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Scale 767: "Raptygic"

Scale 767: Raptygic, 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
Raptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,5,6,7,9}
Forte Number9-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 4073
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections3
Modes8
Prime?yes
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{0,4,7}342.29
D{2,6,9}342.43
F{5,9,0}342.14
A{9,1,4}342.14
Minor Triadscm{0,3,7}342.43
dm{2,5,9}242.43
f♯m{6,9,1}342.29
am{9,0,4}442.07
Augmented TriadsC♯+{1,5,9}442.07
Diminished Triads{0,3,6}242.57
c♯°{1,4,7}242.5
d♯°{3,6,9}242.57
f♯°{6,9,0}242.5
{9,0,3}242.43
Parsimonious Voice Leading Between Common Triads of Scale 767. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° C C cm->C cm->a° c#° c#° C->c#° am am C->am A A c#°->A C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m C#+->A D D dm->D D->d#° D->f#m f#° f#° F->f#° F->am f#°->f#m a°->am 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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 767 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2431
Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
3rd mode:
Scale 3263
Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
4th mode:
Scale 3679
Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
5th mode:
Scale 3887
Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
6th mode:
Scale 3991
Scale 3991: Badygic, Ian Ring Music TheoryBadygic
7th mode:
Scale 4043
Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
8th mode:
Scale 4069
Scale 4069: Starygic, Ian Ring Music TheoryStarygic
9th mode:
Scale 2041
Scale 2041: Aeolacrygic, Ian Ring Music TheoryAeolacrygic

Prime

This is the prime form of this scale.

Complement

The nonatonic modal family [767, 2431, 3263, 3679, 3887, 3991, 4043, 4069, 2041] (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 767 is 4073

Scale 4073Scale 4073: Sathygic, Ian Ring Music TheorySathygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 767 is chiral, and its enantiomorph is scale 4073

Scale 4073Scale 4073: Sathygic, Ian Ring Music TheorySathygic

Transformations:

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

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 765Scale 765, Ian Ring Music Theory
Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic
Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic
Scale 751Scale 751, Ian Ring Music Theory
Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic
Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic
Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic
Scale 1023Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllian
Scale 255Scale 255, Ian Ring Music Theory
Scale 511Scale 511: Polygic, Ian Ring Music TheoryPolygic
Scale 1279Scale 1279: Sarygic, Ian Ring Music TheorySarygic
Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian
Scale 2815Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian

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.