The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3639: "Paptyllic"

Scale 3639: Paptyllic, 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
Paptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,9,10,11}
Forte Number8-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3471
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 447
Deep Scaleno
Interval Vector655552
Interval Spectrump5m5n5s5d6t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation3
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3639 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3867
Scale 3867: Storyllic, Ian Ring Music TheoryStoryllic
3rd mode:
Scale 3981
Scale 3981: Phrycryllic, Ian Ring Music TheoryPhrycryllic
4th mode:
Scale 2019
Scale 2019: Palyllic, Ian Ring Music TheoryPalyllic
5th mode:
Scale 3057
Scale 3057: Phroryllic, Ian Ring Music TheoryPhroryllic
6th mode:
Scale 447
Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllicThis is the prime mode
7th mode:
Scale 2271
Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
8th mode:
Scale 3183
Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic

Prime

The prime form of this scale is Scale 447

Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic

Complement

The octatonic modal family [3639, 3867, 3981, 2019, 3057, 447, 2271, 3183] (Forte: 8-4) is the complement of the tetratonic modal family [39, 897, 2067, 3081] (Forte: 4-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3639 is 3471

Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3639 is chiral, and its enantiomorph is scale 3471

Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic

Transformations:

T0 3639  T0I 3471
T1 3183  T1I 2847
T2 2271  T2I 1599
T3 447  T3I 3198
T4 894  T4I 2301
T5 1788  T5I 507
T6 3576  T6I 1014
T7 3057  T7I 2028
T8 2019  T8I 4056
T9 4038  T9I 4017
T10 3981  T10I 3939
T11 3867  T11I 3783

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 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 3635Scale 3635: Katygian, Ian Ring Music TheoryKatygian
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3647Scale 3647: Eporygic, Ian Ring Music TheoryEporygic
Scale 3623Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian
Scale 3631Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic
Scale 3607Scale 3607, Ian Ring Music Theory
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
Scale 3767Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
Scale 3895Scale 3895: Eparygic, Ian Ring Music TheoryEparygic
Scale 3127Scale 3127, Ian Ring Music Theory
Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 2615Scale 2615: Thoptian, Ian Ring Music TheoryThoptian
Scale 1591Scale 1591: Rodian, Ian Ring Music TheoryRodian

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.