Scale 1113: "Locrian Pentatonic 2"

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

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

Cardinality	5 (pentatonic)
Pitch Class Set	{0,3,4,6,10}
Forte Number	5-28
Rotational Symmetry	none
Reflection Axes	none
Palindromic	no
Chirality	yes enantiomorph: 837
Hemitonia	1 (unhemitonic)
Cohemitonia	0 (ancohemitonic)
Imperfections	4
Modes	4
Prime?	no prime: 333
Deep Scale	no
Interval Vector	122212
Interval Spectrum	pm²n²s²dt²
Distribution Spectra	<1> = {1,2,3,4} <2> = {3,4,5,6} <3> = {6,7,8,9} <4> = {8,9,10,11}
Spectra Variation	2.4
Maximally Even	no
Myhill Property	no
Balanced	no
Ridge Tones	none
Propriety	Improper
Heliotonic	no

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				Golitonic
3rd mode: Scale 2373				Dyptitonic
4th mode: Scale 1617				Phronitonic
5th mode: Scale 357				Banitonic

Prime

The prime form of this scale is Scale 333

Scale 333

Bogitonic

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 837

Epaditonic

Enantiomorph

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

Scale 837

Epaditonic

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 1115				Superlocrian Hexamirror
Scale 1117				Raptimic
Scale 1105				Messiaen Truncated Mode 6 Inverse
Scale 1109				Kataditonic
Scale 1097				Aeraphic
Scale 1129				Raga Jayakauns
Scale 1145				Zygimic
Scale 1049
Scale 1081
Scale 1177				Garitonic
Scale 1241				Pygimic
Scale 1369				Boptimic
Scale 1625				Lythimic
Scale 89
Scale 601				Bycritonic
Scale 2137
Scale 3161				Kodimic

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.