Meantone and well-tempering gradually evolved into the modern Equal Temperament, and
just as with the earlier system, there was a proliferation of methods and
schools, with a very conservative rate of progress.
The Yamaha or Japanese style adopted by the Sydney Conservatorium was developed in
a research setting, unconstricted by loyalties and traditions. The academics who
developed it looked at as many traditions as they could and developed the method
using the best practices as the basis.
The Design of the temperament has these goals: Accuracy, Stability
and Speed. They are inter-related. As an example, if a piano can
be completely tuned in less than an hour, starting with the
temperament in the middle and tuning to the top and then from the
temperament towards the low end, then it can be expected to be stable.
This is because the iron-frame and cabinet take some time to react to
the change in stress. The bass strings are positioned at an angle, with
the lower part of the strings more towards the middle of the piano than
the top part. Putting extra tension on the bass end can make the top
end increase in tension by way of a see-saw effect centred aroung the
A temperament obviously encompasses an octave. Any more than
one octave introduces uncertainty, unnecessary retuning within the procedure,
- On many pianos, the tenor strings change from
plain-wire to copper-wound in the low tenor, and a large
number make this change at F33, with E being the last
copper-wound string. Copper-wound strings have a lower
inharmonicity, and including a wound string in the
temperament complicates tuning tht temperament.
For this reason the temperament is set between F33 and F45. This
octave is in the most audible range, centred around middle C. The
beat speeds are easy to count here.
If the temperament area were shifted down a semitone or two, the beat speeds to be
counted would be slower and would take more time to judge. Similarly, taking the
temperament area up would mean that more notes would be in the uncountable area, and
in the same area (above F45) the inharmonicity increases making for uncertainty.
- In general, strings increase in inharmonicity from the
notes upwards. There is often a slight bump in the inharmonicity curve
at the lowest notes of the bass, where the strings are thicker due to the
compromise in string length, and there is a similar slight rise in the
low tenor for the same reason.
Tuning the temperament in this octave just above the low tenor
allows for a smooth rise in pitch, and even if the
lowest note or two do increase in inharmonicity, the
pitch-curve of the higher partials will be smooth, making
it possible to have a neat tuning curve across the
- By fortunate coincidence, when starting on A37 the
first interval tuned is a fourth above, D42s, and the beat
speed for A-D is 1 per second. The first third chord which
is checked is F33-A37, and the beat speed here is exactly 7
beats per second. (This is all at A=440hz). Other tuning
methods starting on C or F do not have such a neat
reference so near the beginning of the process.
- Historically discussion of Equal Temperament referred
to a "flattening of the fifth" as the characteristic, the
fifth interval being seen as important. In practice, the
inversion — sharpening of the fourth, is faster to
achieve. Hammer/pin technique requires each tuning event to
involve taking the string over the intended pitch, and
striking the key hard enough to force the string down to
the intended position. This is known as setting the
pins. So if you are intending to hear 1 beat per
second pull the D up so that (for instance), there are
2bps. It will take no more than 1 second to hear the two
beats, possibly less. Then after the hard blow on the key,
it will take no more than a second to recognise 1 beat.
Going the other way, dropping a fifth from, say, zero
beats down to 1bps, might involve 2 to 3 seconds listening
to ascertain that the interval is beatless, another 2 or 3
to hear that there is only, say, 1 beat every 2 seconds, and
finally 1 second to hear the intended speed of 1bps.
Obviously not the way to do it.