The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1985

Scale 1985, 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.

6 (hexatonic)

Pitch Class Set

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

{0,6,7,8,9,10}

Forte Number

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

6-2

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: 125

Hemitonia

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

4 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

3 (tricohemitonic)

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: 95

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

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.

[6, 1, 1, 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.

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

Interval Spectrum

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

pm2n3s4d4t

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

Spectra Variation

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

4.667

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.

1.433

Polygon Perimeter

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

5.071

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

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(34, 13, 55)

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
Diminished Triadsf♯°{6,9,0}000

The following pitch classes are not present in any of the common triads: {7,8,10}

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 1985 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 95
Scale 95, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2095
Scale 2095, Ian Ring Music Theory
4th mode:
Scale 3095
Scale 3095, Ian Ring Music Theory
5th mode:
Scale 3595
Scale 3595, Ian Ring Music Theory
6th mode:
Scale 3845
Scale 3845, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 95

Scale 95Scale 95, Ian Ring Music Theory

Complement

The hexatonic modal family [1985, 95, 2095, 3095, 3595, 3845] (Forte: 6-2) is the complement of the hexatonic modal family [95, 1985, 2095, 3095, 3595, 3845] (Forte: 6-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1985 is 125

Scale 125Scale 125, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1985 is chiral, and its enantiomorph is scale 125

Scale 125Scale 125, Ian Ring Music Theory

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 1985       T0I <11,0> 125
T1 <1,1> 3970      T1I <11,1> 250
T2 <1,2> 3845      T2I <11,2> 500
T3 <1,3> 3595      T3I <11,3> 1000
T4 <1,4> 3095      T4I <11,4> 2000
T5 <1,5> 2095      T5I <11,5> 4000
T6 <1,6> 95      T6I <11,6> 3905
T7 <1,7> 190      T7I <11,7> 3715
T8 <1,8> 380      T8I <11,8> 3335
T9 <1,9> 760      T9I <11,9> 2575
T10 <1,10> 1520      T10I <11,10> 1055
T11 <1,11> 3040      T11I <11,11> 2110
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2645      T0MI <7,0> 1355
T1M <5,1> 1195      T1MI <7,1> 2710
T2M <5,2> 2390      T2MI <7,2> 1325
T3M <5,3> 685      T3MI <7,3> 2650
T4M <5,4> 1370      T4MI <7,4> 1205
T5M <5,5> 2740      T5MI <7,5> 2410
T6M <5,6> 1385      T6MI <7,6> 725
T7M <5,7> 2770      T7MI <7,7> 1450
T8M <5,8> 1445      T8MI <7,8> 2900
T9M <5,9> 2890      T9MI <7,9> 1705
T10M <5,10> 1685      T10MI <7,10> 3410
T11M <5,11> 3370      T11MI <7,11> 2725

The transformations that map this set to itself are: T0

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 1987Scale 1987, Ian Ring Music Theory
Scale 1989Scale 1989: Dydian, Ian Ring Music TheoryDydian
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
Scale 2001Scale 2001: Gydian, Ian Ring Music TheoryGydian
Scale 2017Scale 2017, Ian Ring Music Theory
Scale 1921Scale 1921, Ian Ring Music Theory
Scale 1953Scale 1953, Ian Ring Music Theory
Scale 1857Scale 1857, Ian Ring Music Theory
Scale 1729Scale 1729, Ian Ring Music Theory
Scale 1473Scale 1473, Ian Ring Music Theory
Scale 961Scale 961, Ian Ring Music Theory
Scale 3009Scale 3009, Ian Ring Music Theory
Scale 4033Scale 4033: Heptatonic Chromatic Descending, Ian Ring Music TheoryHeptatonic Chromatic Descending

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. All other diagrams and visualizations are © Ian Ring. 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.