tone is 12 Hz under ideal laboratory conditions. Tones between 4 and 16 Hz can be perceived via the body's sense of touch. Frequency resolution of the ear is about 3.6 Hz within the octave of That is, changes in pitch larger than 3.6 Hz can be perceived in a clinical setting. However, even smaller pitch differences can be perceived through other means. For example, the interference of two pitches can often be heard as a repetitive variation in volume of the tone. This amplitude modulation occurs with a frequency equal to the difference in frequencies of the two tones and is known as beating. The semitone scale used in Western musical notation is not a linear frequency scale but logarithmic. Other scales have been derived directly from experiments on human hearing perception, such as the mel scale and Bark scale (these are used in studying perception, but not usually in musical composition), and these are approximately logarithmic in frequency at the high-frequency end, but nearly linear at the low-frequency end. The intensity range of audible sounds is enormous. Human eardrums are sensitive to variations in the sound pressure, and can detect pressure changes from as small as a few micropascals (μPa) to greater than For this reason, sound pressure level is also measured logarithmically, with all pressures referenced to (or 1.97385×10−10 atm). The lower limit of audibility is therefore defined as but the upper limit is not as clearly defined. The upper limit is more a question of the limit where the ear will be physically harmed or with the potential to cause noise-induced hearing loss. A more rigorous exploration of the lower limits of audibility determines that the minimum threshold at which a sound can be heard is frequency dependent. By measuring this minimum intensity for testing tones of various frequencies, a frequency-dependent absolute threshold of hearing (ATH) curve may be derived. Typically, the ear shows a peak of sensitivity (i.e., its lowest ATH) between though the threshold changes with age, with older ears showing decreased sensitivity above 2 kHz. The ATH is the lowest of the equal-loudness contours. Equal-loudness contours indicate the sound pressure level (dB SPL), over the range of audible frequencies, that are perceived as being of equal loudness. Equal-loudness contours were first measured by Fletcher and Munson at Bell Labs in 1933 using pure tones reproduced via headphones, and the data they collected are