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Scale 2647: "Dadian"

Scale 2647: Dadian, 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
Dadian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,6,9,11}
Forte Number7-23
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3403
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?no
prime: 701
Deep Scaleno
Interval Vector354351
Interval Spectrump5m3n4s5d3t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}231.5
A{9,1,4}231.5
Minor Triadsf♯m{6,9,1}321.17
am{9,0,4}241.83
bm{11,2,6}142.17
Diminished Triadsf♯°{6,9,0}231.5
Parsimonious Voice Leading Between Common Triads of Scale 2647. Created by Ian Ring ©2019 D D f#m f#m D->f#m bm bm D->bm f#° f#° f#°->f#m am am f#°->am A A f#m->A 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
Radius2
Self-Centeredno
Central Verticesf♯m
Peripheral Verticesam, bm

Modes

Modes are the rotational transformation of this scale. Scale 2647 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3371
Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
3rd mode:
Scale 3733
Scale 3733: Gycrian, Ian Ring Music TheoryGycrian
4th mode:
Scale 1957
Scale 1957: Pyrian, Ian Ring Music TheoryPyrian
5th mode:
Scale 1513
Scale 1513: Stathian, Ian Ring Music TheoryStathian
6th mode:
Scale 701
Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphianThis is the prime mode
7th mode:
Scale 1199
Scale 1199: Magian, Ian Ring Music TheoryMagian

Prime

The prime form of this scale is Scale 701

Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian

Complement

The heptatonic modal family [2647, 3371, 3733, 1957, 1513, 701, 1199] (Forte: 7-23) is the complement of the pentatonic modal family [173, 1067, 1441, 1669, 2581] (Forte: 5-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2647 is 3403

Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2647 is chiral, and its enantiomorph is scale 3403

Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian

Transformations:

T0 2647  T0I 3403
T1 1199  T1I 2711
T2 2398  T2I 1327
T3 701  T3I 2654
T4 1402  T4I 1213
T5 2804  T5I 2426
T6 1513  T6I 757
T7 3026  T7I 1514
T8 1957  T8I 3028
T9 3914  T9I 1961
T10 3733  T10I 3922
T11 3371  T11I 3749

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 2645Scale 2645: Raga Mruganandana, Ian Ring Music TheoryRaga Mruganandana
Scale 2643Scale 2643: Raga Hamsanandi, Ian Ring Music TheoryRaga Hamsanandi
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 2655Scale 2655, Ian Ring Music Theory
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 2639Scale 2639: Dothian, Ian Ring Music TheoryDothian
Scale 2663Scale 2663: Lalian, Ian Ring Music TheoryLalian
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
Scale 2583Scale 2583, Ian Ring Music Theory
Scale 2615Scale 2615: Thoptian, Ian Ring Music TheoryThoptian
Scale 2711Scale 2711: Stolian, Ian Ring Music TheoryStolian
Scale 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 2135Scale 2135, Ian Ring Music Theory
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic
Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian

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.