Tune: A37 to a Tuning Fork.
Test: F33 - A37 = F33 - Fork
Note—i. The two notes used are within the temperament octave. F33 may be adjusted to beat 6 or 7 times a second to be within the usual speed range, before being properly tuned as a fifth from C40. (Using F21 as in the RP tuning school, is a last resort if F33 has a defect).
Note—ii. The third F33-A37 will beat faster than the seventeenth F21-A49, allowing for an easier assessment of the speed.
Note—iii. Although the tuning fork's fundamental frequency is A-440, its second harmonic vibrates at 880 cycles, and this is the harmonic which is aligned with the 4th harmonic in A37 when F33 is used to provide the interference.
Tune: A37 → D42 . Count 7 in 7 seconds, with saying 'nought' or 'bang' on impact. This gets the mind ready to find 'one' 'two' etc., in the chaos of interfering sounds.
Test: If F33 has been roughly set, compare F33-A37 and F33-D42. Play the third until you have counted 7 (with the count of one being on impact) and play the sixth for the same time, checking that it is almost 1 beat faster.
Note—i. If the complete cycle of fourths is tuned to the theoretical speeds, inharmonicity will force them to be sharp. If you play the A-D chord and count 1 at the start, and count up to 7 in 7 seconds, the beats will be slower than one a second by 1/7.
Tune: D42 → G35. Count 4.5 beats per 7 seconds, starting with 'nought' on impact.
Note—. Because of inharmonicity, on most pianos you may have to compromise this speed, perhaps down to 2 beats in 7 seconds. or occasionally to a point where no beat in heard.
You can check that G is on the sharp side of D by listening to the tenth A#26—D42 and the sixth A#26—G35. This is not part of the orthodox temperament method, but is a handy check if A#26 is not too far from pitch. The sixth should beat slightly faster than the tenth.