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Scale 1851: "Zacryllic"

Scale 1851: Zacryllic, 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
Zacryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,5,8,9,10}
Forte Number8-20
Rotational Symmetrynone
Reflection Axes0.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 951
Deep Scaleno
Interval Vector545662
Interval Spectrump6m6n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tones[1]
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♯{1,5,8}342
F{5,9,0}331.83
G♯{8,0,3}252.5
A{9,1,4}431.67
Minor Triadsc♯m{1,4,8}331.83
fm{5,8,0}342
am{9,0,4}431.67
a♯m{10,1,5}252.5
Augmented TriadsC+{0,4,8}441.83
C♯+{1,5,9}441.83
Diminished Triads{9,0,3}242.33
a♯°{10,1,4}242.33
Parsimonious Voice Leading Between Common Triads of Scale 1851. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm G# G# C+->G# am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->fm F F C#+->F C#+->A a#m a#m C#+->a#m fm->F F->am G#->a° a°->am am->A a#° a#° A->a#° a#°->a#m

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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♯m, F, am, A
Peripheral VerticesG♯, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 1851 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2973
Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
3rd mode:
Scale 1767
Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic
4th mode:
Scale 2931
Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic
5th mode:
Scale 3513
Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
6th mode:
Scale 951
Scale 951: Thogyllic, Ian Ring Music TheoryThogyllicThis is the prime mode
7th mode:
Scale 2523
Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale
8th mode:
Scale 3309
Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic

Prime

The prime form of this scale is Scale 951

Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic

Complement

The octatonic modal family [1851, 2973, 1767, 2931, 3513, 951, 2523, 3309] (Forte: 8-20) is the complement of the tetratonic modal family [291, 393, 561, 2193] (Forte: 4-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1851 is 2973

Scale 2973Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic

Transformations:

T0 1851  T0I 2973
T1 3702  T1I 1851
T2 3309  T2I 3702
T3 2523  T3I 3309
T4 951  T4I 2523
T5 1902  T5I 951
T6 3804  T6I 1902
T7 3513  T7I 3804
T8 2931  T8I 3513
T9 1767  T9I 2931
T10 3534  T10I 1767
T11 2973  T11I 3534

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 1849Scale 1849: Chromatic Hypodorian Inverse, Ian Ring Music TheoryChromatic Hypodorian Inverse
Scale 1853Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic
Scale 1855Scale 1855: Gaptygic, Ian Ring Music TheoryGaptygic
Scale 1843Scale 1843: Ionygian, Ian Ring Music TheoryIonygian
Scale 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
Scale 1835Scale 1835: Byptian, Ian Ring Music TheoryByptian
Scale 1819Scale 1819: Pydian, Ian Ring Music TheoryPydian
Scale 1883Scale 1883, Ian Ring Music Theory
Scale 1915Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
Scale 1979Scale 1979: Aeradygic, Ian Ring Music TheoryAeradygic
Scale 1595Scale 1595: Dacrian, Ian Ring Music TheoryDacrian
Scale 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
Scale 1339Scale 1339: Kycrian, Ian Ring Music TheoryKycrian
Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
Scale 2875Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic
Scale 3899Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic

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.