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Scale 2497: "PEQIAN"

Scale 2497: PEQIAN, 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

{0,6,7,8,11}

Forte Number

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

5-6

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: 115

Hemitonia

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

3 (trihemitonic)

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: 103

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.

[3, 1, 1, 2, 2, 1]

Interval Spectrum

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

p2m2nsd3t

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

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.

1.25

Polygon Perimeter

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

4.967

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

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 2497 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 103
Scale 103: APUIAN, Ian Ring Music TheoryAPUIANThis is the prime mode
3rd mode:
Scale 2099
Scale 2099: Raga Megharanji, Ian Ring Music TheoryRaga Megharanji
4th mode:
Scale 3097
Scale 3097: TIWIAN, Ian Ring Music TheoryTIWIAN
5th mode:
Scale 899
Scale 899: FOQIAN, Ian Ring Music TheoryFOQIAN

Prime

The prime form of this scale is Scale 103

Scale 103Scale 103: APUIAN, Ian Ring Music TheoryAPUIAN

Complement

The pentatonic modal family [2497, 103, 2099, 3097, 899] (Forte: 5-6) is the complement of the heptatonic modal family [415, 995, 2255, 2545, 3175, 3635, 3865] (Forte: 7-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2497 is 115

Scale 115Scale 115: ASHIAN, Ian Ring Music TheoryASHIAN

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2497 is chiral, and its enantiomorph is scale 115

Scale 115Scale 115: ASHIAN, Ian Ring Music TheoryASHIAN

Transformations:

T0 2497  T0I 115
T1 899  T1I 230
T2 1798  T2I 460
T3 3596  T3I 920
T4 3097  T4I 1840
T5 2099  T5I 3680
T6 103  T6I 3265
T7 206  T7I 2435
T8 412  T8I 775
T9 824  T9I 1550
T10 1648  T10I 3100
T11 3296  T11I 2105

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 2499Scale 2499: PIRIAN, Ian Ring Music TheoryPIRIAN
Scale 2501Scale 2501: Ralimic, Ian Ring Music TheoryRalimic
Scale 2505Scale 2505: Mydimic, Ian Ring Music TheoryMydimic
Scale 2513Scale 2513: Aerycrimic, Ian Ring Music TheoryAerycrimic
Scale 2529Scale 2529: PIKIAN, Ian Ring Music TheoryPIKIAN
Scale 2433Scale 2433: PACIAN, Ian Ring Music TheoryPACIAN
Scale 2465Scale 2465: Raga Devaranjani, Ian Ring Music TheoryRaga Devaranjani
Scale 2369Scale 2369: OFFIAN, Ian Ring Music TheoryOFFIAN
Scale 2241Scale 2241: NOXIAN, Ian Ring Music TheoryNOXIAN
Scale 2753Scale 2753: RITIAN, Ian Ring Music TheoryRITIAN
Scale 3009Scale 3009: SUVIAN, Ian Ring Music TheorySUVIAN
Scale 3521Scale 3521: WANIAN, Ian Ring Music TheoryWANIAN
Scale 449Scale 449: CUJIAN, Ian Ring Music TheoryCUJIAN
Scale 1473Scale 1473: JAVIAN, Ian Ring Music TheoryJAVIAN

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.