Careful observation of the amplified signal showed that envelope clipping was identical to the steady-state clipping level (Fig. 14). There were no glitches or other fast transient phenomena in the output signal.
SIGNIFICANCE OF MUSICAL HARMONICS
Having divided amplifiers into three groups of distortion characteristics, the next step is to determine how theharmonics relate to hearing. There is a close parallel here between electronic distortion and musical tone coloration that is the real key to why tubes and transistors sound different. Perhaps the most knowledgeable authorities in this area are the craftsman who build organs and musical instruments , . Through many years of careful experimentation these artisans have determined how various harmonics relate to the coloration of an instrument's tonal quality.
The primary color characteristic of an instrument is determined by the strength of the first few harmonics. Each of the lower harmonics produces its own characteristic effect when it is dominant or it can modify the effect of another dominant harmonic if it is prominent. In the simplest classification, the lower harmonics are divided into two tonal groups. The odd harmonics (third and fifth) produce a "stopped" or "covered" sound. The even harmonics (second, fourth, and sixth) produce "choral" or "singing" sounds.
The second and third harmonics are the most important from the viewpoint of the electronic distortion graphs in the previous section. Musically the second is an octave above the fundamental and is almost inaudible; yet it adds body to the sound, making it fuller. The third is termed quint or musical twelfth. It produces a sound many musicians refer to as "blanketed." Instead of making the tone fuller, a strong third actually gives the sound a metallic quality that gets annoying in character as its amplitude increases. A strong second with a strong third tends to open the "covered" effect. Adding the fourth and fifth to this changes the sound to an "open horn" like character.
The higher harmonics, above the seventh, give the tone "edge" or "bite." Provided the edge is balanced to the basic musical tone, it tends to reinforce the fundamental, giving the sound a sharp attack quality. Many of the edge harmonics are musically unrelated pitches such as the seventh, ninth, and eleventh. Therefore, too much edge can produce a raspy dissonant quality. Since the ear seems very sensitive to the edge harmonics, controlling their amplitude is of paramount importance. The previously mentioned study of the trumpet tone  shows that the edge effect is directly related to the loudness of the tone. Playing the same trumpet note loud or soft makes little difference in the amplitude of the fundamental and the lower harmonics. However, harmonics above the sixth increase and decrease in amplitude in almost direct proportion to the loudness. This edge balance is a critically important loudness signal for the human ear.
RELATIONSHIP OF FACTORS AND FINDINGS
The basic cause of the difference in tube and transistor sound is the weighting of harmonic distortion components in the amplifier's overload region. Transistor amplifiers exhibit a strong component of third harmonic distortion when driven into overload. This harmonic produces a "covered" sound, giving a recording a restricted quality. Alternatively a tube amplifier when overloaded generates a whole spectrum of harmonics. Particularly strong are the second, third, fourth, and fifth overtones, which give a full-bodies "brassy" quality to the sound. The further any amplifier is driven into saturation, the greater the amplitude of the higher harmonics like the seventh, eighth, ninth, etc. These add edge to the sound which the ear translates to loudness information. Overloading an operational amplifier produces such steeply rising edge harmonics that they become objectionable within a 5-dB range. Transistors extend this overload range to about 10 dB and tubes widen it to 20 dB or more. Using this basic analysis, the psychoacoustic characteristics stated in the beginning of this paper can be related to the electrical harmonic properties of each type of amplifier.
It was not part of the original intent of this paper to analyze operational amplifiers. However, the tests show that they fall into a distinct class of their own. Basically, operational amplifiers produce strong third, fifth and seventh harmonics when driven only a few dB into overload. The resultant sound is metallic with a very harsh edge which the ear hears as strong distortion. Since this sound is so objectionable, it acts as a clearly audible overload warning signal. Consequently, operational amplifiers are rarely operated in their saturation region. This results in a very cleanly amplified sound with little coloration and true dynamic range within the limitations of the amplifier. True dynamic range is not necessarily the determinant of good sound reproduction, however, since it is much greater than any disc or tape system presently available. Because of their characteristics, operational amplifiers produce only the top end of the dynamic range which contains all the transients but lacks the solid pitch information which the ear hears as music. When records of true dynamic range are played on a limited-range system, they sound very thin. This relates directly to the originally cited listener's comment that transistor records were very clean but sounded sibilant and cymbally.
The transistor characteristics which our subjects noted were the buzzing or white-noise sound and the lack of "punch." The buzz is of course directly related to the edge produced by overloading on transients. The guess that this is white noise is due to the fact that many of the edge harmonics like the seventh and ninth are not musically related to the fundamental. The ear hears these dissonant tones as a kind of noise accompanying every attack. The lack of punch is due to the strong third harmonic which is inaudibly "blanketing" the sound. This is correctable by using a large enough pad to prevent all peaks from reaching the amplifier's saturated region. But from a practical standpoint, there is no way of determining this on most consoles. Adding auxiliary peak indicators on the input preamplifiers could alleviate both these problems, and the sound would be very close to that of the operational amplifier in its linear region.
Vacuum-tube amplifiers differ from transistor and operational amplifiers because they can be operated in the overload region without adding objectionable distortion. The combination of the slow rising edge and the open harmonic structure of the overload characteristics form an almost ideal sound- recording compressor. Within the 15-20 dB "safe" overload range, the electrical output of the tube amplifier increases by only 2-4 dB, acting like a limiter. However, since the edge is increasing within this range, the subjective loudness remains uncompressed to the ear. This effect causes tube-amplified signals to have a high apparent level which is not indicated on a volume indicator (VU meter). Tubes sound louder and have a better signal-to-noise ratio because of this extra subjective head room that transistor amplifiers do not have. Tubes get punch from their naturally brassy overload characteristics. Since the loud signals can be recorded at higher levels, the softer signals are also louder, so they are not lost in tape hiss and they effectively give the tube sound greater clarity. The feeling of more bass response is directly related to the strong second and third harmonic components which reinforce the "natural" bass with "synthetic" bass . In the context of a limited dynamic range system like the phonograph, recordings made with vacuum-tube preamplifiers will have more apparent level and a greater signal to system noise ratio than recordings made with transistors or operational amplifiers.
The author wishes to thank Walter Sear and Peter Scheiber for innumerable helpful discussions on the musician's viewpoint of sound. He also wishes to thank John Olson of RCA and Steve Temmer of Gotham Audio for the loaning of amplifiers
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Russell O. Hamm received his engineering training at the University of New Hampshire. He worked for Vidcom Electronics and later the Fine Recording division of that company, designing and supervising the installation of their extensive 16-track recording facilities. While with Fine Recordings, Mr. Hamm did a great deal of experimentation in stereophonic and quadraphonic sound for records and motion pictures which, in conjunction with Peter Scheiber, formed the basis for the development of the present matrix-quad record. Mr. Hamm's record-producing and engineering credits include albums, commercials, and motion-picture sound tracks by many well-known artists. Mr. Hamm presently serves as a Consultant to Sear Sound Studios in New York and is constructing Ditanfra Studios in the Virgin Islands.