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Scale 1481: "Zagimic"

Scale 1481: Zagimic, 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
Zagimic

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

{0,3,6,7,8,10}

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-Z46

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: 629

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.

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.

5

Prime Form

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

no
prime: 599

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.

no

Interval Formula

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

[3, 3, 1, 1, 2, 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, 3, 3, 1>

Interval Spectrum

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

p3m3n3s3d2t

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

Spectra Variation

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

2.667

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 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.

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.

(12, 17, 65)

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 TriadsD♯{3,7,10}221.2
G♯{8,0,3}131.6
Minor Triadscm{0,3,7}321
d♯m{3,6,10}231.4
Diminished Triads{0,3,6}221.2
Parsimonious Voice Leading Between Common Triads of Scale 1481. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# G# G# cm->G# d#m->D#

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesc°, cm, D♯
Peripheral Verticesd♯m, G♯

Modes

Modes are the rotational transformation of this scale. Scale 1481 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 697
Scale 697: Lagimic, Ian Ring Music TheoryLagimic
3rd mode:
Scale 599
Scale 599: Thyrimic, Ian Ring Music TheoryThyrimicThis is the prime mode
4th mode:
Scale 2347
Scale 2347: Raga Viyogavarali, Ian Ring Music TheoryRaga Viyogavarali
5th mode:
Scale 3221
Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic
6th mode:
Scale 1829
Scale 1829: Pathimic, Ian Ring Music TheoryPathimic

Prime

The prime form of this scale is Scale 599

Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic

Complement

The hexatonic modal family [1481, 697, 599, 2347, 3221, 1829] (Forte: 6-Z46) is the complement of the hexatonic modal family [347, 1457, 1579, 1733, 2221, 2837] (Forte: 6-Z24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1481 is 629

Scale 629Scale 629: Aeronimic, Ian Ring Music TheoryAeronimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1481 is chiral, and its enantiomorph is scale 629

Scale 629Scale 629: Aeronimic, Ian Ring Music TheoryAeronimic

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> 1481       T0I <11,0> 629
T1 <1,1> 2962      T1I <11,1> 1258
T2 <1,2> 1829      T2I <11,2> 2516
T3 <1,3> 3658      T3I <11,3> 937
T4 <1,4> 3221      T4I <11,4> 1874
T5 <1,5> 2347      T5I <11,5> 3748
T6 <1,6> 599      T6I <11,6> 3401
T7 <1,7> 1198      T7I <11,7> 2707
T8 <1,8> 2396      T8I <11,8> 1319
T9 <1,9> 697      T9I <11,9> 2638
T10 <1,10> 1394      T10I <11,10> 1181
T11 <1,11> 2788      T11I <11,11> 2362
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2141      T0MI <7,0> 1859
T1M <5,1> 187      T1MI <7,1> 3718
T2M <5,2> 374      T2MI <7,2> 3341
T3M <5,3> 748      T3MI <7,3> 2587
T4M <5,4> 1496      T4MI <7,4> 1079
T5M <5,5> 2992      T5MI <7,5> 2158
T6M <5,6> 1889      T6MI <7,6> 221
T7M <5,7> 3778      T7MI <7,7> 442
T8M <5,8> 3461      T8MI <7,8> 884
T9M <5,9> 2827      T9MI <7,9> 1768
T10M <5,10> 1559      T10MI <7,10> 3536
T11M <5,11> 3118      T11MI <7,11> 2977

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 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
Scale 1485Scale 1485: Minor Romani, Ian Ring Music TheoryMinor Romani
Scale 1473Scale 1473, Ian Ring Music Theory
Scale 1477Scale 1477: Raga Jaganmohanam, Ian Ring Music TheoryRaga Jaganmohanam
Scale 1489Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti
Scale 1497Scale 1497: Mela Jyotisvarupini, Ian Ring Music TheoryMela Jyotisvarupini
Scale 1513Scale 1513: Stathian, Ian Ring Music TheoryStathian
Scale 1417Scale 1417: Raga Shailaja, Ian Ring Music TheoryRaga Shailaja
Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 1225Scale 1225: Raga Samudhra Priya, Ian Ring Music TheoryRaga Samudhra Priya
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
Scale 457Scale 457: Staptitonic, Ian Ring Music TheoryStaptitonic
Scale 969Scale 969: Ionogimic, Ian Ring Music TheoryIonogimic
Scale 2505Scale 2505: Mydimic, Ian Ring Music TheoryMydimic
Scale 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian

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.