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Scale 829: "Lygian"

Scale 829: Lygian, 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
Lygian

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

{0,2,3,4,5,8,9}

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-Z18

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: 1945

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.

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: 755

Deep Scale

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

no

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, 4, 4, 2]

Interval Spectrum

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

p4m4n4s3d4t2

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

Spectra Variation

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

2.571

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.

2.433

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

Harmonic Chords

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 TriadsF{5,9,0}331.5
G♯{8,0,3}242
Minor Triadsdm{2,5,9}242
fm{5,8,0}331.5
am{9,0,4}331.5
Augmented TriadsC+{0,4,8}331.5
Diminished Triads{2,5,8}242
{9,0,3}242
Parsimonious Voice Leading Between Common Triads of Scale 829. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm G# G# C+->G# am am C+->am dm dm d°->dm d°->fm F F dm->F fm->F F->am G#->a° a°->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
Radius3
Self-Centeredno
Central VerticesC+, fm, F, am
Peripheral Verticesd°, dm, G♯, a°

Modes

Modes are the rotational transformation of this scale. Scale 829 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1231
Scale 1231: Logian, Ian Ring Music TheoryLogian
3rd mode:
Scale 2663
Scale 2663: Lalian, Ian Ring Music TheoryLalian
4th mode:
Scale 3379
Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
5th mode:
Scale 3737
Scale 3737: Phrocrian, Ian Ring Music TheoryPhrocrian
6th mode:
Scale 979
Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari
7th mode:
Scale 2537
Scale 2537: Laptian, Ian Ring Music TheoryLaptian

Prime

The prime form of this scale is Scale 755

Scale 755Scale 755: Phrythian, Ian Ring Music TheoryPhrythian

Complement

The heptatonic modal family [829, 1231, 2663, 3379, 3737, 979, 2537] (Forte: 7-Z18) is the complement of the pentatonic modal family [179, 779, 1633, 2137, 2437] (Forte: 5-Z18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 829 is 1945

Scale 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 829 is chiral, and its enantiomorph is scale 1945

Scale 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian

Transformations:

T0 829  T0I 1945
T1 1658  T1I 3890
T2 3316  T2I 3685
T3 2537  T3I 3275
T4 979  T4I 2455
T5 1958  T5I 815
T6 3916  T6I 1630
T7 3737  T7I 3260
T8 3379  T8I 2425
T9 2663  T9I 755
T10 1231  T10I 1510
T11 2462  T11I 3020

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 831Scale 831: Rodyllic, Ian Ring Music TheoryRodyllic
Scale 825Scale 825: Thyptimic, Ian Ring Music TheoryThyptimic
Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
Scale 821Scale 821: Aeranimic, Ian Ring Music TheoryAeranimic
Scale 813Scale 813: Larimic, Ian Ring Music TheoryLarimic
Scale 797Scale 797: Katocrimic, Ian Ring Music TheoryKatocrimic
Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian
Scale 893Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic
Scale 957Scale 957: Phronyllic, Ian Ring Music TheoryPhronyllic
Scale 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian
Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic
Scale 1341Scale 1341: Madian, Ian Ring Music TheoryMadian
Scale 1853Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic
Scale 2877Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. 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.