The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3045: "Raptyllic"

Scale 3045: Raptyllic, 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
Raptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,5,6,7,8,9,11}
Forte Number8-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1275
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 735
Deep Scaleno
Interval Vector556453
Interval Spectrump5m4n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<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}341.91
F{5,9,0}341.91
G{7,11,2}242.27
Minor Triadsdm{2,5,9}441.82
fm{5,8,0}342
bm{11,2,6}342
Diminished Triads{2,5,8}242.09
{5,8,11}242.27
f♯°{6,9,0}242.18
g♯°{8,11,2}242.36
{11,2,5}242.09
Parsimonious Voice Leading Between Common Triads of Scale 3045. Created by Ian Ring ©2019 dm dm d°->dm fm fm d°->fm D D dm->D F F dm->F dm->b° f#° f#° D->f#° bm bm D->bm f°->fm g#° g#° f°->g#° fm->F F->f#° Parsimonious Voice Leading Between Common Triads of Scale 3045. Created by Ian Ring ©2019 G G->g#° G->bm b°->bm

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 3045 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1785
Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
3rd mode:
Scale 735
Scale 735: Sylyllic, Ian Ring Music TheorySylyllicThis is the prime mode
4th mode:
Scale 2415
Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
5th mode:
Scale 3255
Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
6th mode:
Scale 3675
Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
7th mode:
Scale 3885
Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
8th mode:
Scale 1995
Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic

Prime

The prime form of this scale is Scale 735

Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic

Complement

The octatonic modal family [3045, 1785, 735, 2415, 3255, 3675, 3885, 1995] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3045 is 1275

Scale 1275Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3045 is chiral, and its enantiomorph is scale 1275

Scale 1275Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic

Transformations:

T0 3045  T0I 1275
T1 1995  T1I 2550
T2 3990  T2I 1005
T3 3885  T3I 2010
T4 3675  T4I 4020
T5 3255  T5I 3945
T6 2415  T6I 3795
T7 735  T7I 3495
T8 1470  T8I 2895
T9 2940  T9I 1695
T10 1785  T10I 3390
T11 3570  T11I 2685

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 3047Scale 3047: Panygic, Ian Ring Music TheoryPanygic
Scale 3041Scale 3041, Ian Ring Music Theory
Scale 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
Scale 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 3053Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic
Scale 3061Scale 3061: Apinygic, Ian Ring Music TheoryApinygic
Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian
Scale 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
Scale 2917Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
Scale 2789Scale 2789: Zolian, Ian Ring Music TheoryZolian
Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian
Scale 3557Scale 3557, Ian Ring Music Theory
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic
Scale 997Scale 997: Rycrian, Ian Ring Music TheoryRycrian
Scale 2021Scale 2021: Katycryllic, Ian Ring Music TheoryKatycryllic

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.