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Scale 185

Scale 185, 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).

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

{0,3,4,5,7}

Forte Number

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

5-11

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: 929

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.

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.

4

Prime Form

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

no
prime: 157

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.

[3, 1, 1, 2, 5] 9

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, 2, 2, 2, 2, 0>

Interval Spectrum

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

p2m2n2s2d2

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

Spectra Variation

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

4

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.

1.683

Polygon Perimeter

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

5.381

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 TriadsC{0,4,7}110.5
Minor Triadscm{0,3,7}110.5

The following pitch classes are not present in any of the common triads: {5}

Parsimonious Voice Leading Between Common Triads of Scale 185. Created by Ian Ring ©2019 cm cm C C cm->C

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 185 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 535
Scale 535, Ian Ring Music Theory
3rd mode:
Scale 2315
Scale 2315, Ian Ring Music Theory
4th mode:
Scale 3205
Scale 3205, Ian Ring Music Theory
5th mode:
Scale 1825
Scale 1825, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 157

Scale 157Scale 157, Ian Ring Music Theory

Complement

The pentatonic modal family [185, 535, 2315, 3205, 1825] (Forte: 5-11) is the complement of the heptatonic modal family [379, 1583, 1969, 2237, 2839, 3467, 3781] (Forte: 7-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 185 is 929

Scale 929Scale 929, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 185 is chiral, and its enantiomorph is scale 929

Scale 929Scale 929, Ian Ring Music Theory

Transformations:

T0 185  T0I 929
T1 370  T1I 1858
T2 740  T2I 3716
T3 1480  T3I 3337
T4 2960  T4I 2579
T5 1825  T5I 1063
T6 3650  T6I 2126
T7 3205  T7I 157
T8 2315  T8I 314
T9 535  T9I 628
T10 1070  T10I 1256
T11 2140  T11I 2512

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 187Scale 187, Ian Ring Music Theory
Scale 189Scale 189, Ian Ring Music Theory
Scale 177Scale 177, Ian Ring Music Theory
Scale 181Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari
Scale 169Scale 169: Vietnamese Tetratonic, Ian Ring Music TheoryVietnamese Tetratonic
Scale 153Scale 153, Ian Ring Music Theory
Scale 217Scale 217, Ian Ring Music Theory
Scale 249Scale 249, Ian Ring Music Theory
Scale 57Scale 57, Ian Ring Music Theory
Scale 121Scale 121, Ian Ring Music Theory
Scale 313Scale 313: Goritonic, Ian Ring Music TheoryGoritonic
Scale 441Scale 441: Thycrimic, Ian Ring Music TheoryThycrimic
Scale 697Scale 697: Lagimic, Ian Ring Music TheoryLagimic
Scale 1209Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
Scale 2233Scale 2233: Donimic, Ian Ring Music TheoryDonimic

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.