Popular version of paper 2pMUa2
Presented Tuesday afternoon, December 2, 1997
134th ASA Meeting, San Diego, CA
Embargoed until December 2, 1997
Upright pianos, even those of high quality, are not considered by pianists to be instruments of professional quality. Many factors, some previously investigated and others of potential interest, may be responsible for this judgment. In this paper, we list both design factors and acoustical properties resulting from design factors. Our interest in acoustical differences between large grands and small uprights is both academic and practical. A goal of manufacturers of upright pianos is to bring the tone quality of the upright piano closer to that of the grand piano tone.
The shape of an upright, initially designed for home use, provides a "directional discomfort" on the concert stage. It is impossible, at the same time, for the pianist to see the conductor, for the audience to see the pianist, and for the sound to be radiated effectively to the audience. Moreover, upright pianos don't have una-corda and sostenuto pedals, required by the piano literature.
Grands have a key action that utilizes gravity to return parts to their initial position. In uprights this function is executed by springs. Key action is so important part of the feedback from a piano that influences the pianist's judgment about tone quality.
Dampers in grand pianos are more effective because they dampen the strings at the same places where the hammers excite them. In upright pianos dampers are shifted and therefore are not so effective. However, the acoustical consequences of dampening processes in a piano, important for tone quality in melody, have not been investigated.
The disposition of the soundboard is more rational in grand pianos than in uprights. In grand pianos both sides of the soundboard are exposed to the room well enough for extensive sound radiation. In upright pianos, the soundboard is isolated from the room by the cover plate, and is typically very close to a wall. The result is a tone that sounds soft and dull compared with that of a grand piano.
Two instruments of similar appearance may have drastically different tone quality due to different degrees of technological thoroughness. Usually grand piano technology provides more detailed and accurate regulation of key action, finer voicing, use of better materials, and so forth. These technological differences are surely audible, and are known to practical piano engineers.
Many acoustical privileges of a grand piano are due to its size relative to the contemporary upright. Other advantages are connected to the horizontal disposition of strings and the soundboard, which yields better conditions for tone radiation.
Larger pianos generally have longer bass strings, a larger soundboard and a heavier iron frame. Therefore larger pianos tend to have:
Schuck and Young in 1943 were the first to measure the spectral inharmonicity in piano tones. They found that the spectral partials in piano tones are progressively stretched and hypothesized that the lower inharmonicity of longer strings in the bass range explains why musicians prefer grand piano tone quality over that of uprights.
Nineteen years later, Harvey Fletcher with collaborators found that the spectral inharmonicity is important for tones to sound piano-like. They proposed that inharmonicity is responsible for the "warmth" property common to real piano tones.
Fletcher et al.'s statement about the importance of inharmonicity for timbre provided a perceptual basis to the hypothesis of Shuck and Young. Since then, experts have commonly attributed the primary difference in the quality of bass tones in small vs. large pianos to the difference in the inharmonicity between short and long strings. The influences of other acoustical or design factors have never been given serious experimental consideration.
We report two experiments comparing the strength of the inharmonicity factor with that of the spectral envelope in the timbre of piano-like tones. Previously, the importance of inharmonicity for timbre was demonstrated by having listeners compare multicomponent harmonic and inharmonic tones that were identical in quantity and intensity of spectral partials. Although these demonstrations appeared effective, they overlooked one perceptually important covariant of inharmonicity, namely, the width of the spectrum. As an illustration, the spectral width of a 50-component bass tone with minimal inharmonicity will increase more than twice after inharmonicity is changed to the maximal value. An increase of spectral width changes the energy balance between high and low frequencies and influences the perceived brightness of the tone. To disambiguate the influence of inharmonicity and spectral width, we designed an experiment in which they did not covary.
We synthesized twelve E1 piano-like tones differing by both spectral width and inharmonicity. Four levels of spectral width were combined with three levels of inharmonicity. The number of partials and the steps between ascending values of spectral width were chosen to obtain the same difference in spectral width produced in two ways: by changing inharmonicity without changing number of partials, and by changing number of partials without changing inharmonicity. The synthesized tone that had minimal spectral width and minimal inharmonicity served as the standard tone. Each of the 12 tones served as a test tone and was paired with the standard tone. The listener's task was to scale the timbral difference between the tones of a tone pair. Results showed that the effect of the spectral width on ratings of timbral difference was greater than the effect of inharmonicity.
In the second experiment, we synthesized an A0 tone, 1 second long, whose spectrum was the combination of the spectral envelope of the real tone of the small upright piano 114-cm high with the inharmonicity of a concert grand piano tone. We prepared tone pairs consisting of different combinations of three tones--the hybrid tone, an upright prototype, and a grand prototype.
Listeners were asked to scale the perceived timbral difference between
the members of each tone pair. Results suggested that the hybrid tone was
significantly closer in timbre to the upright prototype than to the grand
prototype. This finding means that the spectral envelope had a stronger
influence on perceived timbral difference than the inharmonicity. 
In the sound example HERE , the first tone is the upright prototype, the second tone is the hybrid tone, and the third tone is the grand prototype.
We can conclude that to improve the sound quality of small upright pianos, the spectral envelope parameters, particularly spectral width and spectral irregularity, are of great importance.
This conclusion does not mean however, that inharmonicity is irrelevant. Support for the importance of inharmonicity is reflected in our synthesis of a hybrid tone with the spectral envelope of a grand piano tone and the inharmonicity of the upright tone. The presence of strong inharmonicity in the hybrid makes it impossible to produce an acceptable imitation of the grand piano tone. The plausible explanation here is that when detractions from tone quality related to the spectral envelope are minimal, the influence of inharmonicity becomes audible and hence important.
" There are many ways to make matters worse
but very few to improve "