The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3645: "Zycryllic"

Scale 3645: Zycryllic, 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
Zycryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,5,9,10,11}
Forte Number8-6
Rotational Symmetrynone
Reflection Axes1
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[2]
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 TriadsF{5,9,0}231.5
A♯{10,2,5}241.83
Minor Triadsdm{2,5,9}231.5
am{9,0,4}241.83
Diminished Triads{9,0,3}152.5
{11,2,5}152.5
Parsimonious Voice Leading Between Common Triads of Scale 3645. Created by Ian Ring ©2019 dm dm F F dm->F A# A# dm->A# am am F->am a°->am A#->b°

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 Verticesdm, F
Peripheral Verticesa°, b°

Modes

Modes are the rotational transformation of this scale. Scale 3645 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1935
Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic
3rd mode:
Scale 3015
Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
4th mode:
Scale 3555
Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic
5th mode:
Scale 3825
Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic
6th mode:
Scale 495
Scale 495: Bocryllic, Ian Ring Music TheoryBocryllicThis is the prime mode
7th mode:
Scale 2295
Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
8th mode:
Scale 3195
Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic

Prime

The prime form of this scale is Scale 495

Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic

Complement

The octatonic modal family [3645, 1935, 3015, 3555, 3825, 495, 2295, 3195] (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 3645 is 1935

Scale 1935Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic

Transformations:

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

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 3647Scale 3647: Eporygic, Ian Ring Music TheoryEporygic
Scale 3641Scale 3641: Thocrian, Ian Ring Music TheoryThocrian
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 3613Scale 3613, Ian Ring Music Theory
Scale 3677Scale 3677, Ian Ring Music Theory
Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic
Scale 3773Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
Scale 3901Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
Scale 2621Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
Scale 1597Scale 1597: Aeolodian, Ian Ring Music TheoryAeolodian

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.