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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

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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

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,5,6,8,9}
Forte Number8-12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2009
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 763
Deep Scaleno
Interval Vector556543
Interval Spectrump4m5n6s5d5t3
Distribution Spectra<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 Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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

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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: Thydyllian, Ian Ring Music TheoryThydyllian
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.