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Scale 3151: "Pacrian"

Scale 3151: Pacrian, 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
Pacrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,6,10,11}
Forte Number7-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3655
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
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 TriadsF♯{6,10,1}142
B{11,3,6}331.33
Minor Triadsd♯m{3,6,10}221.33
bm{11,2,6}221.33
Augmented TriadsD+{2,6,10}331.33
Diminished Triads{0,3,6}142
Parsimonious Voice Leading Between Common Triads of Scale 3151. Created by Ian Ring ©2019 B B c°->B D+ D+ d#m d#m D+->d#m F# F# D+->F# bm bm D+->bm d#m->B bm->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
Radius2
Self-Centeredno
Central Verticesd♯m, bm
Peripheral Verticesc°, F♯

Modes

Modes are the rotational transformation of this scale. Scale 3151 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3623
Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian
3rd mode:
Scale 3859
Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
4th mode:
Scale 3977
Scale 3977: Kythian, Ian Ring Music TheoryKythian
5th mode:
Scale 1009
Scale 1009: Katyptian, Ian Ring Music TheoryKatyptian
6th mode:
Scale 319
Scale 319: Epodian, Ian Ring Music TheoryEpodianThis is the prime mode
7th mode:
Scale 2207
Scale 2207: Mygian, Ian Ring Music TheoryMygian

Prime

The prime form of this scale is Scale 319

Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian

Complement

The heptatonic modal family [3151, 3623, 3859, 3977, 1009, 319, 2207] (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 3151 is 3655

Scale 3655Scale 3655: Mathian, Ian Ring Music TheoryMathian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3151 is chiral, and its enantiomorph is scale 3655

Scale 3655Scale 3655: Mathian, Ian Ring Music TheoryMathian

Transformations:

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

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 3149Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3183Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic
Scale 3087Scale 3087, Ian Ring Music Theory
Scale 3119Scale 3119, Ian Ring Music Theory
Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
Scale 3407Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
Scale 3663Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
Scale 2127Scale 2127, Ian Ring Music Theory
Scale 2639Scale 2639: Dothian, Ian Ring Music TheoryDothian
Scale 1103Scale 1103: Lynimic, Ian Ring Music TheoryLynimic

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.