Reverse Well ??

[jason kanter]

Ric, I only just got around to analyzing this bearing plan with the desired
beat rates. Frankly it doesn't compute in theory. My spreadsheet does not
take inharmonicity or stretch into account, and assumes therefore that F-F
is a perfect 2:1 octave, which was no doubt NOT the case, but what happens
in theory is this: start with A3 and tune by fourths and fifths as follows:
A3 D4 G3 C4 F3 Bb3 Eb4 Ab3 Db4 Gb3 B3 E4, using the beat rates you specify
below for the 4ths and 5ths; now the last interval to close the circle,
which is the AE fifth, comes out beating at 1.4 per second, NOT the .69 per
second that they specify; this fifth is narrow by 3.72 cents instead of the
theoretical 1.96 cents, and sticks out like a sore thumb. All the other
fifths are "cleaner" than theoretical ET, ranging from -1.70 to -1.86 cents.
But it's not a reverse well, it's actually a very mild well; the thirds on
C, G, D and A are all 12.4 or 12.5 cents expanded (compared to 13.7
theoretical), while the thirds on E, B, Gb, Db, Ab, Eb, Bb, and F are all
14.2 to 14.4 cents expanded. And the M3 beat rates as calculated do not
tally with what you provide below. Starting with F3A3 and proceeding
chromatically to C4E4, they compute at 7.2, 7.7, 7.1, 8.6, 7.9, 9.6, 10.2,
9.4.
FWIW. How did they judge beat rates?

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jason kanter . piano tuning/regulation/repair
bellevue, wa . 425 562 4127 . cell 425 831 1561
orcas island . 360 376 2799
[see historic temperaments at www.rollingball.com]


----- Original Message ----- 
From: "Richard Brekne" <Richard.Brekne@grieg.uib.no>
To: "Newtonburg" <pianotech@ptg.org>
Sent: Friday, August 20, 2004 4:13 PM
Subject: Reverse Well ??


> Hi folks...
>
> A couple weeks back I posted a few things about my experiences this past
> june at the Yamaha Academy in Hamamatsu. Amoung those was a quick
> reference to the temperment that they require of you there.  Off list I
> got a single note from Bill Bremmer.... you all remember good ol Bill
> now dont you :):).... Anyways.. it was short and sweet and simply stated
> that he thought it sounded like a recipie for the Reverse Well.
>
> I got to thinking about this... and realized I'd never gotten around to
> picking apart his reverse well claim (about  Steinways recommended
> temperament)... so much to do all the time. Well I dont have Steinways
> recipie.. but I have the particulars from Yamaha... which I will give
> below.  If someone can explain how this leads to a reverse well tempered
> piano (if it doesn) I'd be very appreciative.
>
> Here ya go.
>
> First off... one starts at A3 and tunes up a 4th then down a 5th till
> you come around... two successive 4ths (up) from F to Bb and Bb to Eb
> before continuing the pattern to completion with again two successive
> 4ths... Gb to B to E.  The manual throws in C40 to F45 in the middle of
> this routine.. but my instructors did not and I was scored only for the
> notes F33 to E44
>
> Here are the specified beat rates that I mentioned they were realllllly
> picky about and very good at judging.
>
>
> 4th beat rates starting with F33 - Bb38 and ending at C40 - F45 are
>
> 0.73 / 0.77 / 0.81 / 0.85 / 0.89 / 0.93 / 0.97 / 1.3
>
> 5th beat rates starting at F33 - C40 and ending at Bb38 - F45 are
>
> 0.56 / 0.59 / 0.63 / 0.66 / 0.69 / 0.73
>
> M3rds --- 
>
> 6.5 / 7.0 / 7.6 / 7.9 / 8.6 / 8.8 / 9.7 / 10.4 / 10.8
>
> I do note that in the middle of this there are two M3rds with nearly the
> same beat rate... and I note that the increase in beat rates for M3rds
> is not exactly the most symetrical thing in the world.  But... reverse
> well ???
>
> Cheers
> RicB
>
>
>
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