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<DIV><FONT face=Arial size=2>This is the chart that I did to go along with the
calculations; ignore the other attachment, I attached the wrong file.</FONT><IMG
alt="" hspace=0 src="cid:001701c20f55$ab217a90$6401a8c0@VAIO" align=baseline
border=0></DIV>
<DIV><BR><FONT face=Arial size=2>Bradley M. Snook</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
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<DIV><FONT face=Arial size=2>----- Original Message ----- </FONT>
<DIV><FONT face=Arial size=2>From: "Richard Brekne" <</FONT><A
href="mailto:richard.brekne@grieg.uib.no"><FONT face=Arial
size=2>richard.brekne@grieg.uib.no</FONT></A><FONT face=Arial
size=2>></FONT></DIV>
<DIV><FONT face=Arial size=2>To: "PTG" <</FONT><A
href="mailto:pianotech@ptg.org"><FONT face=Arial
size=2>pianotech@ptg.org</FONT></A><FONT face=Arial size=2>></FONT></DIV>
<DIV><FONT face=Arial size=2>Sent: Saturday, June 08, 2002 12:30 PM</FONT></DIV>
<DIV><FONT face=Arial size=2>Subject: Re: A Different Temperament / Tuning
Approach</FONT></DIV></DIV>
<DIV><FONT face=Arial><BR><FONT size=2></FONT></FONT></DIV><FONT face=Arial
size=2>> <BR>> <BR>> Bradley M. Snook wrote:<BR>> <BR>>
>It took me a while, but was able to run through some of the numbers;
if<BR>> >you<BR>> >are interested I can give you my results from
A4-C7.<BR>> ><BR>> >The difference between 3:1 and 2:1 is not that
much, but it does add a<BR>> >small<BR>> >amount of "extra" stretch
to the overall temperament. Why do you feel that<BR>> >this small amount
of stretch past a 2:1 octave is helpful? <BR>> <BR>> Well, its not so much
that I think stretching past a 2:1 octave is helpful or<BR>> not.... as it is
that I think that making the 12th perfect is desirable, and<BR>> doesnt
sacrifice enough relative to any octave type to worry about. <BR>> <BR>>
Further it seems, and I underline seems as I am just starting to really
pick<BR>> this idea apart myself, that tuning the whole piano this way keeps
the<BR>> differeing octave types in a very nice and consistant relationship.
And I have<BR>> from almost day one (from my first experiences with ETD's)
liked the idea of<BR>> directly referencing a pianos built in
inharmonicity.<BR>> <BR>> <BR>> >Using your<BR>>
>method<BR>> >with my piano, I get a .190 total beatrate and a +0.3729
cent additional<BR>> >stretch at A4-A5; at C7-C8 I get a 3.819 beatrate
with a +1.5476 cent<BR>> >additional stretch. It is an interesting
approach, but I'm not sure that it<BR>> >is a good idea to sacrifice the
sound of a single octave like that.<BR>> <BR>> I am unfamiliar with what
you mean by 0.190 total beatrate, or 3.819 beatrate.<BR>> How is this
quantity calculated and what does it represent. As far as the<BR>> stretch is
concerned, could you tell me what tuning scheme you are comparing<BR>> this
method against ? Are you useing RCT and if so what OT. <BR>> <BR>>
><BR>> >I personally do add a very small amount of "extra" stretch to
my single<BR>> >octaves (past that of a non-beating 2:1). But for me, I
feel I get a better<BR>> >result by balancing the sound of a 2:1/4:1
single octave. In addition to<BR>> >closer coinciding overtones, this
method also allows for a better sounding<BR>> >double octaves.<BR>>
<BR>> I gotta admit that there is a slight roll in the basic feel of the
Octaves when<BR>> keeping all 12ths pure. But then I was really suprised when
doing the note for<BR>> note check against RCT's calculated curve for this
just tuned piano. Like I<BR>> said in my last almost all the notes showed
some blush, and those that didnt<BR>> had only slight movement one way or the
other in the spinner. <BR>> <BR>> You may be right about "better sounding
double octaves" or this may really<BR>> belong in the realm of personal
tastes....as perhaps may my taste for the<BR>> perfect 12th. But the real
point of this excercise for me is to pick apart the<BR>> whole process of
calculated tuning curves... what they really are and what else<BR>> can be
done. On the surface of it it appears that this method presents a really<BR>>
easy way of tuning that results in a very pleasing result with its own<BR>>
character. And it also seems like it creates very much this same
character<BR>> regardless of the piano.<BR>> <BR>> Grin... I'll know
more when I do :)<BR>> <BR>> ><BR>> >Bradley M. Snook<BR>>
<BR>> Thanks for the interesting reply Bradley <BR>> <BR>>
Cheers<BR>> RicB<BR>> Richard Brekne<BR>> RPT NPTF<BR>>
Griegakadamiet UiB<BR>> </FONT></BODY></HTML>