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Scale 2773: "Lydian"

Scale 2773: Lydian, 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

Western
Lydian
Ancient Greek
Greek Hypolydian
Greek Medieval Hypolocrian
Medieval
Medieval Lydian
Unknown / Unsorted
Rut biscale ascending
Ping
Gu
Hindustani
Kalyan That
Kalyan Theta
Carnatic Mela
Mela Mecakalyani
Carnatic Raga
Raga Shuddh Kalyan
Japanese
Kung
Zeitler
Lydian

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

{0,2,4,6,7,9,11}

Forte Number

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

7-35

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.

[3]

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.

2 (dihemitonic)

Cohemitonia

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

0 (ancohemitonic)

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.

1

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: 1387

Deep Scale

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

yes

Interval Formula

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

[2, 2, 2, 1, 2, 2, 1] 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.

<2, 5, 4, 3, 6, 1>

Interval Spectrum

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

p6m3n4s5d2t

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

Spectra Variation

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

0.857

Maximally Even

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

yes

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.

yes

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.

2.665

Polygon Perimeter

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

6.035

Myhill Property

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

yes

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.

[6]

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".

Proper

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}231.71
D{2,6,9}231.71
G{7,11,2}231.71
Minor Triadsem{4,7,11}231.71
am{9,0,4}231.71
bm{11,2,6}231.71
Diminished Triadsf♯°{6,9,0}231.71
Parsimonious Voice Leading Between Common Triads of Scale 2773. Created by Ian Ring ©2019 C C em em C->em am am C->am D D f#° f#° D->f#° bm bm D->bm Parsimonious Voice Leading Between Common Triads of Scale 2773. Created by Ian Ring ©2019 G em->G f#°->am G->bm

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

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 2773 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1717
Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
3rd mode:
Scale 1453
Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
4th mode:
Scale 1387
Scale 1387: Locrian, Ian Ring Music TheoryLocrianThis is the prime mode
5th mode:
Scale 2741
Scale 2741: Major, Ian Ring Music TheoryMajor
6th mode:
Scale 1709
Scale 1709: Dorian, Ian Ring Music TheoryDorian
7th mode:
Scale 1451
Scale 1451: Phrygian, Ian Ring Music TheoryPhrygian

Prime

The prime form of this scale is Scale 1387

Scale 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian

Complement

The heptatonic modal family [2773, 1717, 1453, 1387, 2741, 1709, 1451] (Forte: 7-35) is the complement of the pentatonic modal family [661, 677, 1189, 1193, 1321] (Forte: 5-35)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2773 is 1387

Scale 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian

Transformations:

T0 2773  T0I 1387
T1 1451  T1I 2774
T2 2902  T2I 1453
T3 1709  T3I 2906
T4 3418  T4I 1717
T5 2741  T5I 3434
T6 1387  T6I 2773
T7 2774  T7I 1451
T8 1453  T8I 2902
T9 2906  T9I 1709
T10 1717  T10I 3418
T11 3434  T11I 2741

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 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 2769Scale 2769: Dyrimic, Ian Ring Music TheoryDyrimic
Scale 2771Scale 2771: Marva That, Ian Ring Music TheoryMarva That
Scale 2777Scale 2777: Aeolian Harmonic, Ian Ring Music TheoryAeolian Harmonic
Scale 2781Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
Scale 2757Scale 2757: Raga Nishadi, Ian Ring Music TheoryRaga Nishadi
Scale 2765Scale 2765: Lydian Flat 3, Ian Ring Music TheoryLydian Flat 3
Scale 2789Scale 2789: Zolian, Ian Ring Music TheoryZolian
Scale 2805Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho
Scale 2709Scale 2709: Raga Kumud, Ian Ring Music TheoryRaga Kumud
Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor
Scale 2645Scale 2645: Raga Mruganandana, Ian Ring Music TheoryRaga Mruganandana
Scale 2901Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented
Scale 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 2261Scale 2261: Raga Caturangini, Ian Ring Music TheoryRaga Caturangini
Scale 2517Scale 2517: Harmonic Lydian, Ian Ring Music TheoryHarmonic Lydian
Scale 3285Scale 3285: Mela Citrambari, Ian Ring Music TheoryMela Citrambari
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
Scale 725Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic

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.