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Scale 1173: "Dominant Pentatonic"

Scale 1173: Dominant Pentatonic, Ian Ring Music Theory

Named the Dominant Pentatonic because its tones include a dominant seventh chord.


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).

Common Names

Western Modern
Dominant Pentatonic
Zeitler
Phropitonic

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

{0,2,4,7,10}

Forte Number

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

5-34

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.

[1]

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.

no

Hemitonia

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

0 (anhemitonic)

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.

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: 597

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.

[2, 2, 3, 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.

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

Interval Spectrum

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

p2m2n2s3t

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

Spectra Variation

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

1.2

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.

yes

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.

2.299

Polygon Perimeter

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

5.828

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.

[2]

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".

Proper

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{0,4,7}121
Minor Triadsgm{7,10,2}121
Diminished Triads{4,7,10}210.67
Parsimonious Voice Leading Between Common Triads of Scale 1173. Created by Ian Ring ©2019 C C C->e° gm gm e°->gm

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
Radius1
Self-Centeredno
Central Vertices
Peripheral VerticesC, gm

Modes

Modes are the rotational transformation of this scale. Scale 1173 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1317
Scale 1317: Chaio, Ian Ring Music TheoryChaio
3rd mode:
Scale 1353
Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
4th mode:
Scale 681
Scale 681: Kyemyonjo, Ian Ring Music TheoryKyemyonjo
5th mode:
Scale 597
Scale 597: Kung, Ian Ring Music TheoryKungThis is the prime mode

Prime

The prime form of this scale is Scale 597

Scale 597Scale 597: Kung, Ian Ring Music TheoryKung

Complement

The pentatonic modal family [1173, 1317, 1353, 681, 597] (Forte: 5-34) is the complement of the heptatonic modal family [1371, 1389, 1461, 1707, 1749, 2733, 2901] (Forte: 7-34)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1173 is 1317

Scale 1317Scale 1317: Chaio, Ian Ring Music TheoryChaio

Transformations:

T0 1173  T0I 1317
T1 2346  T1I 2634
T2 597  T2I 1173
T3 1194  T3I 2346
T4 2388  T4I 597
T5 681  T5I 1194
T6 1362  T6I 2388
T7 2724  T7I 681
T8 1353  T8I 1362
T9 2706  T9I 2724
T10 1317  T10I 1353
T11 2634  T11I 2706

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 1175Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
Scale 1169Scale 1169: Raga Mahathi, Ian Ring Music TheoryRaga Mahathi
Scale 1171Scale 1171: Raga Manaranjani I, Ian Ring Music TheoryRaga Manaranjani I
Scale 1177Scale 1177: Garitonic, Ian Ring Music TheoryGaritonic
Scale 1181Scale 1181: Katagimic, Ian Ring Music TheoryKatagimic
Scale 1157Scale 1157, Ian Ring Music Theory
Scale 1165Scale 1165: Gycritonic, Ian Ring Music TheoryGycritonic
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic
Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji
Scale 1237Scale 1237: Salimic, Ian Ring Music TheorySalimic
Scale 1045Scale 1045, Ian Ring Music Theory
Scale 1109Scale 1109: Kataditonic, Ian Ring Music TheoryKataditonic
Scale 1301Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic
Scale 1429Scale 1429: Bythimic, Ian Ring Music TheoryBythimic
Scale 1685Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
Scale 149Scale 149: Eskimo Tetratonic, Ian Ring Music TheoryEskimo Tetratonic
Scale 661Scale 661: Major Pentatonic, Ian Ring Music TheoryMajor Pentatonic
Scale 2197Scale 2197: Raga Hamsadhvani, Ian Ring Music TheoryRaga Hamsadhvani
Scale 3221Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic

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.