Among quite some number of proposed temperaments, as being the one applied by

J. S. Bach    for his   Well  Tempered  Clavier ,

it is highly probable that

the   Well  Tempered  Meantone    stands among the most plausible ones.

Within the   C–major   tonality, this   Well-Tempered Meantone   contains five fifths and three major thirds holding perfectly equal interval beating rates, when measured in a chromatic scale on   F   , the partition normally used for the initialization of the auditory tuning of a keyboard. This equality of beating rates allows quick and easy tuning of a keyboard.

The characteristics of all the fifths of this   Well-Tempered Meantone   are perfectly at par with those of the loops in the figure above, taken from a   Well-Tempered Clavier   score, handwritten by   J. S. Bach.

A video demonstration of the auditory tuning of this    Well-Tempered Meantone   is made on the website

https://www.youtube.com/watch?v=lwfESoMxd8Y

An explanatory text is available here.

The fifths circle, and the corresponding interval data are shown below.

Tuning Table (A3 = 220)
A3 = 220	Equal beating of 5 fifths and 3 major thirds
Partition F3 - F 4	Beats	Major Thirds	Beats
A4 - A3	0.00	F3 - A3	1.95
A3 - D4	1.95	Gb3 - Bb3	12.51
D4 - G3	-1.95	G3 - B3	1.95
G3 - C4	1.95	Ab3 - C4	12.32
C4 - F3	-1.17	A3 - C#4	8.27
F3 - F4	0.00	Bb3 - D4	5.84
F4 - Bb3	0.39	B3 - D#4	16.17
Bb3 - Eb4	-0.39	C4 - E4	1.95
Eb4 - Ab3	0.39	Db4 - F4	19.54
G#3 - C#4	0.00	F4 - A4	3.89
C#4 - F#3	0.00
F#3 - B3	0.00
B3 - E4	1.95
E4 - A3	-1.95
E4 - A4	-3.89

Broekaert Johan 2021-01-05   broekaert.devriendt (at) gmail.com