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Scale 3861: "Phroptian"

Scale 3861: Phroptian, 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
Phroptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,4,8,9,10,11}
Forte Number7-9
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1311
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 351
Deep Scaleno
Interval Vector453432
Interval Spectrump3m4n3s5d4t2
Distribution Spectra<1> = {1,2,4}
<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> = {8,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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 TriadsE{4,8,11}221
Minor Triadsam{9,0,4}131.5
Augmented TriadsC+{0,4,8}221
Diminished Triadsg♯°{8,11,2}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3861. Created by Ian Ring ©2019 C+ C+ E E C+->E am am C+->am g#° g#° E->g#°

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
Radius2
Self-Centeredno
Central VerticesC+, E
Peripheral Verticesg♯°, am

Modes

Modes are the rotational transformation of this scale. Scale 3861 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1989
Scale 1989: Dydian, Ian Ring Music TheoryDydian
3rd mode:
Scale 1521
Scale 1521: Stanian, Ian Ring Music TheoryStanian
4th mode:
Scale 351
Scale 351: Epanian, Ian Ring Music TheoryEpanianThis is the prime mode
5th mode:
Scale 2223
Scale 2223: Konian, Ian Ring Music TheoryKonian
6th mode:
Scale 3159
Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
7th mode:
Scale 3627
Scale 3627: Kalian, Ian Ring Music TheoryKalian

Prime

The prime form of this scale is Scale 351

Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian

Complement

The heptatonic modal family [3861, 1989, 1521, 351, 2223, 3159, 3627] (Forte: 7-9) is the complement of the pentatonic modal family [87, 1473, 1797, 2091, 3093] (Forte: 5-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3861 is 1311

Scale 1311Scale 1311: Bynian, Ian Ring Music TheoryBynian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3861 is chiral, and its enantiomorph is scale 1311

Scale 1311Scale 1311: Bynian, Ian Ring Music TheoryBynian

Transformations:

T0 3861  T0I 1311
T1 3627  T1I 2622
T2 3159  T2I 1149
T3 2223  T3I 2298
T4 351  T4I 501
T5 702  T5I 1002
T6 1404  T6I 2004
T7 2808  T7I 4008
T8 1521  T8I 3921
T9 3042  T9I 3747
T10 1989  T10I 3399
T11 3978  T11I 2703

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 3863Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic
Scale 3857Scale 3857: Ponimic, Ian Ring Music TheoryPonimic
Scale 3859Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
Scale 3865Scale 3865: Starian, Ian Ring Music TheoryStarian
Scale 3869Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic
Scale 3845Scale 3845, Ian Ring Music Theory
Scale 3853Scale 3853, Ian Ring Music Theory
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 3989Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic
Scale 3605Scale 3605, Ian Ring Music Theory
Scale 3733Scale 3733: Gycrian, Ian Ring Music TheoryGycrian
Scale 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic
Scale 2837Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
Scale 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.