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Scale 697: "Lagimic"

Scale 697: Lagimic, 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
Lagimic
Dozenal
Egoian

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

{0,3,4,5,7,9}

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: 937

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 Structure

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

[3, 1, 1, 2, 2, 3]

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 TriadsC{0,4,7}221.2
F{5,9,0}131.6
Minor Triadscm{0,3,7}231.4
am{9,0,4}321
Diminished Triads{9,0,3}221.2
Parsimonious Voice Leading Between Common Triads of Scale 697. Created by Ian Ring ©2019 cm cm C C cm->C cm->a° am am C->am F F F->am a°->am

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, a°, am
Peripheral Verticescm, F

Modes

Modes are the rotational transformation of this scale. Scale 697 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 599
Scale 599: Thyrimic, Ian Ring Music TheoryThyrimicThis is the prime mode
3rd mode:
Scale 2347
Scale 2347: Raga Viyogavarali, Ian Ring Music TheoryRaga Viyogavarali
4th mode:
Scale 3221
Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic
5th mode:
Scale 1829
Scale 1829: Pathimic, Ian Ring Music TheoryPathimic
6th mode:
Scale 1481
Scale 1481: Zagimic, Ian Ring Music TheoryZagimic

Prime

The prime form of this scale is Scale 599

Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic

Complement

The hexatonic modal family [697, 599, 2347, 3221, 1829, 1481] (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 697 is 937

Scale 937Scale 937: Stothimic, Ian Ring Music TheoryStothimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 697 is chiral, and its enantiomorph is scale 937

Scale 937Scale 937: Stothimic, Ian Ring Music TheoryStothimic

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

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 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian
Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian
Scale 689Scale 689: Raga Nagasvaravali, Ian Ring Music TheoryRaga Nagasvaravali
Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord
Scale 681Scale 681: Kyemyonjo, Ian Ring Music TheoryKyemyonjo
Scale 665Scale 665: Raga Mohanangi, Ian Ring Music TheoryRaga Mohanangi
Scale 729Scale 729: Stygimic, Ian Ring Music TheoryStygimic
Scale 761Scale 761: Ponian, Ian Ring Music TheoryPonian
Scale 569Scale 569: Mothitonic, Ian Ring Music TheoryMothitonic
Scale 633Scale 633: Kydimic, Ian Ring Music TheoryKydimic
Scale 825Scale 825: Thyptimic, Ian Ring Music TheoryThyptimic
Scale 953Scale 953: Mela Yagapriya, Ian Ring Music TheoryMela Yagapriya
Scale 185Scale 185: Becian, Ian Ring Music TheoryBecian
Scale 441Scale 441: Thycrimic, Ian Ring Music TheoryThycrimic
Scale 1209Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
Scale 1721Scale 1721: Mela Vagadhisvari, Ian Ring Music TheoryMela Vagadhisvari
Scale 2745Scale 2745: Mela Sulini, Ian Ring Music TheoryMela Sulini

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, and George Howlett for assistance with the Carnatic ragas.