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I have explored a bit in the newsgroups section of google. One =
discussion about stretching and orchestras contained a link to =
http://www.mmk.ei.tum.de/persons/ter/top/scalestretch.html -- a German =
site -- where an erudite explanation of how piano inharmonicity creates =
the need for stretching is followed by the following remarks. They are =
worth the lengthy read, and wind up arguing (in different words) that =
the appropriate stretch at the extreme treble is somewhere about 50 =
cents:
So, on first sight - and if the above explanation were the whole story - =
it would appear that - what intonation is concerened - the piano were =
exceptional among the musical instruments. However, it turns out that =
stretching of the tone scale is very common in musical performance. Solo =
instruments such as the wind and string families, as well as singers, =
tend to play sharp in the high pitch region. And in the orchestra the =
bass string players are often advised to avoid tuning their instruments =
sharp but instead rather to tune slightly flat. These tendencies are =
clearly visible in the results of statistical frequency measurements on =
solo performances by expert players on the violin, flute, and oboe =
(Fransson et al. 1970a). Although these instruments produce truly =
harmonic complex tones, a stretch of the tone scale was found that =
resembles that of the piano - with the only exception that even the =
middle octaves were not unstretched. So, in fact, the aforementioned =
non-stretched keyboard instruments (the organs) turn out to be the =
exception rather than the rule.=20
The explanation for the universal tendency to stretch the musical scale =
emerges from taking pitch perception into account. Naturally, in =
evaluating musical intervals by ear, it is primarily the pitch that =
communicates the necessary information to the cognitive auditory system. =
The fine intonation produced on violins, flutes, oboes, clarinets, =
trumpets, etc. is controlled by ear, i.e. in terms of pitches and pitch =
intervals in comparison to memorised templates. So it must be concluded =
that it is the internal standard pitch scale of a musician and listener =
that on the average is stretched. This has been documented by Ward =
(1954a) in a most direct manner, namely, by having absolute-pitch =
possessors adjust (on an electronic oscillator) each and every tone of =
the scale without any reference. The result indeed was a stretched tone =
scale. For the octave interval it is particularly easy and safe to =
verify that the corresponding internal pitch template indeed is =
stretched, and this does not require the faculty of absolute pitch. As =
the phenomenon of octave stretch practically is sufficient to enforce =
stretch of the entire tone scale, one may say that scale stretch is =
explained by octave stretch. And the psychophysical explanation of =
octave stretch in turn is included in the theory of virtual pitch [16] , =
[17], [18] , [22] , [38], [55], [56].
In summary, one may say that it is primarily the stretch of the internal =
pitch scale of the auditory system that is responsible for the =
universally observed tendency to stretch the musical tone scale. That =
tendency indeed is so pronounced that even solo instruments such as =
flutes and clarinets are built in such a way that they even without =
corrections by the player produce a stretched scale (cf. Meyer 1961a, =
1969a, Coltman 1990a, Nederveen 1973a). This does not disprove the above =
primary explanation of the piano's scale stretch. Rather, the role of =
the piano among the other musical instruments is elucidated. The =
inharmonicity of piano strings which as such enforces stretched tuning =
turns out to be beneficial, as it enables reconciliation of two =
phenomenomena that with truly harmonic complex tones can hardly be =
reconciled: The preference of the ear for stretched successive pitch =
intervals on the one hand, and the occurrence of beats from the =
simultaneous sounding of simultaneous tones in stretched intonation, on =
the other. It is only the piano on which you can have both stretched and =
beat-free octaves.=20
These considerations further suggest that there cannot even =
theoretically exist such a thing as an optimal fixed intonation. As the =
occurrence of, and the disturbance by, beats depends on the complexity =
of the musical sound in every instant, and as the fine tuning of pitch =
and pitch intervals are subject to pitch shift effects which as well =
depend on the sound's degree of complexity, fine intonation must adapt =
to the sounds performed, i.e., it must be temporally variable [26] , =
[80] .
With a special tunable electronic organ we have performed listening =
tests on musical examples with normal, stretched, and even contracted =
intonation [28]. As a result it turned out that the preferred kind and =
amount of stretch depends on the type of music excerpt presented (solo =
melody vs. melody plus accompaniment vs. complex polyphonic sounds). =
This can be regarded as an experimental verification of the above =
conclusions.
