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Scale 1847: "Thacryllic"

Scale 1847: Thacryllic, 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
Thacryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,8,9,10}
Forte Number8-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3485
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 887
Deep Scaleno
Interval Vector545752
Interval Spectrump5m7n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.75
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 TriadsC♯{1,5,8}431.77
F{5,9,0}331.92
A{9,1,4}431.77
A♯{10,2,5}252.62
Minor Triadsc♯m{1,4,8}342
dm{2,5,9}342.08
fm{5,8,0}342.15
am{9,0,4}342.15
a♯m{10,1,5}342.08
Augmented TriadsC+{0,4,8}352.38
C♯+{1,5,9}531.54
Diminished Triads{2,5,8}242.31
a♯°{10,1,4}242.31
Parsimonious Voice Leading Between Common Triads of Scale 1847. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F C#+->A a#m a#m C#+->a#m d°->dm A# A# dm->A# fm->F F->am am->A a#° a#° A->a#° a#°->a#m a#m->A#

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♯, C♯+, F, A
Peripheral VerticesC+, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1847 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2971
Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
3rd mode:
Scale 3533
Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
4th mode:
Scale 1907
Scale 1907: Lynyllic, Ian Ring Music TheoryLynyllic
5th mode:
Scale 3001
Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
6th mode:
Scale 887
Scale 887: Sathyllic, Ian Ring Music TheorySathyllicThis is the prime mode
7th mode:
Scale 2491
Scale 2491: Layllic, Ian Ring Music TheoryLayllic
8th mode:
Scale 3293
Scale 3293: Saryllic, Ian Ring Music TheorySaryllic

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [1847, 2971, 3533, 1907, 3001, 887, 2491, 3293] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1847 is 3485

Scale 3485Scale 3485: Sabach, Ian Ring Music TheorySabach

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1847 is chiral, and its enantiomorph is scale 3485

Scale 3485Scale 3485: Sabach, Ian Ring Music TheorySabach

Transformations:

T0 1847  T0I 3485
T1 3694  T1I 2875
T2 3293  T2I 1655
T3 2491  T3I 3310
T4 887  T4I 2525
T5 1774  T5I 955
T6 3548  T6I 1910
T7 3001  T7I 3820
T8 1907  T8I 3545
T9 3814  T9I 2995
T10 3533  T10I 1895
T11 2971  T11I 3790

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 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian
Scale 1843Scale 1843: Ionygian, Ian Ring Music TheoryIonygian
Scale 1851Scale 1851: Zacryllic, Ian Ring Music TheoryZacryllic
Scale 1855Scale 1855: Gaptygic, Ian Ring Music TheoryGaptygic
Scale 1831Scale 1831: Pothian, Ian Ring Music TheoryPothian
Scale 1839Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
Scale 1815Scale 1815: Godian, Ian Ring Music TheoryGodian
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 1911Scale 1911: Messiaen Mode 3, Ian Ring Music TheoryMessiaen Mode 3
Scale 1975Scale 1975: Ionocrygic, Ian Ring Music TheoryIonocrygic
Scale 1591Scale 1591: Rodian, Ian Ring Music TheoryRodian
Scale 1719Scale 1719: Lyryllic, Ian Ring Music TheoryLyryllic
Scale 1335Scale 1335: Elephant Scale, Ian Ring Music TheoryElephant Scale
Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 3895Scale 3895: Eparygic, Ian Ring Music TheoryEparygic

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.