The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2651: "Panian"

Scale 2651: Panian, 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).

Common Names

Zeitler
Panian

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

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

{0,1,3,4,6,9,11}

Forte Number

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

7-25

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: 2891

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.

6

Prime Form

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

no
prime: 733

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, 1, 2, 3, 2, 1]

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, 4, 5, 3, 4, 2>

Interval Spectrum

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

p4m3n5s4d3t2

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

Spectra Variation

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

2.286

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.

2.549

Polygon Perimeter

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

5.967

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

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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 TriadsA{9,1,4}231.75
B{11,3,6}231.88
Minor Triadsf♯m{6,9,1}331.63
am{9,0,4}331.63
Diminished Triads{0,3,6}231.88
d♯°{3,6,9}231.75
f♯°{6,9,0}231.75
{9,0,3}231.75
Parsimonious Voice Leading Between Common Triads of Scale 2651. Created by Ian Ring ©2019 c°->a° B B c°->B d#° d#° f#m f#m d#°->f#m d#°->B f#° f#° f#°->f#m am am f#°->am A A f#m->A a°->am am->A

view full size

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2651 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3373
Scale 3373: Lodian, Ian Ring Music TheoryLodian
3rd mode:
Scale 1867
Scale 1867: Solian, Ian Ring Music TheorySolian
4th mode:
Scale 2981
Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
5th mode:
Scale 1769
Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
6th mode:
Scale 733
Scale 733: Donian, Ian Ring Music TheoryDonianThis is the prime mode
7th mode:
Scale 1207
Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian

Prime

The prime form of this scale is Scale 733

Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian

Complement

The heptatonic modal family [2651, 3373, 1867, 2981, 1769, 733, 1207] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2651 is 2891

Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2651 is chiral, and its enantiomorph is scale 2891

Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian

Transformations:

T0 2651  T0I 2891
T1 1207  T1I 1687
T2 2414  T2I 3374
T3 733  T3I 2653
T4 1466  T4I 1211
T5 2932  T5I 2422
T6 1769  T6I 749
T7 3538  T7I 1498
T8 2981  T8I 2996
T9 1867  T9I 1897
T10 3734  T10I 3794
T11 3373  T11I 3493

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 2649Scale 2649: Aeolythimic, Ian Ring Music TheoryAeolythimic
Scale 2653Scale 2653: Sygian, Ian Ring Music TheorySygian
Scale 2655Scale 2655, Ian Ring Music Theory
Scale 2643Scale 2643: Raga Hamsanandi, Ian Ring Music TheoryRaga Hamsanandi
Scale 2647Scale 2647: Dadian, Ian Ring Music TheoryDadian
Scale 2635Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic
Scale 2667Scale 2667: Byrian, Ian Ring Music TheoryByrian
Scale 2683Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic
Scale 2587Scale 2587, Ian Ring Music Theory
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 2779Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich
Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2
Scale 2139Scale 2139, Ian Ring Music Theory
Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3675Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 1627Scale 1627: Zyptian, Ian Ring Music TheoryZyptian

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.