On an electronic organ (which, as mentioned above, is ordinarily tuned =
in an unstretched tempered intonation) the ear's preference of stretched =
intonation can readily be demonstrated, as follows. Play a melody in a =
high-pitched register, accompanied by a simple bass-tone sequence in a =
low-pitched register, such that melody and accompaniment are several =
octaves apart. Evaluate by ear how well the accompaniment's intonation =
corresponds to that of the high-pitched melody (and vice versa). You =
will probably notice that the melody appears somewhat flat relative to =
the accompaniment although it is "mathematically correct". Now play the =
melody in a key one semitone sharp relative to the accompaniment. You =
may notice that this kind of "intonation", which corresponds to an =
oversized stretch of 6%, still is almost acceptable. To verify that this =
is not due to a failure of your auditory evaluation capabilities, do the =
same experiment with playing the melody one semitone flat. This will =
appear totally inacceptable - at least within the standards of =
conventional tonal music. From what was said about the intonation of the =
piano and about the size of octave stretch, one would predict that a =
strech of about 3% should be optimal for the above type of music sample. =
So, relative to aurally optimal intonation, the +1-semitone stretch is =
sharp by about the same amount as unstretched intonation is flat. =
Through many years I have played the above example to audiences of =
scientists, and of my students. When asked to rank the above three =
intonations in terms of acceptability, 60% of the listeners voted for =
[1) unstretched; 2) 1 ST stretch; 3) 1 ST contraction]. Fourty percent =
of the listeners voted for [1) 1 ST stretch; 2) unstretched; 3) 1 ST =
contraction]. All listeners pointed out that 1 ST contraction was =
totally inacceptable. This result fits well into the above =
consideration, i.e., that a stretch of about 3% would have been optimal =
(cf. the CD attached to [104]).
Cordially
|| ||| || ||| || ||| || ||| || ||| || ||| || ||| || |||
jason kanter . piano tuning/regulation/repair
bellevue, wa . 425 562 4127 . cell 425 831 1561
orcas island . 360 376 2799
[see historic temperaments at www.rollingball.com]
----- Original Message -----=20
From: Isaac OLEG=20
To: Pianotech=20
Sent: Monday, August 02, 2004 2:42 PM
Subject: RE: Re: a violonist trained ear (was tuning for violinist)]
Hello,
A common idea is that higher or larger stretch, may be more musically =
forgiving that what tend to follow the natural justness of the =
instrument.
IMHO, this is because the extra stretch is adding a new temperament or =
justness method, and that fraud the ear, that instinctively tend to =
agree with the pitches as being good.
A concert tuners told me once that if a note is too low it will be =
more easily noticed that if it is too high.
Adding that to the acoustic effect of the room, that ask for higher =
treble, and it is understandable that highly stretched tunings are =
rarely problematic.
What I've find is that they are less good for all close harmony music, =
and I like to avoid the kind of "straightness" that I feel is induced =
with high stretch.
But seems evident to me that it is easier to open the tuning a lot, =
depending of the room and the instrument, as we listen for a tone that =
is reflected by the room's acoustic.
Violinist like to play the high treble really high, but when they play =
with the piano they correct themselves, because they understand the =
features of the instrument.
That is easier for them to correct their justness than for the piano =
tuner to try to meet the violin high treble I think.
Best regards.
Isaac OLEG
-----Message d'origine-----
De : pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]De la =
part de hubert liverman
Envoy=E9 : lundi 2 ao=FBt 2004 22:44
=C0 : Pianotech
Objet : Re: Re: a violonist trained ear (was tuning for violonist)]
I was trained as a bass trombonist.I attended Auburn =
University,Manhattan School of Music and Columbia University. I have =
played everything from Symphony to Cercus. That is the lot of a free =
lance musician.Trombonists need to play 'pure' 3rds,4ths =
5ths,unisons,and octaves. Then we adjust it on the fly, dependant on the =
key, type of ensemble, era, and style of music being performed. The =
Beethoven Three Equali is an example. Things get tougher, as in Bhrams =
1'st Symphony (in C major) when we sit around for 35 minutes or so and =
come in pianissimo on a chorale in A major. It is difficult for the 2nd =
trombone to play the 3rd of the chord in tune on that very exposed =
entrance. When you add a piano to the mix, as in a piano Concerto, the =
strech factor comes into play and we must learn to adjust. Especially =
the lower parts, we have to think low to what we hear natrually (?). I =
have known many excellent musicians of all ilk who stumble over the =
"comma", and confuse themselves. Jazz and commercial musicians are more =
forgiving than some of the classical types in regards to Piano verses =
the rest of the "Band". This discussion has been going on for 2500 some =
odd years and will continue forever.
Hubert Liverman
Opelika, AL
Interesting enough, slide trombone players tend to like and favor =
pure thirds when performing in trombone ensembles. Beethoven's trombone =
trio, one of his first compositions, performed at his funeral, gives a =
very nice exemple of this. It requires something like "just intonation", =
pure thirds and pure fifths, so that the players have to adapt and =
correct their pitch constantly, depending on the harmonic function of =
the interval they play. When performed by great trombone players, it =
sounds magnificent. Anybody ever got complaints about the beating major =
3rds on a trombone player's piano ? :-)=20
Of course this is my experience as a music-loving amateur, and =
deductions I make from my not-very-exhaustive knowledge of those =
instruments and the temperament theory. Any thoughts ? =20
Jean Debefve,
Belgium =20
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