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Large grand vs. small upright pianos:

Factors of timbral difference

Alexander Galembo galembo@ief.spb.su

Lola L. Cuddy

Dept. of Psychology, Queen's University,

Kingston, ON K7L 3N6 !n!"!

Popular version of paper 2p!a2

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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. goal of manufacturers of upright pianos is to bring the tone quality of the

upright piano closer to that of the grand piano tone.

!he shape of an upright, initially designed for home use, provides a "directionaldiscomfort" 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.

%rands have a &ey action that utili'es gravity to return parts to their initial position. In

uprights this function is e(ecuted by springs. )ey action is so important part of the

feedbac& from a piano that influences the pianist#s judgment about tone quality.

*ampers in grand pianos are more effective because they dampen the strings at the

same places where the hammers e(cite them. In upright pianos dampers are shifted and

therefore are not so effective. +owever, the acoustical consequences of dampening

processes in a piano, important for tone quality in melody, have not been investigated.

!he disposition of the soundboard is more rational in grand pianos than in uprights. In

grand pianos both sides of the soundboard are e(posed to the room well enough for

e(tensive sound radiation. In upright pianos, the soundboard is isolated from the room

by the cover plate, and is typically very close to a wall. !he result is a tone that sounds

soft and dull compared with that of a grand piano.

!wo instruments of similar appearance may have drastically different tone quality dueto different degrees of technological thoroughness. Usually grand piano technology

provides more detailed and accurate regulation of &ey action, finer voicing, use of better

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materials, and so forth. !hese technological differences are surely audible, and are

&nown to practical piano engineers.

Many acoustical privileges of a grand piano are due to its si'e relative to the

contemporary upright. Other advantages are connected to the hori'ontal disposition of

strings and the soundboard, which yields better conditions for tone radiation.

arger pianos generally have longer bass strings, a larger soundboard and a heavier iron

frame. !herefore larger pianos tend to have

$ louder tone and wider dynamic range-

$ less inharmonic spectrum of the radiated tone-

$ less "stretched" tuning of the bass section-

$ slower decay of high partials in bass tones-

$ wider spectrum brighter timbre/ of bass tones -

$ more regular spectrum of tones-

$ different character of treble tones.

In the last part of this paper, we discuss our investigations of the main acoustical

properties of a piano tone resulting from design factors. !hese properties are the

inharmonicity of spectral partials and the spectral envelope.

0chuc& and 1oung in 2345 were the first to measure the spectral inharmonicity in piano

tones. !hey found that the spectral partials in piano tones are progressively stretched

and hypothesi'ed that the lower inharmonicity of longer strings in the bass range

e(plains why musicians prefer grand piano tone quality over that of uprights.

6ineteen years later, +arvey 7letcher with collaborators found that the spectral

inharmonicity is important for tones to sound piano$li&e. !hey proposed that

inharmonicity is responsible for the "warmth" property common to real piano tones.

7letcher et al.#s statement about the importance of inharmonicity for timbre provided a

perceptual basis to the hypothesis of 0huc& and 1oung. 0ince then, e(perts 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. !he

influences of other acoustical or design factors have never been given serious

e(perimental consideration.

8e report two e(periments comparing the strength of the inharmonicity factor with that

of the spectral envelope in the timbre of piano$li&e tones. 9reviously, the importance ofinharmonicity for timbre was demonstrated by having listeners compare

multicomponent harmonic and inharmonic tones that were identical in quantity and

intensity of spectral partials. lthough these demonstrations appeared effective, they

overloo&ed one perceptually important covariant of inharmonicity, namely, the width of

the spectrum. s an illustration, the spectral width of a :;$component bass tone with

minimal inharmonicity will increase more than twice after inharmonicity is changed to

the ma(imal value. n increase of spectral width changes the energy balance between

high and low frequencies and influences the perceived brightness of the tone. !o

disambiguate the influence of inharmonicity and spectral width, we designed an

e(periment in which they did not covary.

8e synthesi'ed twelve

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inharmonicity. 7our levels of spectral width were combined with three levels of

inharmonicity. !he 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. !he synthesi'ed tone that

had minimal spectral width and minimal inharmonicity served as the standard tone. tones served as a test tone and was paired with the standard tone. !he

listener#s tas& was to scale the timbral difference between the tones of a tone pair.

?esults showed that the effect of the spectral width on ratings of timbral difference was

greater than the effect of inharmonicity.

In the second e(periment, we synthesi'ed an ; tone, 2 second long, whose spectrum

was the combination of the spectral envelope of the real tone of the small upright piano

224$cm high with the inharmonicity of a concert grand piano tone. 8e prepared tone

pairs consisting of different combinations of three tones$$the hybrid tone, an upright

prototype, and a grand prototype.

isteners were as&ed to scale the perceived timbral difference between the members of

each tone pair. ?esults suggested that the hybrid tone was significantly closer in timbre

to the upright prototype than to the grand prototype. !his finding means that the spectral

envelope had a stronger influence on perceived timbral difference than the

inharmonicity.

In the sound e(ample clic& +