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Scale 3047: "Panygic"

Scale 3047: Panygic, 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
Panygic

Analysis

Cardinality

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

9 (enneatonic)

Pitch Class Set

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

{0,1,2,5,6,7,8,9,11}

Forte Number

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

9-5

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: 3323

Hemitonia

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

7 (multihemitonic)

Cohemitonia

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

5 (multicohemitonic)

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.

8

Prime Form

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

no
prime: 991

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, 1, 3, 1, 1, 1, 1, 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.

<7, 6, 6, 6, 7, 4>

Interval Spectrum

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

p7m6n6s6d7t4

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

Spectra Variation

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

1.778

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.

2.683

Polygon Perimeter

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

6.038

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♯{1,5,8}342.21
D{2,6,9}342.14
F{5,9,0}342.21
G{7,11,2}242.64
Minor Triadsdm{2,5,9}442.07
fm{5,8,0}342.29
f♯m{6,9,1}342.21
bm{11,2,6}342.36
Augmented TriadsC♯+{1,5,9}442
Diminished Triads{2,5,8}242.43
{5,8,11}242.57
f♯°{6,9,0}242.57
g♯°{8,11,2}242.71
{11,2,5}242.43
Parsimonious Voice Leading Between Common Triads of Scale 3047. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m d°->dm D D dm->D dm->b° D->f#m bm bm D->bm f°->fm g#° g#° f°->g#° fm->F f#° f#° F->f#° f#°->f#m Parsimonious Voice Leading Between Common Triads of Scale 3047. Created by Ian Ring ©2019 G G->g#° G->bm b°->bm

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3047 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3571
Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
3rd mode:
Scale 3833
Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
4th mode:
Scale 991
Scale 991: Aeolygic, Ian Ring Music TheoryAeolygicThis is the prime mode
5th mode:
Scale 2543
Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
6th mode:
Scale 3319
Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
7th mode:
Scale 3707
Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
8th mode:
Scale 3901
Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
9th mode:
Scale 1999
Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic

Prime

The prime form of this scale is Scale 991

Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic

Complement

The enneatonic modal family [3047, 3571, 3833, 991, 2543, 3319, 3707, 3901, 1999] (Forte: 9-5) is the complement of the tritonic modal family [67, 193, 2081] (Forte: 3-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3047 is 3323

Scale 3323Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3047 is chiral, and its enantiomorph is scale 3323

Scale 3323Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic

Transformations:

T0 3047  T0I 3323
T1 1999  T1I 2551
T2 3998  T2I 1007
T3 3901  T3I 2014
T4 3707  T4I 4028
T5 3319  T5I 3961
T6 2543  T6I 3827
T7 991  T7I 3559
T8 1982  T8I 3023
T9 3964  T9I 1951
T10 3833  T10I 3902
T11 3571  T11I 3709

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 3045Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
Scale 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
Scale 3055Scale 3055: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 3063Scale 3063: Solyllian, Ian Ring Music TheorySolyllian
Scale 3015Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
Scale 3031Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 2791Scale 2791: Mixothyllic, Ian Ring Music TheoryMixothyllic
Scale 2535Scale 2535: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4
Scale 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic
Scale 4071Scale 4071: Decatonic Chromatic 8, Ian Ring Music TheoryDecatonic Chromatic 8
Scale 999Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic
Scale 2023Scale 2023: Zodygic, Ian Ring Music TheoryZodygic

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.