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Scale 1511: "Styptyllic"

Scale 1511: Styptyllic, 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
Styptyllic

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

{0,1,2,5,6,7,8,10}

Forte Number

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

8-16

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: 3317

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.

2

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: 943

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.

[1, 1, 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.

<5, 5, 4, 5, 6, 3>

Interval Spectrum

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

p6m5n4s5d5t3

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

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

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}341.89
F♯{6,10,1}331.67
A♯{10,2,5}331.67
Minor Triadsfm{5,8,0}152.67
gm{7,10,2}252.33
a♯m{10,1,5}331.56
Augmented TriadsD+{2,6,10}341.78
Diminished Triads{2,5,8}242
{7,10,1}242.22
Parsimonious Voice Leading Between Common Triads of Scale 1511. Created by Ian Ring ©2019 C# C# C#->d° fm fm C#->fm a#m a#m C#->a#m A# A# d°->A# D+ D+ F# F# D+->F# gm gm D+->gm D+->A# F#->g° F#->a#m g°->gm 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 VerticesF♯, a♯m, A♯
Peripheral Verticesfm, gm

Modes

Modes are the rotational transformation of this scale. Scale 1511 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2803
Scale 2803: Raga Bhatiyar, Ian Ring Music TheoryRaga Bhatiyar
3rd mode:
Scale 3449
Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
4th mode:
Scale 943
Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllicThis is the prime mode
5th mode:
Scale 2519
Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic
6th mode:
Scale 3307
Scale 3307: Boptyllic, Ian Ring Music TheoryBoptyllic
7th mode:
Scale 3701
Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
8th mode:
Scale 1949
Scale 1949: Mathyllic, Ian Ring Music TheoryMathyllic

Prime

The prime form of this scale is Scale 943

Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic

Complement

The octatonic modal family [1511, 2803, 3449, 943, 2519, 3307, 3701, 1949] (Forte: 8-16) is the complement of the tetratonic modal family [163, 389, 1121, 2129] (Forte: 4-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1511 is 3317

Scale 3317Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1511 is chiral, and its enantiomorph is scale 3317

Scale 3317Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic

Transformations:

T0 1511  T0I 3317
T1 3022  T1I 2539
T2 1949  T2I 983
T3 3898  T3I 1966
T4 3701  T4I 3932
T5 3307  T5I 3769
T6 2519  T6I 3443
T7 943  T7I 2791
T8 1886  T8I 1487
T9 3772  T9I 2974
T10 3449  T10I 1853
T11 2803  T11I 3706

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 1509Scale 1509: Ragian, Ian Ring Music TheoryRagian
Scale 1507Scale 1507: Zynian, Ian Ring Music TheoryZynian
Scale 1515Scale 1515: Phrygian/Locrian Mixed, Ian Ring Music TheoryPhrygian/Locrian Mixed
Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed
Scale 1527Scale 1527: Aeolyrigic, Ian Ring Music TheoryAeolyrigic
Scale 1479Scale 1479: Mela Jalarnava, Ian Ring Music TheoryMela Jalarnava
Scale 1495Scale 1495: Messiaen Mode 6, Ian Ring Music TheoryMessiaen Mode 6
Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
Scale 1383Scale 1383: Pynian, Ian Ring Music TheoryPynian
Scale 1255Scale 1255: Chromatic Mixolydian, Ian Ring Music TheoryChromatic Mixolydian
Scale 1767Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic
Scale 2023Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
Scale 487Scale 487: Dynian, Ian Ring Music TheoryDynian
Scale 999Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic
Scale 2535Scale 2535: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4
Scale 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic

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.