ideally) pure fifth would be beating more than eight times per second. Modern western ears easily tolerate fast beating in non-just intervals (seconds and sevenths, thirds and sixths), but not in perfect octaves or fifths. Happily for pianists, the string stretch that accommodates inharmonicity on a concert grand also nearly exactly mitigates the accumulation of dissonance in the perfect fifth. Other factors, physical and psychoacoustic, affect the tuner's ability to achieve a temperament. Among physical factors are inharmonic effects due to soundboard resonance in the bass strings, poorly manufactured strings, or peculiarities that can cause "false beats" (false because they are unrelated to the manipulation of beats during tuning). The principal psychoacoustic factor is that the human ear tends to perceive the higher notes as being flat when compared to those in the midrange. Stretching the tuning to account for string inharmonicity is often not sufficient to overcome this phenomenon, so piano tuners may stretch the top octave or so of the piano even more. Tools and methods Common tools for tuning pianos include the tuning lever or "hammer", a variety of mutes, and a tuning fork or electronic tuning device. The tuning lever is used to turn and 'set' the tuning pins, increasing or decreasing the tension of the string. Mutes are used to silence strings that are not being tuned. While tuning the temperament octave, a felt strip is typically placed within the temperament (middle) section of the piano; it is inserted between each note's trichord, muting its outer two strings so that only the middle string is free to vibrate. A Papps mute performs the same function in an upright piano and is placed through the piano action to mute either the 2 left strings (of a trichord), or the 2 right strings similarly. After the center strings are all tuned (or right if a Papps mute is used) the felt strip can be removed note by note, tuning the outer strings to the center strings. Wedge-shaped mutes are inserted between two strings to mute them, and the Papps mute is commonly used for tuning the high notes in upright pianos because it slides more easily between hammer shanks. In an aural tuning a tuning fork is used to tune the first note (generally A4) of the piano, and then a temperament octave is tuned between F3 and F4 using a variety of intervals and checks, until