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Scale 1117: "Raptimic"

Scale 1117: Raptimic, 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
Raptimic

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

{0,2,3,4,6,10}

Forte Number

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

6-21

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: 1861

Hemitonia

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

2 (dihemitonic)

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.

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.

5

Prime Form

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

no
prime: 349

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.

[2, 4, 2, 4, 1, 2]

Interval Spectrum

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

pm4n2s4d2t2

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

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.

2.232

Polygon Perimeter

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

5.767

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
Minor Triadsd♯m{3,6,10}210.67
Augmented TriadsD+{2,6,10}121
Diminished Triads{0,3,6}121

The following pitch classes are not present in any of the common triads: {4}

Parsimonious Voice Leading Between Common Triads of Scale 1117. Created by Ian Ring ©2019 d#m d#m c°->d#m D+ D+ D+->d#m

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
Radius1
Self-Centeredno
Central Verticesd♯m
Peripheral Verticesc°, D+

Modes

Modes are the rotational transformation of this scale. Scale 1117 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1303
Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic
3rd mode:
Scale 2699
Scale 2699: Sythimic, Ian Ring Music TheorySythimic
4th mode:
Scale 3397
Scale 3397: Sydimic, Ian Ring Music TheorySydimic
5th mode:
Scale 1873
Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
6th mode:
Scale 373
Scale 373: Epagimic, Ian Ring Music TheoryEpagimic

Prime

The prime form of this scale is Scale 349

Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic

Complement

The hexatonic modal family [1117, 1303, 2699, 3397, 1873, 373] (Forte: 6-21) is the complement of the hexatonic modal family [349, 1111, 1489, 1861, 2603, 3349] (Forte: 6-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1117 is 1861

Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1117 is chiral, and its enantiomorph is scale 1861

Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic

Transformations:

T0 1117  T0I 1861
T1 2234  T1I 3722
T2 373  T2I 3349
T3 746  T3I 2603
T4 1492  T4I 1111
T5 2984  T5I 2222
T6 1873  T6I 349
T7 3746  T7I 698
T8 3397  T8I 1396
T9 2699  T9I 2792
T10 1303  T10I 1489
T11 2606  T11I 2978

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 1119Scale 1119: Rarian, Ian Ring Music TheoryRarian
Scale 1113Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
Scale 1109Scale 1109: Kataditonic, Ian Ring Music TheoryKataditonic
Scale 1101Scale 1101: Stothitonic, Ian Ring Music TheoryStothitonic
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 1149Scale 1149: Bydian, Ian Ring Music TheoryBydian
Scale 1053Scale 1053, Ian Ring Music Theory
Scale 1085Scale 1085, Ian Ring Music Theory
Scale 1181Scale 1181: Katagimic, Ian Ring Music TheoryKatagimic
Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian
Scale 1373Scale 1373: Storian, Ian Ring Music TheoryStorian
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 93Scale 93, Ian Ring Music Theory
Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic
Scale 2141Scale 2141, Ian Ring Music Theory
Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian

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.