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Scale 3875: "Aeryptian"

Scale 3875: Aeryptian, 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
Aeryptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,5,8,9,10,11}
Forte Number7-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2207
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 319
Deep Scaleno
Interval Vector544431
Interval Spectrump3m4n4s4d5t
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5,7}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {5,7,8,10}
<6> = {8,9,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area2.183
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}221.33
F{5,9,0}221.33
Minor Triadsfm{5,8,0}331.33
a♯m{10,1,5}142
Augmented TriadsC♯+{1,5,9}331.33
Diminished Triads{5,8,11}142
Parsimonious Voice Leading Between Common Triads of Scale 3875. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F a#m a#m C#+->a#m f°->fm fm->F

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♯, F
Peripheral Verticesf°, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3875 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3985
Scale 3985: Thadian, Ian Ring Music TheoryThadian
3rd mode:
Scale 505
Scale 505: Sanian, Ian Ring Music TheorySanian
4th mode:
Scale 575
Scale 575: Ionydian, Ian Ring Music TheoryIonydian
5th mode:
Scale 2335
Scale 2335: Epydian, Ian Ring Music TheoryEpydian
6th mode:
Scale 3215
Scale 3215: Katydian, Ian Ring Music TheoryKatydian
7th mode:
Scale 3655
Scale 3655: Mathian, Ian Ring Music TheoryMathian

Prime

The prime form of this scale is Scale 319

Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian

Complement

The heptatonic modal family [3875, 3985, 505, 575, 2335, 3215, 3655] (Forte: 7-3) is the complement of the pentatonic modal family [55, 1795, 2075, 2945, 3085] (Forte: 5-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3875 is 2207

Scale 2207Scale 2207: Mygian, Ian Ring Music TheoryMygian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3875 is chiral, and its enantiomorph is scale 2207

Scale 2207Scale 2207: Mygian, Ian Ring Music TheoryMygian

Transformations:

T0 3875  T0I 2207
T1 3655  T1I 319
T2 3215  T2I 638
T3 2335  T3I 1276
T4 575  T4I 2552
T5 1150  T5I 1009
T6 2300  T6I 2018
T7 505  T7I 4036
T8 1010  T8I 3977
T9 2020  T9I 3859
T10 4040  T10I 3623
T11 3985  T11I 3151

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 3873Scale 3873, Ian Ring Music Theory
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
Scale 3843Scale 3843, Ian Ring Music Theory
Scale 3859Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
Scale 3907Scale 3907, Ian Ring Music Theory
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 3363Scale 3363: Rogimic, Ian Ring Music TheoryRogimic
Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
Scale 1827Scale 1827: Katygimic, Ian Ring Music TheoryKatygimic

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.