<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD><TITLE></TITLE> <META http-equiv=Content-Type = content=text/html;charset=ISO-8859-1> <META content="MSHTML 6.00.2800.1458" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY text=#000000 bgColor=#ccccff> <DIV><FONT face=Verdana size=2>I have explored a bit in the = newsgroups section of google. One discussion about stretching and orchestras contained a = link to <A href="http://www.mmk.ei.tum.de/persons/ter/top/scalestretch.html">http:= //www.mmk.ei.tum.de/persons/ter/top/scalestretch.html</A> -- 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:</FONT></DIV> <DIV><FONT face=Verdana size=2></FONT> </DIV> <DIV> <P>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 (<A href="http://www.mmk.ei.tum.de/persons/ter/ref/Fransson+1970a.html">Fra= nsson et al. 1970a</A>). 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 <I>not</I> = unstretched. So, in fact, the aforementioned non-stretched keyboard instruments (the = organs) turn out to be the exception rather than the rule. </P> <P>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 <A href="http://www.mmk.ei.tum.de/persons/ter/ref/Ward1954a.html">Ward = (1954a)</A> 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 = <EM>octave</EM> interval it is particularly easy and safe to verify that the = corresponding internal pitch template indeed is <A href="http://www.mmk.ei.tum.de/persons/ter/top/octstretch.html">stretch= ed</A>, and this does not require the faculty of <A href="http://www.mmk.ei.tum.de/persons/ter/top/absolute.html">absolute = pitch</A>. 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 <A href="http://www.mmk.ei.tum.de/persons/ter/top/virtualp.html">virtual = pitch</A> <A href="http://www.mmk.ei.tum.de/persons/ter/ab/016.html">[16]</A> , = <A href="http://www.mmk.ei.tum.de/persons/ter/ab/017.html">[17]</A>, <A href="http://www.mmk.ei.tum.de/persons/ter/ab/018.html">[18]</A> , <A href="http://www.mmk.ei.tum.de/persons/ter/ab/022.html">[22]</A> , <A href="http://www.mmk.ei.tum.de/persons/ter/ab/038.html">[38]</A>, <A href="http://www.mmk.ei.tum.de/persons/ter/ab/055.html">[55]</A>, <A href="http://www.mmk.ei.tum.de/persons/ter/ab/056.html">[56]</A>.</P> <P>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. <A href="http://www.mmk.ei.tum.de/persons/ter/ref/Meyer1961a.html">Meyer = 1961a</A>, <A = href="http://www.mmk.ei.tum.de/persons/ter/ref/Meyer1969a.html">1969a</= A>, <A href="http://www.mmk.ei.tum.de/persons/ter/ref/Coltman1990a.html">Coltm= an 1990a</A>, <A href="http://www.mmk.ei.tum.de/persons/ter/ref/Nederveen1973a.html">Ned= erveen 1973a</A>). 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. </P> <P>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 <A href="http://www.mmk.ei.tum.de/persons/ter/top/pshifts.html">pitch = shift effects</A> 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 <A = href="http://www.mmk.ei.tum.de/persons/ter/ab/026.html">[26]</A> , <A href="http://www.mmk.ei.tum.de/persons/ter/ab/080.html">[80]</A> = .</P> <P>With a special tunable electronic organ we have performed listening = tests on musical examples with normal, stretched, and even contracted intonation = <A href="http://www.mmk.ei.tum.de/persons/ter/ab/028.html">[28]</A>. 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.</P> <P>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 <A href="http://www.mmk.ei.tum.de/persons/ter/ab/104.html">[104]</A>).</P>= <P>Cordially</P> <P><FONT face=Verdana size=2>||  |||  ||  |||  = ||  |||  ||  |||  ||  |||  ||  |||  = ||  |||  ||  |||<BR>jason kanter � piano tuning/regulation/repair<BR>bellevue, wa � 425 562 4127 � cell 425 = 831 1561<BR>orcas island � 360 376 2799<BR>[see historic temperaments at = <A href="http://www.rollingball.com">www.rollingball.com</A>]</FONT></P></= DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=oleg-i@noos.fr href="mailto:oleg-i@noos.fr">Isaac = OLEG</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">Pianotech</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Monday, August 02, 2004 = 2:42 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> RE: Re: a violonist = trained ear (was tuning for violinist)]</DIV> <DIV><BR></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>Hello,</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>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.</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>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.</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>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.</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>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.</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>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.</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>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.</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>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.</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>That is easier for them to correct their justness than for the piano tuner = to try to meet the violin high treble I think.</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>Best regards.</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2>Isaac OLEG</FONT></SPAN></DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=563013321-02082004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV class=OutlookMessageHeader dir=ltr align=left><FONT = face=Tahoma size=2>-----Message d'origine-----<BR><B>De :</B> pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]<B>De la = part de</B> hubert liverman<BR><B>Envoy� :</B> lundi 2 ao�t 2004 22:44<BR><B>� :</B> Pianotech<BR><B>Objet :</B> Re: Re: a = violonist trained ear (was tuning for violonist)]<BR><BR></FONT></DIV> <DIV> </DIV> <BLOCKQUOTE style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV><FONT face=Arial size=2>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.</FONT></DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>Hubert Liverman</FONT></DIV> <DIV><FONT face=Arial size=2>Opelika, AL</FONT></DIV> <DIV> </DIV> <DIV> </DIV><BR><BR>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 ?  <SPAN = class=moz-smiley-s1><SPAN>:-) </SPAN></SPAN><BR><BR>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 ?   <BR><BR>Jean Debefve,<BR>Belgium  <BR></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>