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Scale 2517: "Harmonic Lydian"

Scale 2517: Harmonic 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

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 Modern
Harmonic Lydian
Carnatic
Mela Latangi
Raga Gitapriya
Hamsalata
Zeitler
Ryphian
Dozenal
Pician
Carnatic Melakarta
Latangi
Carnatic Numbered Melakarta
63rd Melakarta raga

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

{0,2,4,6,7,8,11}

Forte Number

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

7-30

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: 1395

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.

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 Starr/Rahn algorithm.

no
prime: 855

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, an indicator of maximum hierarchization.

no

Interval Structure

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

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

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

Interval Spectrum

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

p4m5n3s4d3t2

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}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {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.

1.714

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 Distribution Spectra have 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

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.

(2, 22, 86)

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
E{4,8,11}331.43
G{7,11,2}331.43
Minor Triadsem{4,7,11}321.29
bm{11,2,6}142.14
Augmented TriadsC+{0,4,8}241.86
Diminished Triadsg♯°{8,11,2}231.57
Parsimonious Voice Leading Between Common Triads of Scale 2517. Created by Ian Ring ©2019 C C C+ C+ C->C+ em em C->em E E C+->E em->E Parsimonious Voice Leading Between Common Triads of Scale 2517. Created by Ian Ring ©2019 G em->G g#° g#° E->g#° G->g#° bm bm G->bm

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 Verticesem
Peripheral VerticesC+, bm

Modes

Modes are the rotational transformation of this scale. Scale 2517 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1653
Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
3rd mode:
Scale 1437
Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending
4th mode:
Scale 1383
Scale 1383: Pynian, Ian Ring Music TheoryPynian
5th mode:
Scale 2739
Scale 2739: Mela Suryakanta, Ian Ring Music TheoryMela Suryakanta
6th mode:
Scale 3417
Scale 3417: Golian, Ian Ring Music TheoryGolian
7th mode:
Scale 939
Scale 939: Mela Senavati, Ian Ring Music TheoryMela Senavati

Prime

The prime form of this scale is Scale 855

Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian

Complement

The heptatonic modal family [2517, 1653, 1437, 1383, 2739, 3417, 939] (Forte: 7-30) is the complement of the pentatonic modal family [339, 789, 1221, 1329, 2217] (Forte: 5-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2517 is 1395

Scale 1395Scale 1395: Locrian Dominant, Ian Ring Music TheoryLocrian Dominant

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2517 is chiral, and its enantiomorph is scale 1395

Scale 1395Scale 1395: Locrian Dominant, Ian Ring Music TheoryLocrian Dominant

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> 2517       T0I <11,0> 1395
T1 <1,1> 939      T1I <11,1> 2790
T2 <1,2> 1878      T2I <11,2> 1485
T3 <1,3> 3756      T3I <11,3> 2970
T4 <1,4> 3417      T4I <11,4> 1845
T5 <1,5> 2739      T5I <11,5> 3690
T6 <1,6> 1383      T6I <11,6> 3285
T7 <1,7> 2766      T7I <11,7> 2475
T8 <1,8> 1437      T8I <11,8> 855
T9 <1,9> 2874      T9I <11,9> 1710
T10 <1,10> 1653      T10I <11,10> 3420
T11 <1,11> 3306      T11I <11,11> 2745
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3537      T0MI <7,0> 375
T1M <5,1> 2979      T1MI <7,1> 750
T2M <5,2> 1863      T2MI <7,2> 1500
T3M <5,3> 3726      T3MI <7,3> 3000
T4M <5,4> 3357      T4MI <7,4> 1905
T5M <5,5> 2619      T5MI <7,5> 3810
T6M <5,6> 1143      T6MI <7,6> 3525
T7M <5,7> 2286      T7MI <7,7> 2955
T8M <5,8> 477      T8MI <7,8> 1815
T9M <5,9> 954      T9MI <7,9> 3630
T10M <5,10> 1908      T10MI <7,10> 3165
T11M <5,11> 3816      T11MI <7,11> 2235

The transformations that map this set to itself are: T0

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 2519Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic
Scale 2513Scale 2513: Aerycrimic, Ian Ring Music TheoryAerycrimic
Scale 2515Scale 2515: Chromatic Hypolydian, Ian Ring Music TheoryChromatic Hypolydian
Scale 2521Scale 2521: Mela Dhatuvardhani, Ian Ring Music TheoryMela Dhatuvardhani
Scale 2525Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
Scale 2501Scale 2501: Ralimic, Ian Ring Music TheoryRalimic
Scale 2509Scale 2509: Double Harmonic Minor, Ian Ring Music TheoryDouble Harmonic Minor
Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian
Scale 2549Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
Scale 2453Scale 2453: Raga Latika, Ian Ring Music TheoryRaga Latika
Scale 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major
Scale 2389Scale 2389: Eskimo Hexatonic 2, Ian Ring Music TheoryEskimo Hexatonic 2
Scale 2261Scale 2261: Raga Caturangini, Ian Ring Music TheoryRaga Caturangini
Scale 2773Scale 2773: Lydian, Ian Ring Music TheoryLydian
Scale 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 3541Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
Scale 469Scale 469: Katyrimic, Ian Ring Music TheoryKatyrimic
Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor

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.