Piano Tuning Methods
Tuning the Treble
There are different approaches to treble tuning. Some tuners stretch the top 2 octaves more than others. A 4:1 octave is one way of tuning those octaves. That type octave gives some brightness without distracting beats. A 2:1 octave sounds in tune when playing single octaves, but with double octaves the top note could sound flat to some. The flatness is very noticeable when striking a note 2 octaves down by itself and then hitting the top note. There is a tendency for the human ear to hear the top note lower than when playing octaves.
Tuning the Bass
There are some special challenges in tuning this section of the piano. Since all the beats that a tuner listens to are occurring at a slower rate then in the midrange and the treble, one has to take some additional time. Otherwise unisons can be left out of tune. Unisons are the strings that make up a note; there can be 1, 2 or 3 strings per note in the bass. The challenge is in getting the 2 and 3 string bass unisons in tune with each other. As in the treble there are different ways to tune bass octaves. In order to tell which approach works best in the bass, I play 3 octaves at the same time using both hands of course. I try to get the best blend of the various partials.
Creating a stable tuning is an art which takes years to achieve. It comes from skill in using the tuning hammer or lever and also in how the key is struck. I tend to strike the key with a hard blow rather than a light one.
Tuning the Temperament
I tune with equal temperament on many verticals and on some smaller grands where the scaling calls for that. If someone is using a piano along with a keyboard, it is best to use the same temperament as used on the electronic device which in that case would be equal temperament.
I also use a slightly modified equal temperament on many grand pianos and on some verticals. I call it the vibrato temperament. It calms down the keys of F,G and C and some others. The major 3rds that comprise those keys are then more within the normal range of vibrato (in octave 3 and lower octave 4) as heard with most singers and some instruments. There are no wolf tones in any keys. The trade off is that some keys will beat faster than in equal temperament, but that works out well with keys such as F# major.
Temperaments are kind of like fonts in word processing. You can design your own font and then apply the same characteristics to all the letters of the alphabet or you select fonts that someone else designed. The same applies to temperaments except that a temperament is determined by 12 notes and then they are extended out by octaves to the rest of the keyboard.