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Scale 3877: "Thanian"

Scale 3877: Thanian, 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
Thanian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,5,8,9,10,11}
Forte Number7-10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1183
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 607
Deep Scaleno
Interval Vector445332
Interval Spectrump3m3n5s4d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5,6}
<3> = {3,4,5,6,7,8}
<4> = {4,5,6,7,8,9}
<5> = {6,7,8,9,10}
<6> = {9,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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 TriadsF{5,9,0}231.75
A♯{10,2,5}231.75
Minor Triadsdm{2,5,9}331.63
fm{5,8,0}331.63
Diminished Triads{2,5,8}231.75
{5,8,11}231.75
g♯°{8,11,2}231.88
{11,2,5}231.88
Parsimonious Voice Leading Between Common Triads of Scale 3877. Created by Ian Ring ©2019 dm dm d°->dm fm fm d°->fm F F dm->F A# A# dm->A# f°->fm g#° g#° f°->g#° fm->F g#°->b° A#->b°

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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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3877 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1993
Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
3rd mode:
Scale 761
Scale 761: Ponian, Ian Ring Music TheoryPonian
4th mode:
Scale 607
Scale 607: Kadian, Ian Ring Music TheoryKadianThis is the prime mode
5th mode:
Scale 2351
Scale 2351: Gynian, Ian Ring Music TheoryGynian
6th mode:
Scale 3223
Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
7th mode:
Scale 3659
Scale 3659: Polian, Ian Ring Music TheoryPolian

Prime

The prime form of this scale is Scale 607

Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian

Complement

The heptatonic modal family [3877, 1993, 761, 607, 2351, 3223, 3659] (Forte: 7-10) is the complement of the pentatonic modal family [91, 1547, 1729, 2093, 2821] (Forte: 5-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3877 is 1183

Scale 1183Scale 1183: Sadian, Ian Ring Music TheorySadian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3877 is chiral, and its enantiomorph is scale 1183

Scale 1183Scale 1183: Sadian, Ian Ring Music TheorySadian

Transformations:

T0 3877  T0I 1183
T1 3659  T1I 2366
T2 3223  T2I 637
T3 2351  T3I 1274
T4 607  T4I 2548
T5 1214  T5I 1001
T6 2428  T6I 2002
T7 761  T7I 4004
T8 1522  T8I 3913
T9 3044  T9I 3731
T10 1993  T10I 3367
T11 3986  T11I 2639

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 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
Scale 3873Scale 3873, Ian Ring Music Theory
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 3881Scale 3881: Morian, Ian Ring Music TheoryMorian
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 3845Scale 3845, Ian Ring Music Theory
Scale 3861Scale 3861: Phroptian, Ian Ring Music TheoryPhroptian
Scale 3909Scale 3909: Rydian, Ian Ring Music TheoryRydian
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 4005Scale 4005, Ian Ring Music Theory
Scale 3621Scale 3621: Gylimic, Ian Ring Music TheoryGylimic
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 1829Scale 1829: Pathimic, Ian Ring Music TheoryPathimic

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.