[CAUT] P-12ths was: Tuning a Steinway D and a Bosendorfer Imperial together

[Richard Brekne]

Hi Ron.

Nice post... !  comments interspersed below.

    Ric,

    Is this the crossroad between the sciences, acoustical physics and
    human auditory physiology? Where are the piorities and goals in both
    fields? Where are the piano tuners' priorities?

I'm not entirely sure I know where this question is leading. But piano 
tuners priorities have have traditionally fallen into categories that 
have their roots in aural traditions. I get the sense often that most, 
even those who routinely use ETD's today haven't had (or taken) the time 
to look closer at what the various aural tests, or selected octave type 
ETD curves actually mean to their tunings. 

    Ok. Distribute the inharmonicity. Clearcut goal. Smoothest "fit",
    (progression of all the intervals) that the piano instrument's scale
    and design allow. In theory.

Well here is of course where taste and theory will part ways.... at 
least to some degree. In relation to the P-12th tuning tho... the claim 
is (and I agree with it) that by the very nature of each individual 
pianos own inherent inharmonicity (para-inharmonicity aside) a P-12th 
tuning with attention paid to where 12th types intersect/coincide in the 
bass will yield the <<best>> tuning.  I <<>> best because I am acutely 
aware of the overly subjective nature of the term. Yet if <<best>> is 
equated with a mathematical analysis of what results in the smoothest 
matching of the more relevant partials then any other system... then the 
term has a far more objective sense and I defer to Bernhard Stopper to 
defend his treatise on the matter. My own aural experience leads me to 
believe that he has it right. Indeed I stumbled onto the P-12th approach 
entirely independent of his work around the year 2000 after reading a 
short column in the PTG journal from just before 1980  I believe. About 
the same time I ran into several folks who were aurally using a test 
that amounted to a P-12ths test. Using Tune Lab 97 I constructed a 
template and found that the results were indeed quite pleasing. So I've 
been working in that direction ever since. 

    Non-fixed stringed (fretted) instruments can "bend" the pitch of the
    notes -  as if there is more "pleasure" to tailoring the pitch to
    the logarithmic hearing of humans. Fretted instruments are not
    "plagued" by an overabundance partials. It almost appears as if the
    fretted instruments can place their emphasis on the fundamental - or
    at least using no more than the second, and third partials to sound
    "pleasing". Yes, of course, these instruments have (far less)
    inharmoncity too.
     
    The previous paragraph is hopeless towards approaching acoustical
    and physiological questions and inquiries with any analytical
    approach. The whole discussion is thwarthed by words such as
    "pleasure", "pleasing", "sounds good", etc., etc. As long as it is
    not clear what sounds invoke what physiological reactions (human
    emotions and/or feelings) and why, defining what sounds "good" is
    hopeless.

All I can say to this is that it is music to my ears !  I have harped on 
the uselessness of using such terms unqualified and in clearly 
subjective usages for gawd knows how long on both lists. These terms 
need to be used carefully to be sure. 

    I believe the material sciences - still in their infancy - will one
    day be able to tailor the inharmonicity curves of (any solid-state,
    gas, liquid or plasma material) strings to that of the logarithimic
    hearing curves of humans. Tailoring any solid-state materials'
    inharmonicity to that of the logarithimic hearing of humans is the
    first step towards answering what sounds 'good'. We have a long way
    to go.

    Ron

Agreed.  Tho the P-12ths approach if strictly executed yields an 
interesting result that deserves a closer look. Its the first 
<<stretch>> priority I've ever run into that when strictly followed 
guarantees a by any standards superb tuning every time on every piano. 
An ETD can be designed to read a pianos inharmonicity... take advantage 
of this characteristic with the P-12th tuning and offer such a tuning on 
each piano leaving the tuner able to simply follow the dial without 
further ado... again para-inharmonicity aside.  And I say this being a 
person who has stood firmly rooted in the aural tradition and am on 
record countless times underlining the need to keep the ears turned on.  
I still stand there... but I do see this P-12ths approach for what it is.

Cheers
RicB