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Scale 165: "Genus Primum"

Scale 165: Genus Primum, 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

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

Ancient Greek
Genus Primum

Analysis

Cardinality

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

4 (tetratonic)

Pitch Class Set

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

{0,2,5,7}

Forte Number

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

4-23

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.

[3.5]

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.

1

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.

3

Prime Form

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

yes

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, 3, 2, 5]

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, 2, 1, 0, 3, 0>

Interval Spectrum

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

p3ns2

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

Spectra Variation

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

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.

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.

1.616

Polygon Perimeter

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

5.346

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.

[7]

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

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 165 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 1065
Scale 1065, Ian Ring Music Theory
3rd mode:
Scale 645
Scale 645, Ian Ring Music Theory
4th mode:
Scale 1185
Scale 1185: Genus Primum Inverse, Ian Ring Music TheoryGenus Primum Inverse

Prime

This is the prime form of this scale.

Complement

The tetratonic modal family [165, 1065, 645, 1185] (Forte: 4-23) is the complement of the octatonic modal family [1455, 1515, 1725, 1965, 2775, 2805, 3435, 3765] (Forte: 8-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 165 is 1185

Scale 1185Scale 1185: Genus Primum Inverse, Ian Ring Music TheoryGenus Primum Inverse

Transformations:

T0 165  T0I 1185
T1 330  T1I 2370
T2 660  T2I 645
T3 1320  T3I 1290
T4 2640  T4I 2580
T5 1185  T5I 1065
T6 2370  T6I 2130
T7 645  T7I 165
T8 1290  T8I 330
T9 2580  T9I 660
T10 1065  T10I 1320
T11 2130  T11I 2640

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 167Scale 167, Ian Ring Music Theory
Scale 161Scale 161: Raga Sarvasri, Ian Ring Music TheoryRaga Sarvasri
Scale 163Scale 163, Ian Ring Music Theory
Scale 169Scale 169: Vietnamese Tetratonic, Ian Ring Music TheoryVietnamese Tetratonic
Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 181Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari
Scale 133Scale 133, Ian Ring Music Theory
Scale 149Scale 149: Eskimo Tetratonic, Ian Ring Music TheoryEskimo Tetratonic
Scale 197Scale 197, Ian Ring Music Theory
Scale 229Scale 229, Ian Ring Music Theory
Scale 37Scale 37, Ian Ring Music Theory
Scale 101Scale 101, Ian Ring Music Theory
Scale 293Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga Haripriya
Scale 421Scale 421: Han-kumoi, Ian Ring Music TheoryHan-kumoi
Scale 677Scale 677: Scottish Pentatonic, Ian Ring Music TheoryScottish Pentatonic
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic
Scale 2213Scale 2213: Raga Desh, Ian Ring Music TheoryRaga Desh

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.