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Scale 1907: "Lynyllic"

Scale 1907: Lynyllic, 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
Lynyllic

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

8 (octatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,1,4,5,6,8,9,10}

Forte Number

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

8-19

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: 2525

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

5 (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.

7

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 887

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.

[1, 3, 1, 1, 2, 1, 1, 2]

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.

<5, 4, 5, 7, 5, 2>

Interval Spectrum

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

p5m7n5s4d5t2

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

Spectra Variation

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

1.75

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.

2.616

Polygon Perimeter

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

6.002

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

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♯{1,5,8}331.92
F{5,9,0}431.77
F♯{6,10,1}252.62
A{9,1,4}431.77
Minor Triadsc♯m{1,4,8}342.15
fm{5,8,0}342.15
f♯m{6,9,1}342.08
am{9,0,4}342
a♯m{10,1,5}342.08
Augmented TriadsC+{0,4,8}352.38
C♯+{1,5,9}531.54
Diminished Triadsf♯°{6,9,0}242.31
a♯°{10,1,4}242.31
Parsimonious Voice Leading Between Common Triads of Scale 1907. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->fm F F C#+->F f#m f#m C#+->f#m C#+->A a#m a#m C#+->a#m fm->F f#° f#° F->f#° F->am f#°->f#m F# F# f#m->F# F#->a#m am->A a#° a#° A->a#° a#°->a#m

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC♯, C♯+, F, A
Peripheral VerticesC+, F♯

Modes

Modes are the rotational transformation of this scale. Scale 1907 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3001
Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
3rd mode:
Scale 887
Scale 887: Sathyllic, Ian Ring Music TheorySathyllicThis is the prime mode
4th mode:
Scale 2491
Scale 2491: Layllic, Ian Ring Music TheoryLayllic
5th mode:
Scale 3293
Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
6th mode:
Scale 1847
Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
7th mode:
Scale 2971
Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
8th mode:
Scale 3533
Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [1907, 3001, 887, 2491, 3293, 1847, 2971, 3533] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1907 is 2525

Scale 2525Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1907 is chiral, and its enantiomorph is scale 2525

Scale 2525Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic

Transformations:

T0 1907  T0I 2525
T1 3814  T1I 955
T2 3533  T2I 1910
T3 2971  T3I 3820
T4 1847  T4I 3545
T5 3694  T5I 2995
T6 3293  T6I 1895
T7 2491  T7I 3790
T8 887  T8I 3485
T9 1774  T9I 2875
T10 3548  T10I 1655
T11 3001  T11I 3310

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 1905Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian
Scale 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
Scale 1911Scale 1911: Messiaen Mode 3, Ian Ring Music TheoryMessiaen Mode 3
Scale 1915Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
Scale 1891Scale 1891: Thalian, Ian Ring Music TheoryThalian
Scale 1899Scale 1899: Moptyllic, Ian Ring Music TheoryMoptyllic
Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale
Scale 1843Scale 1843: Ionygian, Ian Ring Music TheoryIonygian
Scale 1971Scale 1971: Aerynyllic, Ian Ring Music TheoryAerynyllic
Scale 2035Scale 2035: Aerythygic, Ian Ring Music TheoryAerythygic
Scale 1651Scale 1651: Asian, Ian Ring Music TheoryAsian
Scale 1779Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
Scale 1395Scale 1395: Locrian Dominant, Ian Ring Music TheoryLocrian Dominant
Scale 883Scale 883: Ralian, Ian Ring Music TheoryRalian
Scale 2931Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic

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.