The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 393: "Lothic"

Scale 393: Lothic, 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

Zeitler
Lothic
Dozenal
CIZIAN

Analysis

Cardinality

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

4 (tetratonic)

Pitch Class Set

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

{0,3,7,8}

Forte Number

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

4-20

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.

[1.5]

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.

1 (unhemitonic)

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.

2

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.

3

Prime Form

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

no
prime: 291

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.

[1, 0, 1, 2, 2, 0]

Interval Spectrum

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

p2m2nd

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> = {1,3,4}
<2> = {5,7}
<3> = {8,9,11}

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.

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.

1.616

Polygon Perimeter

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

5.396

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.

[3]

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".

Strictly Proper

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 TriadsG♯{8,0,3}110.5
Minor Triadscm{0,3,7}110.5
Parsimonious Voice Leading Between Common Triads of Scale 393. Created by Ian Ring ©2019 cm cm G# G# cm->G#

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 393 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 561
Scale 561: Phratic, Ian Ring Music TheoryPhratic
3rd mode:
Scale 291
Scale 291: Raga Lavangi, Ian Ring Music TheoryRaga LavangiThis is the prime mode
4th mode:
Scale 2193
Scale 2193: Major Seventh, Ian Ring Music TheoryMajor Seventh

Prime

The prime form of this scale is Scale 291

Scale 291Scale 291: Raga Lavangi, Ian Ring Music TheoryRaga Lavangi

Complement

The tetratonic modal family [393, 561, 291, 2193] (Forte: 4-20) is the complement of the octatonic modal family [951, 1767, 1851, 2523, 2931, 2973, 3309, 3513] (Forte: 8-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 393 is 561

Scale 561Scale 561: Phratic, Ian Ring Music TheoryPhratic

Transformations:

T0 393  T0I 561
T1 786  T1I 1122
T2 1572  T2I 2244
T3 3144  T3I 393
T4 2193  T4I 786
T5 291  T5I 1572
T6 582  T6I 3144
T7 1164  T7I 2193
T8 2328  T8I 291
T9 561  T9I 582
T10 1122  T10I 1164
T11 2244  T11I 2328

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 395Scale 395: Phrygian Pentatonic, Ian Ring Music TheoryPhrygian Pentatonic
Scale 397Scale 397: Aeolian Pentatonic, Ian Ring Music TheoryAeolian Pentatonic
Scale 385Scale 385: CIVIAN, Ian Ring Music TheoryCIVIAN
Scale 389Scale 389: CIXIAN, Ian Ring Music TheoryCIXIAN
Scale 401Scale 401: Epogic, Ian Ring Music TheoryEpogic
Scale 409Scale 409: Laritonic, Ian Ring Music TheoryLaritonic
Scale 425Scale 425: Raga Kokil Pancham, Ian Ring Music TheoryRaga Kokil Pancham
Scale 457Scale 457: Staptitonic, Ian Ring Music TheoryStaptitonic
Scale 265Scale 265: BOXIAN, Ian Ring Music TheoryBOXIAN
Scale 329Scale 329: Lonic, Ian Ring Music TheoryLonic
Scale 137Scale 137: Minor Triad, Ian Ring Music TheoryMinor Triad
Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic
Scale 905Scale 905: Bylitonic, Ian Ring Music TheoryBylitonic
Scale 1417Scale 1417: Raga Shailaja, Ian Ring Music TheoryRaga Shailaja
Scale 2441Scale 2441: Kyritonic, Ian Ring Music TheoryKyritonic

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.