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Scale 1509: "Ragian"

Scale 1509: Ragian, 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
Ragian

Analysis

Cardinality

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

7 (heptatonic)

Pitch Class Set

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

{0,2,5,6,7,8,10}

Forte Number

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

7-24

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: 1269

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

3 (trihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

2 (dicohemitonic)

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.

6

Prime Form

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

no
prime: 687

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.

[2, 3, 1, 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.

<3, 5, 3, 4, 4, 2>

Interval Spectrum

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

p4m4n3s5d3t2

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

Spectra Variation

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

2.571

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.

2.549

Polygon Perimeter

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

5.967

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

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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 TriadsA♯{10,2,5}221.2
Minor Triadsfm{5,8,0}142
gm{7,10,2}142
Augmented TriadsD+{2,6,10}231.4
Diminished Triads{2,5,8}231.4
Parsimonious Voice Leading Between Common Triads of Scale 1509. Created by Ian Ring ©2019 fm fm d°->fm A# A# d°->A# D+ D+ gm gm D+->gm D+->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
Radius2
Self-Centeredno
Central VerticesA♯
Peripheral Verticesfm, gm

Modes

Modes are the rotational transformation of this scale. Scale 1509 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1401
Scale 1401: Pagian, Ian Ring Music TheoryPagian
3rd mode:
Scale 687
Scale 687: Aeolythian, Ian Ring Music TheoryAeolythianThis is the prime mode
4th mode:
Scale 2391
Scale 2391: Molian, Ian Ring Music TheoryMolian
5th mode:
Scale 3243
Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
6th mode:
Scale 3669
Scale 3669: Mothian, Ian Ring Music TheoryMothian
7th mode:
Scale 1941
Scale 1941: Aeranian, Ian Ring Music TheoryAeranian

Prime

The prime form of this scale is Scale 687

Scale 687Scale 687: Aeolythian, Ian Ring Music TheoryAeolythian

Complement

The heptatonic modal family [1509, 1401, 687, 2391, 3243, 3669, 1941] (Forte: 7-24) is the complement of the pentatonic modal family [171, 1377, 1413, 1557, 2133] (Forte: 5-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1509 is 1269

Scale 1269Scale 1269: Katythian, Ian Ring Music TheoryKatythian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1509 is chiral, and its enantiomorph is scale 1269

Scale 1269Scale 1269: Katythian, Ian Ring Music TheoryKatythian

Transformations:

T0 1509  T0I 1269
T1 3018  T1I 2538
T2 1941  T2I 981
T3 3882  T3I 1962
T4 3669  T4I 3924
T5 3243  T5I 3753
T6 2391  T6I 3411
T7 687  T7I 2727
T8 1374  T8I 1359
T9 2748  T9I 2718
T10 1401  T10I 1341
T11 2802  T11I 2682

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 1511Scale 1511: Styptyllic, Ian Ring Music TheoryStyptyllic
Scale 1505Scale 1505, Ian Ring Music Theory
Scale 1507Scale 1507: Zynian, Ian Ring Music TheoryZynian
Scale 1513Scale 1513: Stathian, Ian Ring Music TheoryStathian
Scale 1517Scale 1517: Sagyllic, Ian Ring Music TheorySagyllic
Scale 1525Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
Scale 1477Scale 1477: Raga Jaganmohanam, Ian Ring Music TheoryRaga Jaganmohanam
Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 1253Scale 1253: Zolimic, Ian Ring Music TheoryZolimic
Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian
Scale 2021Scale 2021: Katycryllic, Ian Ring Music TheoryKatycryllic
Scale 485Scale 485: Stoptimic, Ian Ring Music TheoryStoptimic
Scale 997Scale 997: Rycrian, Ian Ring Music TheoryRycrian
Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian
Scale 3557Scale 3557, Ian Ring Music Theory

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.