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Scale 893: "Dadyllic"

Scale 893: Dadyllic, 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
Dadyllic

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

{0,2,3,4,5,6,8,9}

Forte Number

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

8-12

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: 2009

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.

4

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: 763

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, 6, 5, 4, 3]

Interval Spectrum

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

p4m5n6s5d5t3

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

2.5

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 TriadsD{2,6,9}342.17
F{5,9,0}441.83
G♯{8,0,3}342.17
Minor Triadsdm{2,5,9}342
fm{5,8,0}342
am{9,0,4}342
Augmented TriadsC+{0,4,8}342
Diminished Triads{0,3,6}242.33
{2,5,8}242.33
d♯°{3,6,9}242.33
f♯°{6,9,0}242.17
{9,0,3}242.33
Parsimonious Voice Leading Between Common Triads of Scale 893. Created by Ian Ring ©2019 d#° d#° c°->d#° G# G# c°->G# C+ C+ fm fm C+->fm C+->G# am am C+->am dm dm d°->dm d°->fm D D dm->D F F dm->F D->d#° f#° f#° D->f#° fm->F F->f#° F->am G#->a° a°->am

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 893 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1247
Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
3rd mode:
Scale 2671
Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
4th mode:
Scale 3383
Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
5th mode:
Scale 3739
Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
6th mode:
Scale 3917
Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
7th mode:
Scale 2003
Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
8th mode:
Scale 3049
Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic

Prime

The prime form of this scale is Scale 763

Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic

Complement

The octatonic modal family [893, 1247, 2671, 3383, 3739, 3917, 2003, 3049] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 893 is 2009

Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 893 is chiral, and its enantiomorph is scale 2009

Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic

Transformations:

T0 893  T0I 2009
T1 1786  T1I 4018
T2 3572  T2I 3941
T3 3049  T3I 3787
T4 2003  T4I 3479
T5 4006  T5I 2863
T6 3917  T6I 1631
T7 3739  T7I 3262
T8 3383  T8I 2429
T9 2671  T9I 763
T10 1247  T10I 1526
T11 2494  T11I 3052

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 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic
Scale 889Scale 889: Borian, Ian Ring Music TheoryBorian
Scale 891Scale 891: Ionilyllic, Ian Ring Music TheoryIonilyllic
Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian
Scale 877Scale 877: Moravian Pistalkova, Ian Ring Music TheoryMoravian Pistalkova
Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian
Scale 829Scale 829: Lygian, Ian Ring Music TheoryLygian
Scale 957Scale 957: Phronyllic, Ian Ring Music TheoryPhronyllic
Scale 1021Scale 1021: Ladygic, Ian Ring Music TheoryLadygic
Scale 637Scale 637: Debussy's Heptatonic, Ian Ring Music TheoryDebussy's Heptatonic
Scale 765Scale 765, Ian Ring Music Theory
Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian
Scale 1405Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
Scale 1917Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic
Scale 2941Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic

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.