The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1113: "Locrian Pentatonic 2"

Scale 1113: Locrian Pentatonic 2, 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

Western Modern
Locrian Pentatonic 2
Zeitler
Aeronitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,3,4,6,10}
Forte Number5-28
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 837
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 333
Deep Scaleno
Interval Vector122212
Interval Spectrumpm2n2s2dt2
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,4,5,6}
<3> = {6,7,8,9}
<4> = {8,9,10,11}
Spectra Variation2.4
Maximally Evenno
Maximal Area Setno
Interior Area2.049
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
Minor Triadsd♯m{3,6,10}110.5
Diminished Triads{0,3,6}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1113. Created by Ian Ring ©2019 d#m d#m c°->d#m

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1113 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 651
Scale 651: Golitonic, Ian Ring Music TheoryGolitonic
3rd mode:
Scale 2373
Scale 2373: Dyptitonic, Ian Ring Music TheoryDyptitonic
4th mode:
Scale 1617
Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic
5th mode:
Scale 357
Scale 357: Banitonic, Ian Ring Music TheoryBanitonic

Prime

The prime form of this scale is Scale 333

Scale 333Scale 333: Bogitonic, Ian Ring Music TheoryBogitonic

Complement

The pentatonic modal family [1113, 651, 2373, 1617, 357] (Forte: 5-28) is the complement of the heptatonic modal family [747, 1431, 1629, 1881, 2421, 2763, 3429] (Forte: 7-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1113 is 837

Scale 837Scale 837: Epaditonic, Ian Ring Music TheoryEpaditonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1113 is chiral, and its enantiomorph is scale 837

Scale 837Scale 837: Epaditonic, Ian Ring Music TheoryEpaditonic

Transformations:

T0 1113  T0I 837
T1 2226  T1I 1674
T2 357  T2I 3348
T3 714  T3I 2601
T4 1428  T4I 1107
T5 2856  T5I 2214
T6 1617  T6I 333
T7 3234  T7I 666
T8 2373  T8I 1332
T9 651  T9I 2664
T10 1302  T10I 1233
T11 2604  T11I 2466

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 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
Scale 1117Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic
Scale 1105Scale 1105: Messiaen Truncated Mode 6 Inverse, Ian Ring Music TheoryMessiaen Truncated Mode 6 Inverse
Scale 1109Scale 1109: Kataditonic, Ian Ring Music TheoryKataditonic
Scale 1097Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic
Scale 1129Scale 1129: Raga Jayakauns, Ian Ring Music TheoryRaga Jayakauns
Scale 1145Scale 1145: Zygimic, Ian Ring Music TheoryZygimic
Scale 1049Scale 1049, Ian Ring Music Theory
Scale 1081Scale 1081, Ian Ring Music Theory
Scale 1177Scale 1177: Garitonic, Ian Ring Music TheoryGaritonic
Scale 1241Scale 1241: Pygimic, Ian Ring Music TheoryPygimic
Scale 1369Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
Scale 1625Scale 1625: Lythimic, Ian Ring Music TheoryLythimic
Scale 89Scale 89, Ian Ring Music Theory
Scale 601Scale 601: Bycritonic, Ian Ring Music TheoryBycritonic
Scale 2137Scale 2137, Ian Ring Music Theory
Scale 3161Scale 3161: Kodimic, Ian Ring Music TheoryKodimic

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.