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Scale 3423: "Lothygic"

Scale 3423: Lothygic, 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
Lothygic

Analysis

Cardinality

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

9 (nonatonic)

Pitch Class Set

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

{0,1,2,3,4,6,8,10,11}

Forte Number

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

9-6

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.

[1]

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.

6 (multihemitonic)

Cohemitonia

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

5 (multicohemitonic)

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.

8

Prime Form

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

no
prime: 1407

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

<6, 8, 6, 7, 6, 3>

Interval Spectrum

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

p6m7n6s8d6t3

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

Spectra Variation

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

2

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.

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.

2.799

Polygon Perimeter

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

6.106

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.

[2]

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 TriadsE{4,8,11}242.31
F♯{6,10,1}242.54
G♯{8,0,3}342.15
B{11,3,6}442
Minor Triadsc♯m{1,4,8}242.54
d♯m{3,6,10}242.31
g♯m{8,11,3}442
bm{11,2,6}342.15
Augmented TriadsC+{0,4,8}342.31
D+{2,6,10}342.31
Diminished Triads{0,3,6}242.31
g♯°{8,11,2}242.31
a♯°{10,1,4}242.62
Parsimonious Voice Leading Between Common Triads of Scale 3423. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E C+->G# a#° a#° c#m->a#° D+ D+ d#m d#m D+->d#m F# F# D+->F# bm bm D+->bm d#m->B g#m g#m E->g#m F#->a#° g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B bm->B

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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3423 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3759
Scale 3759: Darygic, Ian Ring Music TheoryDarygic
3rd mode:
Scale 3927
Scale 3927: Monygic, Ian Ring Music TheoryMonygic
4th mode:
Scale 4011
Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
5th mode:
Scale 4053
Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
6th mode:
Scale 2037
Scale 2037: Sythygic, Ian Ring Music TheorySythygic
7th mode:
Scale 1533
Scale 1533: Katycrygic, Ian Ring Music TheoryKatycrygic
8th mode:
Scale 1407
Scale 1407: Tharygic, Ian Ring Music TheoryTharygicThis is the prime mode
9th mode:
Scale 2751
Scale 2751: Sylygic, Ian Ring Music TheorySylygic

Prime

The prime form of this scale is Scale 1407

Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic

Complement

The nonatonic modal family [3423, 3759, 3927, 4011, 4053, 2037, 1533, 1407, 2751] (Forte: 9-6) is the complement of the tritonic modal family [21, 1029, 1281] (Forte: 3-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3423 is 3927

Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic

Transformations:

T0 3423  T0I 3927
T1 2751  T1I 3759
T2 1407  T2I 3423
T3 2814  T3I 2751
T4 1533  T4I 1407
T5 3066  T5I 2814
T6 2037  T6I 1533
T7 4074  T7I 3066
T8 4053  T8I 2037
T9 4011  T9I 4074
T10 3927  T10I 4053
T11 3759  T11I 4011

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 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3407Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
Scale 3439Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
Scale 3359Scale 3359: Bonyllic, Ian Ring Music TheoryBonyllic
Scale 3391Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3679Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
Scale 3935Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 2911Scale 2911: Katygic, Ian Ring Music TheoryKatygic
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic

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.