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Scale 2193: "Major Seventh"

Scale 2193: Major Seventh, 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

Chord Names
Major Seventh
Zeitler
Thaptic

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

{0,4,7,11}

Forte Number

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

4-20

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.

[5.5]

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.

1 (unhemitonic)

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.

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.

3

Prime Form

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

no
prime: 291

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.

[4, 3, 4, 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.

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

Interval Spectrum

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

p2m2nd

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> = {1,3,4}
<2> = {5,7}
<3> = {8,9,11}

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.

5.396

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.

[11]

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".

Strictly 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}110.5
Minor Triadsem{4,7,11}110.5
Parsimonious Voice Leading Between Common Triads of Scale 2193. Created by Ian Ring ©2019 C C em em C->em

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2193 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 393
Scale 393: Lothic, Ian Ring Music TheoryLothic
3rd mode:
Scale 561
Scale 561: Phratic, Ian Ring Music TheoryPhratic
4th mode:
Scale 291
Scale 291: Raga Lavangi, Ian Ring Music TheoryRaga LavangiThis is the prime mode

Prime

The prime form of this scale is Scale 291

Scale 291Scale 291: Raga Lavangi, Ian Ring Music TheoryRaga Lavangi

Complement

The tetratonic modal family [2193, 393, 561, 291] (Forte: 4-20) is the complement of the octatonic modal family [951, 1767, 1851, 2523, 2931, 2973, 3309, 3513] (Forte: 8-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2193 is 291

Scale 291Scale 291: Raga Lavangi, Ian Ring Music TheoryRaga Lavangi

Transformations:

T0 2193  T0I 291
T1 291  T1I 582
T2 582  T2I 1164
T3 1164  T3I 2328
T4 2328  T4I 561
T5 561  T5I 1122
T6 1122  T6I 2244
T7 2244  T7I 393
T8 393  T8I 786
T9 786  T9I 1572
T10 1572  T10I 3144
T11 3144  T11I 2193

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 2195Scale 2195: Zalitonic, Ian Ring Music TheoryZalitonic
Scale 2197Scale 2197: Raga Hamsadhvani, Ian Ring Music TheoryRaga Hamsadhvani
Scale 2201Scale 2201: Ionagitonic, Ian Ring Music TheoryIonagitonic
Scale 2177Scale 2177: Major Seventh Omit 3, Ian Ring Music TheoryMajor Seventh Omit 3
Scale 2185Scale 2185: Dygic, Ian Ring Music TheoryDygic
Scale 2209Scale 2209, Ian Ring Music Theory
Scale 2225Scale 2225: Ionian Pentatonic, Ian Ring Music TheoryIonian Pentatonic
Scale 2257Scale 2257: Lydian Pentatonic, Ian Ring Music TheoryLydian Pentatonic
Scale 2065Scale 2065, Ian Ring Music Theory
Scale 2129Scale 2129: Raga Nigamagamini, Ian Ring Music TheoryRaga Nigamagamini
Scale 2321Scale 2321: Zyphic, Ian Ring Music TheoryZyphic
Scale 2449Scale 2449: Zacritonic, Ian Ring Music TheoryZacritonic
Scale 2705Scale 2705: Raga Mamata, Ian Ring Music TheoryRaga Mamata
Scale 3217Scale 3217: Molitonic, Ian Ring Music TheoryMolitonic
Scale 145Scale 145: Raga Malasri, Ian Ring Music TheoryRaga Malasri
Scale 1169Scale 1169: Raga Mahathi, Ian Ring Music TheoryRaga Mahathi

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.