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Scale 2605: "Rylimic"

Scale 2605: Rylimic, 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

Zeitler
Rylimic

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

{0,2,3,5,9,11}

Forte Number

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

6-Z23

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.

[1]

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.

4

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: 365

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, 1, 2, 4, 2, 1] 9

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, 4, 2, 2, 2>

Interval Spectrum

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

p2m2n4s3d2t2

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

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.

2.232

Polygon Perimeter

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

5.767

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.

[2]

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

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}221
Minor Triadsdm{2,5,9}221
Diminished Triads{9,0,3}131.5
{11,2,5}131.5
Parsimonious Voice Leading Between Common Triads of Scale 2605. Created by Ian Ring ©2019 dm dm F F dm->F dm->b° F->a°

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 Verticesdm, F
Peripheral Verticesa°, b°

Modes

Modes are the rotational transformation of this scale. Scale 2605 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1675
Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali
3rd mode:
Scale 2885
Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
4th mode:
Scale 1745
Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
5th mode:
Scale 365
Scale 365: Marimic, Ian Ring Music TheoryMarimicThis is the prime mode
6th mode:
Scale 1115
Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror

Prime

The prime form of this scale is Scale 365

Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic

Complement

The hexatonic modal family [2605, 1675, 2885, 1745, 365, 1115] (Forte: 6-Z23) is the complement of the hexatonic modal family [605, 745, 1175, 1865, 2635, 3365] (Forte: 6-Z45)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2605 is 1675

Scale 1675Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali

Transformations:

T0 2605  T0I 1675
T1 1115  T1I 3350
T2 2230  T2I 2605
T3 365  T3I 1115
T4 730  T4I 2230
T5 1460  T5I 365
T6 2920  T6I 730
T7 1745  T7I 1460
T8 3490  T8I 2920
T9 2885  T9I 1745
T10 1675  T10I 3490
T11 3350  T11I 2885

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 2607Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
Scale 2601Scale 2601: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns
Scale 2603Scale 2603: Gadimic, Ian Ring Music TheoryGadimic
Scale 2597Scale 2597: Raga Rasranjani, Ian Ring Music TheoryRaga Rasranjani
Scale 2613Scale 2613: Raga Hamsa Vinodini, Ian Ring Music TheoryRaga Hamsa Vinodini
Scale 2621Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
Scale 2573Scale 2573, Ian Ring Music Theory
Scale 2589Scale 2589, Ian Ring Music Theory
Scale 2637Scale 2637: Raga Ranjani, Ian Ring Music TheoryRaga Ranjani
Scale 2669Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode
Scale 2733Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 2093Scale 2093, Ian Ring Music Theory
Scale 2349Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
Scale 3117Scale 3117, Ian Ring Music Theory
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 557Scale 557: Raga Abhogi, Ian Ring Music TheoryRaga Abhogi
Scale 1581Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri

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.