¹ See P. K. Potter, G. A. Kopp, and H. Green, Visible speech 65–269 (New York, 1947); R. K. Potter and G. E. Peterson, The representation of vowels and their movements, Journal of the Acoustical Society of America 20.528–35 (1948).

² Cf. Potter and Peterson, op.cit. (fn. 1).

³ See W. Koenig, H. K. Dunn, and L. Y. Lacy, The sound spectrograph, Jour. Ac. Soc. Am. 17.19–49 (1946); IVI. Joos, Acoustic phonetics, Index s.v. spectrogram (Lang. Monogr. No. 23; 1948).

⁴ See L. G. Kerste, Amplitude cross-section representation with the sound spectrograph, Jour. Ac. Soc. Am. 20.796–801 (1948).

The amplitude sections shown in Fig. 1 were made with a 45-cycle analyzing filter. Zero frequency is shown by the long line at the top of each of the four sections, and the frequency and amplitude scales are placed along the sides. The first section is taken from the beginning of the [i] and shows the evenly spaced harmonics of the voiced sound. The second section is taken from the [s] and shows the irregular spectrum of the fricative sound. The third section is taken from the explosion of the [t], the fourth from the [r].

⁵ Cf. C. Van Riper, Speech correction: Principles and methods (New York, 1939).

⁶ B. Bloch, Studies in colloquial Japanese IV: Phonemics, Lg. 26.88–97 (1950).

⁷ See R. West, L. Kennedy, and A. Carr, The rehabilitation of speech (New York, 1937).

⁸ On the terms ‘fundamental pitch’ and ‘loudness’ see Proposed American standard acoustical terminology 21, 22 (published by the American Standards Association, New-York, 1949).

⁹ C. W. Morris, Foundations of the theory of signs (International encyclopedia of unified science, Vol. 1, No. 2; Chicago, 1938).

¹⁰ The term ‘speech’ is employed here as defined by B. Bloch, A set of postulates for phonemic analysis, Lg. 24.7 (1948).

¹¹ M. Joos, Acoustic phonetics (Lang. Monogr. No. 23; 1948).

¹² Bloch, op.cit. (fnn. 6 and 10); K. L. Pike, Tone languages (Ann Arbor, Mich., 1948).

¹³ P. W. Bridgman, The nature of physical theory 5–15 (Princeton, 1936).

¹⁴ See S. S. Stevens, On the theory of scales of measurement, Science 103.677–80 (1946); J. M. Cowan and B. Bloch, An experimental study of pause in English grammar, American Speech 23.89–99 (1948).

¹⁵ T. Chiba and M. Kajiyama, The vowel: Its nature and structure 174–226 (Tokyo, 1941).

¹⁶ W. Pitts and W. S. McCulloch, How we know universale: The perception of auditory and visual forms, Bulletin of mathematical biophysics 9.127–47 (1947).

¹⁷ The non-linearity of the ear is illustrated by the fact that equal increments in the intensity of a tone do not always correspond to equal increments in its loudness. A transformation in the signal occurs when the wave motion within the cochlea is converted to the form of nerve impulses.

¹⁸ See G. O. Russell, Speech and voice (New York, 1931); C. E. Parmenter and S. N. Treviño, Vowel perceptions as shown by X-ray, Quarterly journal of speech 18.351–69 (1932); F. J. Carmody, X-ray studies of speech articulation (Univ. Cal. Publ. in Modern Philology, Vol. 20, No. 4; 1937).

¹⁹ H. K. Dunn, The calculation of vowel resonance and an electrical vocal tract, Jour. Ac. Soc. Am. 22.740–53 (1950).

²⁰ P. Delattre, Un triangle acoustique des voyelles orales du français, French Review 21.477–84 (1948).

²¹ S. S. Stevens and J. Volkman, The relation of pitch to frequency: A revised scale, American journal of psychology 53.329–53 (1940).

A mel is defined as the psycho-physical unit of pitch. A pitch scale may be derived from estimates of the relative height of tones. The unit is arbitrarily chosen such that a frequency of 1000 cps at 40 decibels above normal threshold has a pitch of 1000 mels.

²² For instance as shown in P. Passy and D. Jones, The principles of the IPA (Supplement to Le maître phonétique for September-October 1912).