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Scale 3825: "Pynyllic"

Scale 3825: Pynyllic, 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

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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
Pynyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,4,5,6,7,9,10,11}
Forte Number8-6
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 495
Deep Scaleno
Interval Vector654463
Interval Spectrump6m4n4s5d6t3
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6}
<4> = {5,7}
<5> = {6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[4]
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}231.5
F{5,9,0}241.83
Minor Triadsem{4,7,11}241.83
am{9,0,4}231.5
Diminished Triadse°{4,7,10}152.5
f♯°{6,9,0}152.5
Parsimonious Voice Leading Between Common Triads of Scale 3825. Created by Ian Ring ©2019 C C em em C->em am am C->am e° e° e°->em F F f#° f#° F->f#° F->am

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC, am
Peripheral Verticese°, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 3825 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 495		Scale 495: Bocryllic, Ian Ring Music TheoryBocryllicThis is the prime mode
3rd mode:
Scale 2295		Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
4th mode:
Scale 3195		Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
5th mode:
Scale 3645		Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic
6th mode:
Scale 1935		Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic
7th mode:
Scale 3015		Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
8th mode:
Scale 3555		Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic

Prime

The prime form of this scale is Scale 495

Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic

Complement

The octatonic modal family [3825, 495, 2295, 3195, 3645, 1935, 3015, 3555] (Forte: 8-6) is the complement of the tetratonic modal family [135, 225, 2115, 3105] (Forte: 4-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3825 is 495

Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic

Transformations:

T0 3825  T0I 495
T1 3555  T1I 990
T2 3015  T2I 1980
T3 1935  T3I 3960
T4 3870  T4I 3825
T5 3645  T5I 3555
T6 3195  T6I 3015
T7 2295  T7I 1935
T8 495  T8I 3870
T9 990  T9I 3645
T10 1980  T10I 3195
T11 3960  T11I 2295

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 3827Scale 3827: Bodygic, Ian Ring Music TheoryBodygic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 3793Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
Scale 3761Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri
Scale 3697Scale 3697: Ionarian, Ian Ring Music TheoryIonarian
Scale 3953Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic
Scale 4081Scale 4081: Manygic, Ian Ring Music TheoryManygic
Scale 3313Scale 3313: Aeolacrian, Ian Ring Music TheoryAeolacrian
Scale 3569Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic
Scale 2801Scale 2801: Zogian, Ian Ring Music TheoryZogian
Scale 1777Scale 1777: Saptian, Ian Ring Music TheorySaptian

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.