Tuning Acrosonics

[David M. Porritt]

Bill, Kent et al:

The beat speed of major 3rds depends entirely on the vagaries of the inharmonicity of the 4th and 5th partials.  When you strive for even progression of major 3rds, you are ignoring the pitch of the fundamental, and tempering for the notes to make the 4th or 5th partial "even".  If you compromise 3rds and even out the 5ths, you are setting the pitch of the note based on lower partials (2nd & 3rd).  Since partials get more irrational (non linear) the higher they are, you are tuning the fundamental based on information from flakier partials.  If we really wanted true ET, we would measure the fundamental of each note in the temperament octave and space them evenly letting the partials fall where they will.  That's not practical, so we compromise the fundamental according to the partial structure a particular piano gives us.  Making a temperament based on even 3rds is one way, making one based on even 5ths is another.  Neither one will give fundamentals with exactly even spacing (because of inharmonicity).  Given the problem of uneven inharmonicity in the scale one compromises to his taste.  I don't see how choosing one method (5ths) over the other (3rds) would cause an inside-out well temperament.

dave

*********** REPLY SEPARATOR  ***********

On 12/5/99 at 12:17 PM Billbrpt@AOL.COM wrote:

>In a message dated 12/5/99 8:19:34 AM Pacific Standard Time, 
>kswafford@earthlink.net (Kent Swafford) writes:
>
><< My personal preference when dealing with a 
> large difference in inharmonicity at the tenor break is to give up on 
> smooth beat rates in the 3rds in favor of smooth beat rates in the 4ths, 
> 5ths, and octaves. >>
>
>Dear Kent,
>
>With all due respect to you as someone from who I personally have learned a 
>lot, how do I say it without being inflammatory, condescending, insulting or 
>just plain irritating?  The above statement suggests that one ignore errors 
>or variances which can easily result in the piano being tuned in Reverse Well.
>
>Between the two of us, we have made many fine points about ET.  One principle 
>that I have always believed in regarding ET is that *all* intervals must be 
>given *equal* consideration.  Your own words here, <<...to give up on smooth 
>beat rates in the 3rds in favor of ...>> will make your outcome not really be 
>a true ET.  Granted, the variance may be so slight that it is of no musical 
>consequence but unless you pay attention to the new beat rates of these 3rds, 
>you may not realize that you have actually created a kind of pattern which is 
>actually adverse to the desired musical outcome.
>
>I hear of your idea quite often.  It seems that piano technicians believe 
>that the tempered sound of 4ths, 5ths and even octaves is unacceptable.  We 
>all wish we could make all of these perfectly pure.  In the quest to do so, 
>many people make the error of ignoring the pattern of beating among the 3rds. 
> In my opinion, these Rapidly Beating Intervals (RBI) are actually more 
>important to a good musical sound from the piano than are the Slowly Beating 
>Intervals (SBI).
>
>The reason is that the RBI's produce the resonance and vibrato-like effect 
>that we hear from the piano.  In a musical context, slight impurity and/or 
>inconsistency in the SBI's is virtually imperceptible.  Of course, to the 
>technician who is *constructing* a temperament and tuning, one string and one 
>interval at a time, the impure sound of a tempered interval is quite 
>apparent.  It is easy to argue that 2:1 octaves sound "purer", for example.  
>And while this kind of octave has its own characteristic and value, it is not 
>necessarily "better" simply because of the way it is perceived in a certain 
>context.
>
>Your idea of using a minimally stretched octave when tuning a high 
>inharmonicity scale on a spinet seems contradictory to logic at first 
>consideration.  But as I have learned from both you and Virgil Smith RPT 
>recently, you can give the piano a sweeter, more harmonious sound by doing 
>so.  So, I think it is a good idea and one which should be tried.  If it 
>appeals to the technician doing it and the customer, then it is a good 
>approach to use.
>
>However, deciding <<to give up on smooth beat rates in the 3rds in favor of 
>4ths, 5ths and octaves>> as you have suggested, without considering the 
>consequences can end up making the piano sound just as unpleasant as some 
>other kind of approach such as the ET with pure 5ths which creates harshness 
>in all RBI's.  You would need to be aware of the Cycle of 5ths and Andreas 
>Werkmeister's Rules for Well-Tempered Tuning to avoid this error.
>
>If you really do end up with uneven RBI's, you will no longer have ET.  You 
>may have a Quasi ET or a Victorian style temperament.  There is certainly 
>nothing wrong with either of those.  If the piano sounds good and so does any 
>music played on it, then it is good.  To ignore that these variances create 
>something other than equality merely to avoid the idea that the piano could 
>only be properly and ethically tuned in ET is frankly self deceiving.  It 
>gets into the indefensible position that "It is ET if I say it is and if I 
>mean it to be, any of those little variances don't matter.  No artist or 
>customer *ever* complained about that.  And by the way, I don't like HT's".
>
>In my experience, such thinking *invariably* leads to a piano tuned in 
>Reverse Well but of course, the person who has tuned it that way does not and 
>cannot perceive and recognize that fact.  I completely agree with your 
>opening statement,  <<These are all _very_ successful pianos so we must be 
>careful about how we discuss the 
>tuning of these instruments. >>  
>
>Bill Bremmer RPT
>Madison, Wisconsin




David M. Porritt
dporritt@swbell.net
Meadows School of the Arts
Southern Methodist University
Dallas, TX 75275