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Scale 3879: "Pathyllic"

Scale 3879: Pathyllic, 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
Pathyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,5,8,9,10,11}
Forte Number8-3
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 639
Deep Scaleno
Interval Vector656542
Interval Spectrump4m5n6s5d6t2
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {3,5,7}
<4> = {4,6,8}
<5> = {5,7,9}
<6> = {6,8,10}
<7> = {9,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.5
Myhill Propertyno
Balancedno
Ridge Tones[10]
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}341.91
F{5,9,0}242.09
A♯{10,2,5}342
Minor Triadsdm{2,5,9}341.91
fm{5,8,0}342
a♯m{10,1,5}242.09
Augmented TriadsC♯+{1,5,9}441.82
Diminished Triads{2,5,8}242.18
{5,8,11}242.27
g♯°{8,11,2}242.36
{11,2,5}242.27
Parsimonious Voice Leading Between Common Triads of Scale 3879. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F a#m a#m C#+->a#m d°->dm A# A# dm->A# f°->fm g#° g#° f°->g#° fm->F g#°->b° a#m->A# A#->b°

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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3879 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3987
Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic
3rd mode:
Scale 4041
Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
4th mode:
Scale 1017
Scale 1017: Dythyllic, Ian Ring Music TheoryDythyllic
5th mode:
Scale 639
Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllicThis is the prime mode
6th mode:
Scale 2367
Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
7th mode:
Scale 3231
Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
8th mode:
Scale 3663
Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic

Prime

The prime form of this scale is Scale 639

Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic

Complement

The octatonic modal family [3879, 3987, 4041, 1017, 639, 2367, 3231, 3663] (Forte: 8-3) is the complement of the tetratonic modal family [27, 1539, 2061, 2817] (Forte: 4-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3879 is 3231

Scale 3231Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic

Transformations:

T0 3879  T0I 3231
T1 3663  T1I 2367
T2 3231  T2I 639
T3 2367  T3I 1278
T4 639  T4I 2556
T5 1278  T5I 1017
T6 2556  T6I 2034
T7 1017  T7I 4068
T8 2034  T8I 4041
T9 4068  T9I 3987
T10 4041  T10I 3879
T11 3987  T11I 3663

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 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
Scale 3887Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
Scale 3895Scale 3895: Eparygic, Ian Ring Music TheoryEparygic
Scale 3847Scale 3847, Ian Ring Music Theory
Scale 3863Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic
Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
Scale 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic
Scale 3623Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian
Scale 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 2855Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain
Scale 1831Scale 1831: Pothian, Ian Ring Music TheoryPothian

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.