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Scale 1891: "Thalian"

Scale 1891: Thalian, 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
Thalian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,5,6,8,9,10}
Forte Number7-Z37
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 443
Deep Scaleno
Interval Vector434541
Interval Spectrump4m5n4s3d4t
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {7,9,10}
<6> = {8,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tones[6]
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}231.75
F{5,9,0}331.5
F♯{6,10,1}242
Minor Triadsfm{5,8,0}242
f♯m{6,9,1}331.5
a♯m{10,1,5}231.75
Augmented TriadsC♯+{1,5,9}421.25
Diminished Triadsf♯°{6,9,0}231.75
Parsimonious Voice Leading Between Common Triads of Scale 1891. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m fm->F f#° f#° F->f#° f#°->f#m F# F# f#m->F# F#->a#m

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.

Diameter4
Radius2
Self-Centeredno
Central VerticesC♯+
Peripheral Verticesfm, F♯

Modes

Modes are the rotational transformation of this scale. Scale 1891 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2993
Scale 2993: Stythian, Ian Ring Music TheoryStythian
3rd mode:
Scale 443
Scale 443: Kothian, Ian Ring Music TheoryKothianThis is the prime mode
4th mode:
Scale 2269
Scale 2269: Pygian, Ian Ring Music TheoryPygian
5th mode:
Scale 1591
Scale 1591: Rodian, Ian Ring Music TheoryRodian
6th mode:
Scale 2843
Scale 2843: Sorian, Ian Ring Music TheorySorian
7th mode:
Scale 3469
Scale 3469: Monian, Ian Ring Music TheoryMonian

Prime

The prime form of this scale is Scale 443

Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian

Complement

The heptatonic modal family [1891, 2993, 443, 2269, 1591, 2843, 3469] (Forte: 7-Z37) is the complement of the pentatonic modal family [313, 551, 913, 2323, 3209] (Forte: 5-Z37)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1891 is 2269

Scale 2269Scale 2269: Pygian, Ian Ring Music TheoryPygian

Transformations:

T0 1891  T0I 2269
T1 3782  T1I 443
T2 3469  T2I 886
T3 2843  T3I 1772
T4 1591  T4I 3544
T5 3182  T5I 2993
T6 2269  T6I 1891
T7 443  T7I 3782
T8 886  T8I 3469
T9 1772  T9I 2843
T10 3544  T10I 1591
T11 2993  T11I 3182

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 1889Scale 1889, Ian Ring Music Theory
Scale 1893Scale 1893: Ionylian, Ian Ring Music TheoryIonylian
Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
Scale 1899Scale 1899: Moptyllic, Ian Ring Music TheoryMoptyllic
Scale 1907Scale 1907: Lynyllic, Ian Ring Music TheoryLynyllic
Scale 1859Scale 1859, Ian Ring Music Theory
Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale
Scale 1827Scale 1827: Katygimic, Ian Ring Music TheoryKatygimic
Scale 1955Scale 1955: Sonian, Ian Ring Music TheorySonian
Scale 2019Scale 2019: Palyllic, Ian Ring Music TheoryPalyllic
Scale 1635Scale 1635: Sygimic, Ian Ring Music TheorySygimic
Scale 1763Scale 1763: Katalian, Ian Ring Music TheoryKatalian
Scale 1379Scale 1379: Kycrimic, Ian Ring Music TheoryKycrimic
Scale 867Scale 867: Phrocrimic, Ian Ring Music TheoryPhrocrimic
Scale 2915Scale 2915: Aeolydian, Ian Ring Music TheoryAeolydian
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic

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.