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Scale 4007: "Doptygic"

Scale 4007: Doptygic, 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
Doptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,5,7,8,9,10,11}
Forte Number9-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3263
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 767
Deep Scaleno
Interval Vector777663
Interval Spectrump6m6n7s7d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {7,8,9,10}
<8> = {9,10,11}
Spectra Variation2.444
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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 TriadsC♯{1,5,8}342.29
F{5,9,0}242.43
G{7,11,2}342.43
A♯{10,2,5}442.07
Minor Triadsdm{2,5,9}342.14
fm{5,8,0}342.43
gm{7,10,2}342.29
a♯m{10,1,5}342.14
Augmented TriadsC♯+{1,5,9}442.07
Diminished Triads{2,5,8}242.5
{5,8,11}242.57
{7,10,1}242.5
g♯°{8,11,2}242.57
{11,2,5}242.43
Parsimonious Voice Leading Between Common Triads of Scale 4007. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F a#m a#m C#+->a#m d°->dm A# A# dm->A# f°->fm g#° g#° f°->g#° fm->F gm gm g°->gm g°->a#m Parsimonious Voice Leading Between Common Triads of Scale 4007. Created by Ian Ring ©2019 G gm->G gm->A# G->g#° G->b° a#m->A# A#->b°

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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 4007 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 4051
Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic
3rd mode:
Scale 4073
Scale 4073: Sathygic, Ian Ring Music TheorySathygic
4th mode:
Scale 1021
Scale 1021: Ladygic, Ian Ring Music TheoryLadygic
5th mode:
Scale 1279
Scale 1279: Sarygic, Ian Ring Music TheorySarygic
6th mode:
Scale 2687
Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
7th mode:
Scale 3391
Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
8th mode:
Scale 3743
Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
9th mode:
Scale 3919
Scale 3919: Lynygic, Ian Ring Music TheoryLynygic

Prime

The prime form of this scale is Scale 767

Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic

Complement

The nonatonic modal family [4007, 4051, 4073, 1021, 1279, 2687, 3391, 3743, 3919] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4007 is 3263

Scale 3263Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 4007 is chiral, and its enantiomorph is scale 3263

Scale 3263Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic

Transformations:

T0 4007  T0I 3263
T1 3919  T1I 2431
T2 3743  T2I 767
T3 3391  T3I 1534
T4 2687  T4I 3068
T5 1279  T5I 2041
T6 2558  T6I 4082
T7 1021  T7I 4069
T8 2042  T8I 4043
T9 4084  T9I 3991
T10 4073  T10I 3887
T11 4051  T11I 3679

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 4005Scale 4005, Ian Ring Music Theory
Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 4015Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian
Scale 4023Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
Scale 3975Scale 3975, Ian Ring Music Theory
Scale 3991Scale 3991: Badygic, Ian Ring Music TheoryBadygic
Scale 4039Scale 4039: Ionogygic, Ian Ring Music TheoryIonogygic
Scale 4071Scale 4071: Rygyllian, Ian Ring Music TheoryRygyllian
Scale 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
Scale 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 3495Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 1959Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.