Russell O. Hamm paper

Engineers and musicians have long debated the question of tube sound versus transistor sound. Conventional methods of distortion measurements has shown that no significant difference exist. This paper, however, points out that amplifiers are often severely overloaded by signal transients (THD 30%). Under this condition there is a major difference in the harmonic distortion components of the amplified signal, with tubes, transistors and operational amplifiers separating into distinct groups.

PSYCHOACOUSTICS
Anyone who listens to phonograph records closely can tell that tubes sound different from transistors. Defining what this difference is, however, a complex psychoacoustical problem.
Psychoacoustically, musicians make more objective subjects than engineers. While their terms may not be expressed in standard units, the musicians "by ear" measuring technique seems quite valid.
"Tube records have more bass... The bass actually sounds an octave lower," says one rock guitarist. A couple of studio players have pointed out on numerous occasions that the middle range of tube records is very clear, each instrument has presense. Transistor recordings tend to emphasize the sibilants and cymbals.
"With tubes there is a space between the instruments even when they play loud... transistors make a lot of buzzing." Two people commented that transistors added a lot of musically unrelated harmonics or white noise, especially on attack transients. This same phenomenon was expressed by another person as a "shattered glass" sound that restricted the dynamics. It was generally agreed that tubes did not have this problem because they overload gently.

DISTORTION CHARACTERISTICS OF PREAMPLIFIERS
To get a general representation of the character of harmonic distortion in audio amplifiers, overload curves were plotted for about fifty different circuits. The tube circuits used the popular 12AY7 and 12AX7 triodes, the 8628 and 7586 triode nuvistors, and the 5879 pentode. The 2N3391A, 2N5089 and 2N3117 silicon NPN transistors were chosen. Operational amplifiers included the 709 and LM301 and two commercially available hybrid designs.
The devices are all operating open loop (no feedback) with a bias point which allows for maximum undistorted output swing for one set of test. Another set of test were run with feedback at 40db gain. Both test used 1% total harmonic distortion as a reference. Then test were made 12db into overload from the 1% THD reference. Every harmonic to the seventh was plotted.
The resulting plots divided amplifiers into three distinct categories.

1. TUBE CHARACTERISTICS
For a typical two-stage 12AY7 amplifier, the outstanding characteristic is the dominance of the second harmonic followed closely by the third. The fifth, sixth and seventh remain below 5% out to the 12-db overload point. These curves seem to be a general characteristic of all triode amplifiers tested, single ended or push-pull. The distortion components for a two stage single ended pentode amplifier shows the third harmonic is dominant and the second rises about 3 db later with the same slope. Both the fourth and fifth are prominent while the sixth and seventh remain under 5%.
The major characteristic of the tube amplifier is the presence of strong second and third harmonics, sometimes in concert with the fourth and fifth, but always much greater in amplitude.

2. TRANSISTOR CHARACTERISTICS
The distinguishing feature is the strong third harmonic component. All other harmonics are present, but at a much lower amplitude than the third. When the overload reaches a break point, all the higher harmonics begin to rise simultaneously. This point is generally within 3-6 db of the 1% third harmonic point.

3. OPERATIONAL-AMPLIFIER CHARACTERISTICS
The third harmonic rises steeply as the dominant distortion component in a characteristic similar to the transistor. Also rising very strongly from the same point are the fifth and seventh harmonics. All even harmonics are suppressed completely.
RELATIONS OF FACTORS AND FINDINGS
The basic cause of the difference in tube and transistor sound is the weighting of harmonic distortion components in the amplifiers overload region. Transistor amplifiers exhibit a strong component of third harmonic distortion when driven into overload. This harmonic produces a "covered" sound, giving the 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-bodied "brassy" quality to the sound.
The further any amplifier is driven into saturation, the greater the amplitude of the higher harmonics. 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 odjectional within a 5db range. Transistors extend this overload range to about 10db and tubes widen it 20db or more. Using this basic analysis, the psychoacoustic characteristics stated in the begining of this paper can be related to the electrical harmonic properties of each type of amplifier.
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 objectional, it acts as a clearly audible overload warning signal.
The transistor characteristics which our subjects noted were buzzing or white noise sound and the lack of "punch". The buzz of course is 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.
Vacuum tube amplifiers differ from transistor and operational amplifiers because they can be operated in the overload region without adding objectional 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.
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.

SIGNIFICANCE OF MUSICAL HARMONICS
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. Musically the second is an octave above the fundamental and is almost inaudible; yet it adds body to the sound, making it sound fuller.
The third is termed a quint or musical twelfth. It produces a sound many musicians refer to as "blanketed". Instead of making the tone fuller, a strong third actually makes the tone softer.
Adding a fifth to a strong third 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 the 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 paramont importance.