[CAUT] well tempered

[Fred Sturm]

Hi Chris,
	Cents are proportional throughout the piano. You can apply the cents  
deviations to any and every note (every C the same, every C# the same,  
etc) anywhere in the piano. It doesn't seem like it would work  
intuitively, but it does. With SAT, unfortunately, I think you just  
have to plug in all the numbers, note by note, making sure you add or  
subtract right, and making sure you do a "note up/note down" to clear  
the sometimes handy feature in the save mode: when you save a number,  
the SAT automatically goes up to the next higher note, and leaves the  
same number in the display that you just changed to for the note  
below. So to get back to the original number for the tuning you are  
converting, you have to do a note or octave change, up and down or  
down and up. (Here is one place where the RCT shines: plug those  
offset numbers into a custom user temperament, and you can  
automatically convert any ET tuning in your library to that  
temperament, just a click of the mouse).
	I wouldn't worry about Lehman's talk of 2:1 octaves. He is dealing  
with harpsichords, not pianos.
	An alternative is to do just an octave or two (enter the numbers and  
tune by them), and then tune out octaves aurally (or using the ETD to  
match partials). Just use whatever temperament octave you like.
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu



On Mar 22, 2008, at 8:21 AM, Chris Solliday wrote:

> How about the unadvertised dumb question, do I use the deviations  
> starting at A49 and go up to G#60 or do I use what I would consider  
> the "temperament octave?" If I just have that correct I can manage  
> the rest by ear. Sorry, I don't have time to buy a VT. Having slept  
> on this I now think double and halve is wrong since that would be  
> for cycles per second not cents but maybe the answer lies in putting  
> the temperament onto a page in memory and then applying multi  
> representative stretching techniques using the Double Octave Beat  
> Control as I usually do with my SAT-not your problem Jon. But maybe  
> someone else out there...
> My confusion is compounded by Lehman's suggestion that a C centered  
> tuning (which is supposedly the great discovery contained within the  
> Bach doodles on the title page of the WTC) begins at middle C40  
> instead of C52 and all his indications either aurally or ETD are  
> based there. Then he goes on to say that he gives indications for an  
> "A" centered tuning because that is the sacred tuning note of  
> orchestras and many piano tuners which he never spells out, so I  
> infer he means A49 but I suppose it could be A37. Who knows? not me.
> Thanks for taking the time with this but perhaps it's becoming a  
> more universal thing as Ric B suggests. I am alot like you Jon in  
> that I am doing this just for result and while this may be an  
> opportunity to really dig in and learn something about that which I  
> have been avoiding, I'd really rather just get the thing tuned and  
> go home for some jelly beans. I can appreciate key color but since  
> it is a miniscule part of the available spectrum these days I'm sure  
> Equal Temperament will remain my and most everyone else's tuning of  
> choice. Again the color of jelly beans is much more important...
> Thanks,
> Chris
> ----- Original Message -----
> From: Jon Page
> To: caut at ptg.org
> Sent: Saturday, March 22, 2008 7:49 AM
> Subject: [CAUT] well tempered
>
>> Dumb question - If I were to continue to the next octaves would I  
>> use the
>> same deviations or double them each octave up and halve them going  
>> down?
>
> Dumb answer - dunno.  Which is why I went with the VT. No decisions  
> to make
> other than selecting the correct style (stretch) for a given size/ 
> quality piano.
>
> I have tweaked the styles to tune in a manner which my ears agree  
> with.
> The temperament octave is a combo of partials: sm, med, large pianos:
> 2:1 80%, 4:2 20%
> 4:2 60%, 2:1 40%
> 4:2 60%, 6:3 40%
>
> Aurally check A4-A3 octave size and switch style if needed.  
> Expanding out,
> two or three partials are chosen and given a percentage. No page  
> flipping
> or figuring to do other than assess aurally and either accept or  
> alter the note.
>
> After many tunings and disagreeing with the machine placement, I have
> assigned registers multiple-partial proportions and sampling points  
> such that
> I find no fault. For instance, instead of using the A5/6/7 as  
> sampling points;
> I chose A5, F#6, D#7, C8.  Breaking the top into sixths/samplings,  
> has smoothed
> out inconsistencies at the treble break and the blend of oct's 6 & 7.
>
> I'm no wizard when it comes to this stuff and defer to others more  
> knowledgeable.
> I'm more of the seat-of-the-pants kind of tuner regarding this,  
> meaning, making it
> work for me without really understanding the nuts and bolts of it all.
>
> I recently purchased Rick B's book, On Pitch which I hope will shed  
> some light.
>
> Regards,
>
> Jon Page

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