In the extreme upper tones, the musical ear of the tuner is tried to the utmost.  Here, his judgment of correct harmonic relation is the principal or only guide, while in the middle octaves the beats serve him so faithfully, his musical qualifications being brought into requisition only as a rough guide in determining pitch of the various intervals.  To tune by the beats requires a sharp ear and mental discernment; to tune by pitch requires a fine musical ear and knowledge of the simpler laws of harmony.

As stated above, the tuner will fail in many cases to tune his high octaves sharp enough.  Rarely, if ever, will a tuner with a good ear leave the upper tones too sharp.  Now, there is one more fact which is of the utmost importance in tuning the treble:  it is the fact that the extreme upper octave and a half must be tuned slightly sharper than perfect; if the octaves are tuned perfect, the upper tones of the instrument will sound flat when used in scale and arpeggio passages covering a large portion of the key-board.  Begin to sharpen your octaves slightly from about the seventeenth key from the last; counting both black and white.  In other words, begin to sharpen from the last A[b] but one, in the standard scale of seven and a third octaves of which the last key is C. Sharpen but slightly, and increase the degree of sharpening but little as you proceed.

Tuning the Bass.—­In tuning the bass, listen for the beats only, in bringing up the octaves.  It is sometimes well to try the string tuned, with its fifth, but the octave in the bass should suffice, as the vibrations are so much slower here that if you listen acutely the octave beats will guide you.

It is not necessary to pull the strings higher than the pitch at which they are to stand.  Learn to pull them up gradually and in a way that will “render” the string over the bridges, which is an easy thing to do, the strings being so much heavier here than elsewhere.  Never leave a bass string the slightest amount too sharp.  As flatness is so obnoxious in the treble, just so is sharpness in the bass, so if there must be any variation in any bass tone let it be flat; but aim at perfect octaves throughout the bass.

False Waves.—­We say “false waves” for want of a better name.  You will find a string occasionally that will give forth waves or beats so similar to the real ones that it takes a practiced ear to distinguish the difference.  Where a unison contains a string of this kind, select some other string by which to tune the interval, and leave the bad string until the last; you may then find difficulty in being able to tell when you have it in unison.  The cause may be a twisted string, a fault in the string by imperfect drawing of the wire, or in the construction of the sound-board.

In the low bass tones, a kind of false waves are always present, and will annoy the tuner long after he has been in regular practice.  They are, however, of a different nature from the true waves in that they are of a metallic timbre and of much greater rapidity than the latter.  Close attention will generally enable the tuner to distinguish between them.  They are caused by what is known as “harmonics” or “over-tones”; the string vibrating in fractional segments.