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Scale 2943: "Dathyllian"

Scale 2943: Dathyllian, 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
Dathyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,5,6,8,9,11}
Forte Number10-3
Rotational Symmetrynone
Reflection Axes2.5
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1791
Deep Scaleno
Interval Vector889884
Interval Spectrump8m8n9s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {7,8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1.4
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[5]
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 TriadsC♯{1,5,8}452.67
D{2,6,9}452.75
E{4,8,11}352.75
F{5,9,0}452.58
G♯{8,0,3}452.67
A{9,1,4}352.75
B{11,3,6}452.83
Minor Triadsc♯m{1,4,8}352.75
dm{2,5,9}452.67
fm{5,8,0}452.58
f♯m{6,9,1}352.75
g♯m{8,11,3}452.75
am{9,0,4}452.67
bm{11,2,6}452.83
Augmented TriadsC+{0,4,8}552.5
C♯+{1,5,9}552.5
Diminished Triads{0,3,6}253
{2,5,8}253
d♯°{3,6,9}253
{5,8,11}253
f♯°{6,9,0}253
g♯°{8,11,2}253
{9,0,3}253
{11,2,5}253
Parsimonious Voice Leading Between Common Triads of Scale 2943. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m C#+->A d°->dm D D dm->D dm->b° d#° d#° D->d#° D->f#m bm bm D->bm d#°->B E->f° g#m g#m E->g#m f°->fm fm->F f#° f#° F->f#° F->am f#°->f#m g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B G#->a° a°->am am->A b°->bm bm->B

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
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2943 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3519
Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
3rd mode:
Scale 3807
Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian
4th mode:
Scale 3951
Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
5th mode:
Scale 4023
Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
6th mode:
Scale 4059
Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
7th mode:
Scale 4077
Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
8th mode:
Scale 2043
Scale 2043: Maqam Tarzanuyn, Ian Ring Music TheoryMaqam Tarzanuyn
9th mode:
Scale 3069
Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza
10th mode:
Scale 1791
Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllianThis is the prime mode

Prime

The prime form of this scale is Scale 1791

Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian

Complement

The decatonic modal family [2943, 3519, 3807, 3951, 4023, 4059, 4077, 2043, 3069, 1791] (Forte: 10-3) is the complement of the modal family [9, 513] (Forte: 2-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2943 is 4059

Scale 4059Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian

Transformations:

T0 2943  T0I 4059
T1 1791  T1I 4023
T2 3582  T2I 3951
T3 3069  T3I 3807
T4 2043  T4I 3519
T5 4086  T5I 2943
T6 4077  T6I 1791
T7 4059  T7I 3582
T8 4023  T8I 3069
T9 3951  T9I 2043
T10 3807  T10I 4086
T11 3519  T11I 4077

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 2941Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 2935Scale 2935: Modygic, Ian Ring Music TheoryModygic
Scale 2927Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
Scale 2911Scale 2911: Katygic, Ian Ring Music TheoryKatygic
Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
Scale 3007Scale 3007: Zyryllian, Ian Ring Music TheoryZyryllian
Scale 3071Scale 3071: Solatic, Ian Ring Music TheorySolatic
Scale 2687Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
Scale 2815Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
Scale 3967Scale 3967: Soratic, Ian Ring Music TheorySoratic
Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic
Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian

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.