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Scale 1349: "Tholitonic"

Scale 1349: Tholitonic, 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
Tholitonic

Analysis

Cardinality

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

5 (pentatonic)

Pitch Class Set

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

{0,2,6,8,10}

Forte Number

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

5-33

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.

[4]

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.

0 (anhemitonic)

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.

5

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.

4

Prime Form

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

no
prime: 341

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.

[0, 4, 0, 4, 0, 2]

Interval Spectrum

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

m4s4t2

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> = {2,4}
<2> = {4,6}
<3> = {6,8}
<4> = {8,10}

Spectra Variation

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

1.6

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.

2.165

Polygon Perimeter

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

5.732

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

yes

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.

[8]

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".

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
Augmented TriadsD+{2,6,10}000

The following pitch classes are not present in any of the common triads: {0,8}

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 1349 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1361
Scale 1361: Bolitonic, Ian Ring Music TheoryBolitonic
3rd mode:
Scale 341
Scale 341: Bothitonic, Ian Ring Music TheoryBothitonicThis is the prime mode
4th mode:
Scale 1109
Scale 1109: Kataditonic, Ian Ring Music TheoryKataditonic
5th mode:
Scale 1301
Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic

Prime

The prime form of this scale is Scale 341

Scale 341Scale 341: Bothitonic, Ian Ring Music TheoryBothitonic

Complement

The pentatonic modal family [1349, 1361, 341, 1109, 1301] (Forte: 5-33) is the complement of the heptatonic modal family [1367, 1373, 1397, 1493, 1877, 2731, 3413] (Forte: 7-33)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1349 is 1109

Scale 1109Scale 1109: Kataditonic, Ian Ring Music TheoryKataditonic

Transformations:

T0 1349  T0I 1109
T1 2698  T1I 2218
T2 1301  T2I 341
T3 2602  T3I 682
T4 1109  T4I 1364
T5 2218  T5I 2728
T6 341  T6I 1361
T7 682  T7I 2722
T8 1364  T8I 1349
T9 2728  T9I 2698
T10 1361  T10I 1301
T11 2722  T11I 2602

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 1351Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic
Scale 1345Scale 1345, Ian Ring Music Theory
Scale 1347Scale 1347, Ian Ring Music Theory
Scale 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 1357Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2
Scale 1365Scale 1365: Whole Tone, Ian Ring Music TheoryWhole Tone
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 1285Scale 1285, Ian Ring Music Theory
Scale 1317Scale 1317: Chaio, Ian Ring Music TheoryChaio
Scale 1413Scale 1413, Ian Ring Music Theory
Scale 1477Scale 1477: Raga Jaganmohanam, Ian Ring Music TheoryRaga Jaganmohanam
Scale 1093Scale 1093: Lydic, Ian Ring Music TheoryLydic
Scale 1221Scale 1221: Epyritonic, Ian Ring Music TheoryEpyritonic
Scale 1605Scale 1605: Zanitonic, Ian Ring Music TheoryZanitonic
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 325Scale 325: Messiaen Truncated Mode 6, Ian Ring Music TheoryMessiaen Truncated Mode 6
Scale 837Scale 837: Epaditonic, Ian Ring Music TheoryEpaditonic
Scale 2373Scale 2373: Dyptitonic, Ian Ring Music TheoryDyptitonic
Scale 3397Scale 3397: Sydimic, Ian Ring Music TheorySydimic

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.