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Scale 1841: "Thogimic"

Scale 1841: Thogimic, 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
Thogimic

Analysis

Cardinality

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

6 (hexatonic)

Pitch Class Set

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

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

Forte Number

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

6-16

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: 413

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.

5

Prime Form

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

no
prime: 371

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.

[4, 1, 3, 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.

<3, 2, 2, 4, 3, 1>

Interval Spectrum

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

p3m4n2s2d3t

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> = {1,2,3,4}
<2> = {2,3,4,5,6}
<3> = {4,5,7,8}
<4> = {6,7,8,9,10}
<5> = {8,9,10,11}

Spectra Variation

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

3

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.

2.116

Polygon Perimeter

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

5.699

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 TriadsF{5,9,0}221
Minor Triadsfm{5,8,0}221
am{9,0,4}221
Augmented TriadsC+{0,4,8}221

The following pitch classes are not present in any of the common triads: {10}

Parsimonious Voice Leading Between Common Triads of Scale 1841. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm am am C+->am F F fm->F F->am

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.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1841 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 371
Scale 371: Rythimic, Ian Ring Music TheoryRythimicThis is the prime mode
3rd mode:
Scale 2233
Scale 2233: Donimic, Ian Ring Music TheoryDonimic
4th mode:
Scale 791
Scale 791: Aeoloptimic, Ian Ring Music TheoryAeoloptimic
5th mode:
Scale 2443
Scale 2443: Panimic, Ian Ring Music TheoryPanimic
6th mode:
Scale 3269
Scale 3269: Raga Malarani, Ian Ring Music TheoryRaga Malarani

Prime

The prime form of this scale is Scale 371

Scale 371Scale 371: Rythimic, Ian Ring Music TheoryRythimic

Complement

The hexatonic modal family [1841, 371, 2233, 791, 2443, 3269] (Forte: 6-16) is the complement of the hexatonic modal family [371, 791, 1841, 2233, 2443, 3269] (Forte: 6-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1841 is 413

Scale 413Scale 413: Ganimic, Ian Ring Music TheoryGanimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1841 is chiral, and its enantiomorph is scale 413

Scale 413Scale 413: Ganimic, Ian Ring Music TheoryGanimic

Transformations:

T0 1841  T0I 413
T1 3682  T1I 826
T2 3269  T2I 1652
T3 2443  T3I 3304
T4 791  T4I 2513
T5 1582  T5I 931
T6 3164  T6I 1862
T7 2233  T7I 3724
T8 371  T8I 3353
T9 742  T9I 2611
T10 1484  T10I 1127
T11 2968  T11I 2254

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 1843Scale 1843: Ionygian, Ian Ring Music TheoryIonygian
Scale 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian
Scale 1849Scale 1849: Chromatic Hypodorian Inverse, Ian Ring Music TheoryChromatic Hypodorian Inverse
Scale 1825Scale 1825, Ian Ring Music Theory
Scale 1833Scale 1833: Ionacrimic, Ian Ring Music TheoryIonacrimic
Scale 1809Scale 1809: Ranitonic, Ian Ring Music TheoryRanitonic
Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
Scale 1905Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian
Scale 1969Scale 1969: Stylian, Ian Ring Music TheoryStylian
Scale 1585Scale 1585: Raga Khamaji Durga, Ian Ring Music TheoryRaga Khamaji Durga
Scale 1713Scale 1713: Raga Khamas, Ian Ring Music TheoryRaga Khamas
Scale 1329Scale 1329: Epygitonic, Ian Ring Music TheoryEpygitonic
Scale 817Scale 817: Zothitonic, Ian Ring Music TheoryZothitonic
Scale 2865Scale 2865: Solimic, Ian Ring Music TheorySolimic
Scale 3889Scale 3889: Parian, Ian Ring Music TheoryParian

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.