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Scale 1895: "Salyllic"

Scale 1895: Salyllic, 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
Salyllic
Dozenal
Lotian

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

{0,1,2,5,6,8,9,10}

Forte Number

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

8-19

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: 3293

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.

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.

7

Prime Form

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

no
prime: 887

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, 1, 3, 1, 2, 1, 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.

<5, 4, 5, 7, 5, 2>

Interval Spectrum

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

p5m7n5s4d5t2

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> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<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.

1.75

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

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.

(10, 53, 129)

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♯{1,5,8}342.08
D{2,6,9}342
F{5,9,0}342.08
F♯{6,10,1}342.15
A♯{10,2,5}342.15
Minor Triadsdm{2,5,9}431.77
fm{5,8,0}252.62
f♯m{6,9,1}431.77
a♯m{10,1,5}331.92
Augmented TriadsC♯+{1,5,9}531.54
D+{2,6,10}352.38
Diminished Triads{2,5,8}242.31
f♯°{6,9,0}242.31
Parsimonious Voice Leading Between Common Triads of Scale 1895. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m d°->dm D D dm->D A# A# dm->A# D+ D+ D->D+ D->f#m F# F# D+->F# D+->A# fm->F f#° f#° F->f#° f#°->f#m f#m->F# F#->a#m a#m->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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC♯+, dm, f♯m, a♯m
Peripheral VerticesD+, fm

Modes

Modes are the rotational transformation of this scale. Scale 1895 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2995
Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
3rd mode:
Scale 3545
Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic
4th mode:
Scale 955
Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
5th mode:
Scale 2525
Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
6th mode:
Scale 1655
Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic
7th mode:
Scale 2875
Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic
8th mode:
Scale 3485
Scale 3485: Sabach, Ian Ring Music TheorySabach

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [1895, 2995, 3545, 955, 2525, 1655, 2875, 3485] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1895 is 3293

Scale 3293Scale 3293: Saryllic, Ian Ring Music TheorySaryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1895 is chiral, and its enantiomorph is scale 3293

Scale 3293Scale 3293: Saryllic, Ian Ring Music TheorySaryllic

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> 1895       T0I <11,0> 3293
T1 <1,1> 3790      T1I <11,1> 2491
T2 <1,2> 3485      T2I <11,2> 887
T3 <1,3> 2875      T3I <11,3> 1774
T4 <1,4> 1655      T4I <11,4> 3548
T5 <1,5> 3310      T5I <11,5> 3001
T6 <1,6> 2525      T6I <11,6> 1907
T7 <1,7> 955      T7I <11,7> 3814
T8 <1,8> 1910      T8I <11,8> 3533
T9 <1,9> 3820      T9I <11,9> 2971
T10 <1,10> 3545      T10I <11,10> 1847
T11 <1,11> 2995      T11I <11,11> 3694
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1655      T0MI <7,0> 3533
T1M <5,1> 3310      T1MI <7,1> 2971
T2M <5,2> 2525      T2MI <7,2> 1847
T3M <5,3> 955      T3MI <7,3> 3694
T4M <5,4> 1910      T4MI <7,4> 3293
T5M <5,5> 3820      T5MI <7,5> 2491
T6M <5,6> 3545      T6MI <7,6> 887
T7M <5,7> 2995      T7MI <7,7> 1774
T8M <5,8> 1895       T8MI <7,8> 3548
T9M <5,9> 3790      T9MI <7,9> 3001
T10M <5,10> 3485      T10MI <7,10> 1907
T11M <5,11> 2875      T11MI <7,11> 3814

The transformations that map this set to itself are: T0, T8M

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 1893Scale 1893: Ionylian, Ian Ring Music TheoryIonylian
Scale 1891Scale 1891: Thalian, Ian Ring Music TheoryThalian
Scale 1899Scale 1899: Moptyllic, Ian Ring Music TheoryMoptyllic
Scale 1903Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic
Scale 1911Scale 1911: Messiaen Mode 3, Ian Ring Music TheoryMessiaen Mode 3
Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 1831Scale 1831: Pothian, Ian Ring Music TheoryPothian
Scale 1959Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic
Scale 2023Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
Scale 1639Scale 1639: Aeolothian, Ian Ring Music TheoryAeolothian
Scale 1767Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic
Scale 1383Scale 1383: Pynian, Ian Ring Music TheoryPynian
Scale 871Scale 871: Locrian Double-flat 3 Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 3 Double-flat 7
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic

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.