Scale 71

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).

Analysis

Cardinality	4 (tetratonic)
Pitch Class Set	{0,1,2,6}
Forte Number	4-5
Rotational Symmetry	none
Reflection Axes	none
Palindromic	no
Chirality	yes enantiomorph: 3137
Hemitonia	2 (dihemitonic)
Cohemitonia	1 (uncohemitonic)
Imperfections	3
Modes	3
Prime?	yes
Deep Scale	no
Interval Vector	210111
Interval Spectrum	pmsd²t
Distribution Spectra	<1> = {1,4,6} <2> = {2,5,7,10} <3> = {6,8,11}
Spectra Variation	4.5
Maximally Even	no
Maximal Area Set	no
Interior Area	0.933
Myhill Property	no
Balanced	no
Ridge Tones	none
Propriety	Improper
Heliotonic	no

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 71 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode: Scale 2083
3rd mode: Scale 3089
4th mode: Scale 449

Prime

This is the prime form of this scale.

Complement

The tetratonic modal family [71, 2083, 3089, 449] (Forte: 4-5) is the complement of the octatonic modal family [479, 1991, 2287, 3043, 3191, 3569, 3643, 3869] (Forte: 8-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 71 is 3137

Scale 3137

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 71 is chiral, and its enantiomorph is scale 3137

Scale 3137

Transformations:

T₀	71	T₀I	3137
T₁	142	T₁I	2179
T₂	284	T₂I	263
T₃	568	T₃I	526
T₄	1136	T₄I	1052
T₅	2272	T₅I	2104
T₆	449	T₆I	113
T₇	898	T₇I	226
T₈	1796	T₈I	452
T₉	3592	T₉I	904
T₁₀	3089	T₁₀I	1808
T₁₁	2083	T₁₁I	3616

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 69
Scale 67
Scale 75
Scale 79
Scale 87
Scale 103
Scale 7
Scale 39
Scale 135
Scale 199				Raga Nabhomani
Scale 327				Syptitonic
Scale 583				Aeritonic
Scale 1095				Phrythitonic
Scale 2119

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.