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Scale 1571: "Lagitonic"

Scale 1571: Lagitonic, 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
Lagitonic
Dozenal
Jodian

Analysis

Cardinality

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

5 (pentatonic)

Pitch Class Set

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

{0,1,5,9,10}

Forte Number

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

5-Z17

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]

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.

2 (dihemitonic)

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.

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.

4

Prime Form

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

no
prime: 283

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.

[1, 4, 4, 1, 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, 1, 2, 3, 2, 0>

Interval Spectrum

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

p2m3n2sd2

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> = {1,2,4}
<2> = {3,5,8}
<3> = {4,7,9}
<4> = {8,10,11}

Spectra Variation

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

3.2

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.

1.799

Polygon Perimeter

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

5.499

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.

[10]

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.

(13, 4, 32)

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 TriadsF{5,9,0}121
Minor Triadsa♯m{10,1,5}121
Augmented TriadsC♯+{1,5,9}210.67
Parsimonious Voice Leading Between Common Triads of Scale 1571. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F a#m a#m C#+->a#m

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.

Diameter2
Radius1
Self-Centeredno
Central VerticesC♯+
Peripheral VerticesF, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 1571 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2833
Scale 2833: Dolitonic, Ian Ring Music TheoryDolitonic
3rd mode:
Scale 433
Scale 433: Raga Zilaf, Ian Ring Music TheoryRaga Zilaf
4th mode:
Scale 283
Scale 283: Aerylitonic, Ian Ring Music TheoryAerylitonicThis is the prime mode
5th mode:
Scale 2189
Scale 2189: Zagitonic, Ian Ring Music TheoryZagitonic

Prime

The prime form of this scale is Scale 283

Scale 283Scale 283: Aerylitonic, Ian Ring Music TheoryAerylitonic

Complement

The pentatonic modal family [1571, 2833, 433, 283, 2189] (Forte: 5-Z17) is the complement of the heptatonic modal family [631, 953, 1831, 2363, 2963, 3229, 3529] (Forte: 7-Z17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1571 is 2189

Scale 2189Scale 2189: Zagitonic, Ian Ring Music TheoryZagitonic

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> 1571       T0I <11,0> 2189
T1 <1,1> 3142      T1I <11,1> 283
T2 <1,2> 2189      T2I <11,2> 566
T3 <1,3> 283      T3I <11,3> 1132
T4 <1,4> 566      T4I <11,4> 2264
T5 <1,5> 1132      T5I <11,5> 433
T6 <1,6> 2264      T6I <11,6> 866
T7 <1,7> 433      T7I <11,7> 1732
T8 <1,8> 866      T8I <11,8> 3464
T9 <1,9> 1732      T9I <11,9> 2833
T10 <1,10> 3464      T10I <11,10> 1571
T11 <1,11> 2833      T11I <11,11> 3142
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 551      T0MI <7,0> 3209
T1M <5,1> 1102      T1MI <7,1> 2323
T2M <5,2> 2204      T2MI <7,2> 551
T3M <5,3> 313      T3MI <7,3> 1102
T4M <5,4> 626      T4MI <7,4> 2204
T5M <5,5> 1252      T5MI <7,5> 313
T6M <5,6> 2504      T6MI <7,6> 626
T7M <5,7> 913      T7MI <7,7> 1252
T8M <5,8> 1826      T8MI <7,8> 2504
T9M <5,9> 3652      T9MI <7,9> 913
T10M <5,10> 3209      T10MI <7,10> 1826
T11M <5,11> 2323      T11MI <7,11> 3652

The transformations that map this set to itself are: T0, T10I

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 1569Scale 1569: Jocian, Ian Ring Music TheoryJocian
Scale 1573Scale 1573: Raga Guhamanohari, Ian Ring Music TheoryRaga Guhamanohari
Scale 1575Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic
Scale 1579Scale 1579: Sagimic, Ian Ring Music TheorySagimic
Scale 1587Scale 1587: Raga Rudra Pancama, Ian Ring Music TheoryRaga Rudra Pancama
Scale 1539Scale 1539: Jikian, Ian Ring Music TheoryJikian
Scale 1555Scale 1555: Jotian, Ian Ring Music TheoryJotian
Scale 1603Scale 1603: Juxian, Ian Ring Music TheoryJuxian
Scale 1635Scale 1635: Sygimic, Ian Ring Music TheorySygimic
Scale 1699Scale 1699: Raga Rasavali, Ian Ring Music TheoryRaga Rasavali
Scale 1827Scale 1827: Katygimic, Ian Ring Music TheoryKatygimic
Scale 1059Scale 1059: Gikian, Ian Ring Music TheoryGikian
Scale 1315Scale 1315: Pyritonic, Ian Ring Music TheoryPyritonic
Scale 547Scale 547: Pyrric, Ian Ring Music TheoryPyrric
Scale 2595Scale 2595: Rolitonic, Ian Ring Music TheoryRolitonic
Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic

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.