th mode:
Scale 3351
Scale 3351: Crater Scale, Ian Ring Music TheoryCrater Scale
6th mode:
Scale 3723
Scale 3723: Myptian, Ian Ring Music TheoryMyptian
7th mode:
Scale 3909
Scale 3909: Rydian, Ian Ring Music TheoryRydian

Prime

The prime form of this scale is Scale 381

Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian

Complement

The heptatonic modal family [2001, 381, 1119, 2607, 3351, 3723, 3909] (Forte: 7-8) is the complement of the pentatonic modal family [93, 1047, 1857, 2571, 3333] (Forte: 5-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2001 is 381

Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian

Transformations:

T0 2001  T0I 381
T1 4002  T1I 762
T2 3909  T2I 1524
T3 3723  T3I 3048
T4 3351  T4I 2001
T5 2607  T5I 4002
T6 1119  T6I 3909
T7 2238  T7I 3723
T8 381  T8I 3351
T9 762  T9I 2607
T10 1524  T10I 1119
T11 3048  T11I 2238

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 2003Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 1985Scale 1985, Ian Ring Music Theory
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
Scale 2017Scale 2017, Ian Ring Music Theory
Scale 2033Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic
Scale 1937Scale 1937: Galimic, Ian Ring Music TheoryGalimic
Scale 1969Scale 1969: Stylian, Ian Ring Music TheoryStylian
Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1489Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti
Scale 977Scale 977: Kocrimic, Ian Ring Music TheoryKocrimic
Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
Scale 4049Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic

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.