The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1291

Scale 1291, 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).

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

{0,1,3,8,10}

Forte Number

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

5-23

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: 2581

Hemitonia

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

1 (unhemitonic)

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.

2

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: 173

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.

[1, 2, 5, 2, 2] 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.

<1, 3, 2, 1, 3, 0>

Interval Spectrum

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

p3mn2s3d

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

Spectra Variation

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

3.2

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.

1.799

Polygon Perimeter

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

5.449

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 TriadsG♯{8,0,3}000

The following pitch classes are not present in any of the common triads: {1,10}

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 1291 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2693
Scale 2693, Ian Ring Music Theory
3rd mode:
Scale 1697
Scale 1697: Raga Kuntvarali, Ian Ring Music TheoryRaga Kuntvarali
4th mode:
Scale 181
Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari
5th mode:
Scale 1069
Scale 1069, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 173

Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita

Complement

The pentatonic modal family [1291, 2693, 1697, 181, 1069] (Forte: 5-23) is the complement of the heptatonic modal family [701, 1199, 1513, 1957, 2647, 3371, 3733] (Forte: 7-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1291 is 2581

Scale 2581Scale 2581: Raga Neroshta, Ian Ring Music TheoryRaga Neroshta

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1291 is chiral, and its enantiomorph is scale 2581

Scale 2581Scale 2581: Raga Neroshta, Ian Ring Music TheoryRaga Neroshta

Transformations:

T0 1291  T0I 2581
T1 2582  T1I 1067
T2 1069  T2I 2134
T3 2138  T3I 173
T4 181  T4I 346
T5 362  T5I 692
T6 724  T6I 1384
T7 1448  T7I 2768
T8 2896  T8I 1441
T9 1697  T9I 2882
T10 3394  T10I 1669
T11 2693  T11I 3338

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 1289Scale 1289, Ian Ring Music Theory
Scale 1293Scale 1293, Ian Ring Music Theory
Scale 1295Scale 1295, Ian Ring Music Theory
Scale 1283Scale 1283, Ian Ring Music Theory
Scale 1287Scale 1287, Ian Ring Music Theory
Scale 1299Scale 1299: Aerophitonic, Ian Ring Music TheoryAerophitonic
Scale 1307Scale 1307: Katorimic, Ian Ring Music TheoryKatorimic
Scale 1323Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
Scale 1355Scale 1355: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 1419Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi
Scale 1035Scale 1035, Ian Ring Music Theory
Scale 1163Scale 1163: Raga Rukmangi, Ian Ring Music TheoryRaga Rukmangi
Scale 1547Scale 1547, Ian Ring Music Theory
Scale 1803Scale 1803, Ian Ring Music Theory
Scale 267Scale 267, Ian Ring Music Theory
Scale 779Scale 779, Ian Ring Music Theory
Scale 2315Scale 2315, Ian Ring Music Theory
Scale 3339Scale 3339, Ian Ring Music Theory

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.