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Scale 2907: "Magen Abot 2"

Scale 2907: Magen Abot 2, 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

Jewish
Magen Abot 2
Zeitler
Mogyllic

Analysis

Cardinality

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

8 (octatonic)

Pitch Class Set

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

{0,1,3,4,6,8,9,11}

Forte Number

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

8-26

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.

[0]

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

yes

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.

4 (multihemitonic)

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.

7

Prime Form

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

no
prime: 1467

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

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.

[4, 5, 6, 5, 6, 2]

Interval Spectrum

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

p6m5n6s5d4t2

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

Spectra Variation

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

1.25

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.

2.732

Polygon Perimeter

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

6.071

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.

[0]

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 TriadsE{4,8,11}242.23
G♯{8,0,3}441.92
A{9,1,4}342.15
B{11,3,6}342.23
Minor Triadsc♯m{1,4,8}242.23
f♯m{6,9,1}342.23
g♯m{8,11,3}342.15
am{9,0,4}441.92
Augmented TriadsC+{0,4,8}441.85
Diminished Triads{0,3,6}242.31
d♯°{3,6,9}242.31
f♯°{6,9,0}242.31
{9,0,3}242.15
Parsimonious Voice Leading Between Common Triads of Scale 2907. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E C+->G# am am C+->am A A c#m->A d#° d#° f#m f#m d#°->f#m d#°->B g#m g#m E->g#m f#° f#° f#°->f#m f#°->am f#m->A g#m->G# g#m->B G#->a° a°->am am->A

view full size

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 2907 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3501
Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
3rd mode:
Scale 1899
Scale 1899: Moptyllic, Ian Ring Music TheoryMoptyllic
4th mode:
Scale 2997
Scale 2997: Major Bebop, Ian Ring Music TheoryMajor Bebop
5th mode:
Scale 1773
Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
6th mode:
Scale 1467
Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish PhrygianThis is the prime mode
7th mode:
Scale 2781
Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
8th mode:
Scale 1719
Scale 1719: Lyryllic, Ian Ring Music TheoryLyryllic

Prime

The prime form of this scale is Scale 1467

Scale 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian

Complement

The octatonic modal family [2907, 3501, 1899, 2997, 1773, 1467, 2781, 1719] (Forte: 8-26) is the complement of the tetratonic modal family [297, 549, 657, 1161] (Forte: 4-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2907 is itself, because it is a palindromic scale!

Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2

Transformations:

T0 2907  T0I 2907
T1 1719  T1I 1719
T2 3438  T2I 3438
T3 2781  T3I 2781
T4 1467  T4I 1467
T5 2934  T5I 2934
T6 1773  T6I 1773
T7 3546  T7I 3546
T8 2997  T8I 2997
T9 1899  T9I 1899
T10 3798  T10I 3798
T11 3501  T11I 3501

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 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
Scale 2909Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
Scale 2911Scale 2911: Katygic, Ian Ring Music TheoryKatygic
Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
Scale 2923Scale 2923: Baryllic, Ian Ring Music TheoryBaryllic
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 2843Scale 2843: Sorian, Ian Ring Music TheorySorian
Scale 2875Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic
Scale 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 2779Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich
Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian
Scale 1883Scale 1883, Ian Ring Music Theory

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. 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.