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Scale 2683: "Thodyllic"

Scale 2683: Thodyllic, 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
Thodyllic

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

{0,1,3,4,5,6,9,11}

Forte Number

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

8-Z29

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: 3019

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: 751

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

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 Hansen.

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> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<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 TriadsF{5,9,0}341.9
A{9,1,4}242.1
B{11,3,6}242.3
Minor Triadsf♯m{6,9,1}341.9
am{9,0,4}341.9
Augmented TriadsC♯+{1,5,9}341.9
Diminished Triads{0,3,6}242.3
d♯°{3,6,9}242.1
f♯°{6,9,0}242.1
{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 2683. Created by Ian Ring ©2019 c°->a° B B c°->B C#+ C#+ F F C#+->F f#m f#m C#+->f#m A A C#+->A d#° d#° d#°->f#m d#°->B f#° f#° F->f#° am am F->am f#°->f#m a°->am am->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2683 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3389
Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
3rd mode:
Scale 1871
Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
4th mode:
Scale 2983
Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
5th mode:
Scale 3539
Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic
6th mode:
Scale 3817
Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
7th mode:
Scale 989
Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
8th mode:
Scale 1271
Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic

Prime

The prime form of this scale is Scale 751

Scale 751Scale 751, Ian Ring Music Theory

Complement

The octatonic modal family [2683, 3389, 1871, 2983, 3539, 3817, 989, 1271] (Forte: 8-Z29) is the complement of the tetratonic modal family [139, 353, 1553, 2117] (Forte: 4-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2683 is 3019

Scale 3019Scale 3019, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2683 is chiral, and its enantiomorph is scale 3019

Scale 3019Scale 3019, Ian Ring Music Theory

Transformations:

T0 2683  T0I 3019
T1 1271  T1I 1943
T2 2542  T2I 3886
T3 989  T3I 3677
T4 1978  T4I 3259
T5 3956  T5I 2423
T6 3817  T6I 751
T7 3539  T7I 1502
T8 2983  T8I 3004
T9 1871  T9I 1913
T10 3742  T10I 3826
T11 3389  T11I 3557

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 2681Scale 2681: Aerycrian, Ian Ring Music TheoryAerycrian
Scale 2685Scale 2685: Ionoryllic, Ian Ring Music TheoryIonoryllic
Scale 2687Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
Scale 2675Scale 2675: Chromatic Lydian, Ian Ring Music TheoryChromatic Lydian
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
Scale 2667Scale 2667: Byrian, Ian Ring Music TheoryByrian
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
Scale 2811Scale 2811: Barygic, Ian Ring Music TheoryBarygic
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 2171Scale 2171, Ian Ring Music Theory
Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3707Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 1659Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. 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.