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Scale 2549: "Rydyllic"

Scale 2549: Rydyllic, 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
Rydyllic

Analysis

Cardinality

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

8 (octatonic)

Pitch Class Set

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

{0,2,4,5,6,7,8,11}

Forte Number

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

8-Z15

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: 1523

Hemitonia

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

5 (multihemitonic)

Cohemitonia

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

3 (tricohemitonic)

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.

7

Prime Form

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

no
prime: 863

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

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.

<5, 5, 5, 5, 5, 3>

Interval Spectrum

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

p5m5n5s5d5t3

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

Spectra Variation

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

2.25

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.

2.616

Polygon Perimeter

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

6.002

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

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}242.18
E{4,8,11}441.82
G{7,11,2}342
Minor Triadsem{4,7,11}341.91
fm{5,8,0}342
bm{11,2,6}242.27
Augmented TriadsC+{0,4,8}341.91
Diminished Triads{2,5,8}242.27
{5,8,11}242.09
g♯°{8,11,2}242.09
{11,2,5}242.36
Parsimonious Voice Leading Between Common Triads of Scale 2549. Created by Ian Ring ©2019 C C C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm d°->fm d°->b° em->E Parsimonious Voice Leading Between Common Triads of Scale 2549. Created by Ian Ring ©2019 G em->G E->f° g#° g#° E->g#° f°->fm G->g#° bm bm G->bm b°->bm

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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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2549 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1661
Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
3rd mode:
Scale 1439
Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
4th mode:
Scale 2767
Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic
5th mode:
Scale 3431
Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
6th mode:
Scale 3763
Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
7th mode:
Scale 3929
Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
8th mode:
Scale 1003
Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [2549, 1661, 1439, 2767, 3431, 3763, 3929, 1003] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2549 is 1523

Scale 1523Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2549 is chiral, and its enantiomorph is scale 1523

Scale 1523Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic

Transformations:

T0 2549  T0I 1523
T1 1003  T1I 3046
T2 2006  T2I 1997
T3 4012  T3I 3994
T4 3929  T4I 3893
T5 3763  T5I 3691
T6 3431  T6I 3287
T7 2767  T7I 2479
T8 1439  T8I 863
T9 2878  T9I 1726
T10 1661  T10I 3452
T11 3322  T11I 2809

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 2551Scale 2551: Thocrygic, Ian Ring Music TheoryThocrygic
Scale 2545Scale 2545: Thycrian, Ian Ring Music TheoryThycrian
Scale 2547Scale 2547: Raga Ramkali, Ian Ring Music TheoryRaga Ramkali
Scale 2553Scale 2553: Aeolaptyllic, Ian Ring Music TheoryAeolaptyllic
Scale 2557Scale 2557: Dothygic, Ian Ring Music TheoryDothygic
Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian
Scale 2541Scale 2541: Algerian, Ian Ring Music TheoryAlgerian
Scale 2517Scale 2517: Harmonic Lydian, Ian Ring Music TheoryHarmonic Lydian
Scale 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major
Scale 2421Scale 2421: Malian, Ian Ring Music TheoryMalian
Scale 2293Scale 2293: Gorian, Ian Ring Music TheoryGorian
Scale 2805Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho
Scale 3061Scale 3061: Apinygic, Ian Ring Music TheoryApinygic
Scale 3573Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
Scale 501Scale 501: Katylian, Ian Ring Music TheoryKatylian
Scale 1525Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic

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.