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Scale 1191: "Pyrimic"

Scale 1191: Pyrimic, 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
Pyrimic
Dozenal
Hemian

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

{0,1,2,5,7,10}

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-Z47

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: 3237

Hemitonia

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

2 (dihemitonic)

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.

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.

5

Prime Form

Describes if this scale is in prime form, using the Starr/Rahn algorithm.

no
prime: 663

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, an indicator of maximum hierarchization.

no

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

[1, 1, 3, 2, 3, 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.

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

Interval Spectrum

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

p4m2n3s3d2t

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

Spectra Variation

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

2.333

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.

2.366

Polygon Perimeter

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

5.864

Myhill Property

A scale has Myhill Property if the Distribution Spectra have 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.

(10, 16, 62)

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♯{10,2,5}221
Minor Triadsgm{7,10,2}221
a♯m{10,1,5}221
Diminished Triads{7,10,1}221

The following pitch classes are not present in any of the common triads: {0}

Parsimonious Voice Leading Between Common Triads of Scale 1191. Created by Ian Ring ©2019 gm gm g°->gm a#m a#m g°->a#m A# A# gm->A# a#m->A#

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.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1191 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2643
Scale 2643: Raga Hamsanandi, Ian Ring Music TheoryRaga Hamsanandi
3rd mode:
Scale 3369
Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
4th mode:
Scale 933
Scale 933: Dadimic, Ian Ring Music TheoryDadimic
5th mode:
Scale 1257
Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale
6th mode:
Scale 669
Scale 669: Gycrimic, Ian Ring Music TheoryGycrimic

Prime

The prime form of this scale is Scale 663

Scale 663Scale 663: Phrynimic, Ian Ring Music TheoryPhrynimic

Complement

The hexatonic modal family [1191, 2643, 3369, 933, 1257, 669] (Forte: 6-Z47) is the complement of the hexatonic modal family [363, 1419, 1581, 1713, 2229, 2757] (Forte: 6-Z25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1191 is 3237

Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1191 is chiral, and its enantiomorph is scale 3237

Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang

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> 1191       T0I <11,0> 3237
T1 <1,1> 2382      T1I <11,1> 2379
T2 <1,2> 669      T2I <11,2> 663
T3 <1,3> 1338      T3I <11,3> 1326
T4 <1,4> 2676      T4I <11,4> 2652
T5 <1,5> 1257      T5I <11,5> 1209
T6 <1,6> 2514      T6I <11,6> 2418
T7 <1,7> 933      T7I <11,7> 741
T8 <1,8> 1866      T8I <11,8> 1482
T9 <1,9> 3732      T9I <11,9> 2964
T10 <1,10> 3369      T10I <11,10> 1833
T11 <1,11> 2643      T11I <11,11> 3666
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3111      T0MI <7,0> 3207
T1M <5,1> 2127      T1MI <7,1> 2319
T2M <5,2> 159      T2MI <7,2> 543
T3M <5,3> 318      T3MI <7,3> 1086
T4M <5,4> 636      T4MI <7,4> 2172
T5M <5,5> 1272      T5MI <7,5> 249
T6M <5,6> 2544      T6MI <7,6> 498
T7M <5,7> 993      T7MI <7,7> 996
T8M <5,8> 1986      T8MI <7,8> 1992
T9M <5,9> 3972      T9MI <7,9> 3984
T10M <5,10> 3849      T10MI <7,10> 3873
T11M <5,11> 3603      T11MI <7,11> 3651

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 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic
Scale 1187Scale 1187: Kokin-joshi, Ian Ring Music TheoryKokin-joshi
Scale 1195Scale 1195: Raga Gandharavam, Ian Ring Music TheoryRaga Gandharavam
Scale 1199Scale 1199: Magian, Ian Ring Music TheoryMagian
Scale 1207Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
Scale 1159Scale 1159: Hasian, Ian Ring Music TheoryHasian
Scale 1175Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
Scale 1223Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic
Scale 1255Scale 1255: Chromatic Mixolydian, Ian Ring Music TheoryChromatic Mixolydian
Scale 1063Scale 1063: Gomian, Ian Ring Music TheoryGomian
Scale 1127Scale 1127: Eparimic, Ian Ring Music TheoryEparimic
Scale 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic
Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
Scale 1703Scale 1703: Mela Vanaspati, Ian Ring Music TheoryMela Vanaspati
Scale 167Scale 167: Barian, Ian Ring Music TheoryBarian
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic
Scale 3239Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi

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, and George Howlett for assistance with the Carnatic ragas.