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Scale 507: "Moryllic"

Scale 507: Moryllic, 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
Moryllic

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

{0,1,3,4,5,6,7,8}

Forte Number

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

8-4

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: 3057

Hemitonia

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

6 (multihemitonic)

Cohemitonia

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

4 (multicohemitonic)

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: 447

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

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.

<6, 5, 5, 5, 5, 2>

Interval Spectrum

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

p5m5n5s5d6t2

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> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}

Spectra Variation

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

3

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.

5.838

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.

(75, 56, 136)

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}331.56
C♯{1,5,8}252.33
G♯{8,0,3}231.78
Minor Triadscm{0,3,7}341.89
c♯m{1,4,8}341.78
fm{5,8,0}242
Augmented TriadsC+{0,4,8}431.44
Diminished Triads{0,3,6}152.67
c♯°{1,4,7}231.89
Parsimonious Voice Leading Between Common Triads of Scale 507. Created by Ian Ring ©2019 cm cm c°->cm C C cm->C G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m fm fm C+->fm C+->G# c#°->c#m C# C# c#m->C# C#->fm

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC, C+, c♯°, G♯
Peripheral Verticesc°, C♯

Modes

Modes are the rotational transformation of this scale. Scale 507 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2301
Scale 2301: Bydyllic, Ian Ring Music TheoryBydyllic
3rd mode:
Scale 1599
Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
4th mode:
Scale 2847
Scale 2847: Phracryllic, Ian Ring Music TheoryPhracryllic
5th mode:
Scale 3471
Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
6th mode:
Scale 3783
Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
7th mode:
Scale 3939
Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
8th mode:
Scale 4017
Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic

Prime

The prime form of this scale is Scale 447

Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic

Complement

The octatonic modal family [507, 2301, 1599, 2847, 3471, 3783, 3939, 4017] (Forte: 8-4) is the complement of the tetratonic modal family [39, 897, 2067, 3081] (Forte: 4-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 507 is 3057

Scale 3057Scale 3057: Phroryllic, Ian Ring Music TheoryPhroryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 507 is chiral, and its enantiomorph is scale 3057

Scale 3057Scale 3057: Phroryllic, Ian Ring Music TheoryPhroryllic

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> 507       T0I <11,0> 3057
T1 <1,1> 1014      T1I <11,1> 2019
T2 <1,2> 2028      T2I <11,2> 4038
T3 <1,3> 4056      T3I <11,3> 3981
T4 <1,4> 4017      T4I <11,4> 3867
T5 <1,5> 3939      T5I <11,5> 3639
T6 <1,6> 3783      T6I <11,6> 3183
T7 <1,7> 3471      T7I <11,7> 2271
T8 <1,8> 2847      T8I <11,8> 447
T9 <1,9> 1599      T9I <11,9> 894
T10 <1,10> 3198      T10I <11,10> 1788
T11 <1,11> 2301      T11I <11,11> 3576
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2427      T0MI <7,0> 3027
T1M <5,1> 759      T1MI <7,1> 1959
T2M <5,2> 1518      T2MI <7,2> 3918
T3M <5,3> 3036      T3MI <7,3> 3741
T4M <5,4> 1977      T4MI <7,4> 3387
T5M <5,5> 3954      T5MI <7,5> 2679
T6M <5,6> 3813      T6MI <7,6> 1263
T7M <5,7> 3531      T7MI <7,7> 2526
T8M <5,8> 2967      T8MI <7,8> 957
T9M <5,9> 1839      T9MI <7,9> 1914
T10M <5,10> 3678      T10MI <7,10> 3828
T11M <5,11> 3261      T11MI <7,11> 3561

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 505Scale 505: Sanian, Ian Ring Music TheorySanian
Scale 509Scale 509: Ionothyllic, Ian Ring Music TheoryIonothyllic
Scale 511Scale 511: Chromatic Nonamode, Ian Ring Music TheoryChromatic Nonamode
Scale 499Scale 499: Ionaptian, Ian Ring Music TheoryIonaptian
Scale 503Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic
Scale 491Scale 491: Aeolyrian, Ian Ring Music TheoryAeolyrian
Scale 475Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian
Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian
Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian
Scale 251Scale 251: Borian, Ian Ring Music TheoryBorian
Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic
Scale 1019Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
Scale 1531Scale 1531: Styptygic, Ian Ring Music TheoryStyptygic
Scale 2555Scale 2555: Bythygic, Ian Ring Music TheoryBythygic

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.