P 12ths revisited

[Alan Forsyth]

Yes, that D3 is an extremely important note to get right first time, mainly 
because of it's strategic position. On 90 per cent of pianos it is the first 
note in the bass, or should be. I always include it in my temperament, or 
bearing scale. D3 is the first note I tune after A440.

I'll take you up on your free offer, thanks Ric.

AF


----- Original Message ----- 
From: "Richard Brekne" <rbrekne@broadpark.no>
To: <pianotech@ptg.org>
Sent: Friday, April 01, 2005 11:24 PM
Subject: P 12ths revisited


> Hi Folks
>
> Thought I'd share with you a few thoughts and experiences I've had after a 
> couple years now of using Tunelab to execute a P12ths tuning.  As some of 
> you might remember I used Tunelab 97's numerical curve editor to construct 
> a tuning curve from A1 to F6 with all notes set at the 3rd partial. From 
> D3 to F6 12ths were all spaced so that their first order  coincident 
> frequecies are identical, and I opted for 6:3 octaves in the bass.
>
> One of the neat things this allows for, and I think is a great aid in 
> understanding tuning from a coincident partials perspective, is that one 
> can see exactly the kind of information the aural tuner uses in very much 
> the same fashion.
> By way of example say you have the display on D4.  Both D4 and A5 are 
> tuned directly from this frequency. That is to say the 3rd partial of D4 
> and the 1st partial of A5 are tuned equal yielding a perfect 12th. But at 
> the same time you are able to veiw the 4:2:1 relationship of the double 
> octave A3, A4, and A5.  This because both A4 and A3 also share this 
> coincident.  A3-D3 is a 4th, (4:3 coincident), and D3-A4 is a 5th,( 3:2 
> coincident).
>
> In tuning by ear if you would use any one of a few tests to confirm 
> something between a 6:3 and a 4:2 relationship for A3-A4, and for A4-A5 a 
> somewhat tighter octave. All the while you want to maintain the wide A3-D4 
> 4th and narrow D4-A4 5th.
> Using tunelab set to the 3rd partial of D4 one can readily see exactly 
> whether these relationships are achieved or not.  This is really handy as 
> you tune upwards as one can quickly identify any note that may have moved 
> just a bit. One is able to maintain  a 4:2:1 relationship that leaves the 
> 4:2 essentially pure with the fundemental of the top octave just wide.  As 
> you progress upwards you can visually confirm an even convergence towards 
> a just 4:2:1 for the entire top 12 notes.  All the while maintaining a all 
> 12ths pure.
>
> I usually start at D3 and tune D2, D3, and A4 to this frequency. This 
> gives me a pure 6:3 octave for D2-D3 and a pure 12th for D3-A4.  Moving 
> chromatically upwards, by the time I get to D4 I'm able to also start 
> looking at the octave relationship D4-D3 to make sure it D3 hasnt moved on 
> me, that it stays at a just 6:3.  As I move upwards I expect this to 
> gradually narrow, which is also easy to see watching the same D4 third 
> partial.
>
> So for just one note.  D4. I am able to visually confirm my aural 
> intentions for the notes D3, A3, D4, A4, and A5 which are the 6:4:3:2:1 
> coincidents respectively.  And I have this ability for every note in the 
> curve.
>
> Using this as a template for an aural tuning allows for a very concious 
> and precise execution of a tuning. It also is a great teacher. Just do 
> this a few tens of times and see what lights go on in your mind about 
> tuning in general.  It also helps develope your aural skills as you are 
> getting direct coincident partials visual feedback.
> Anyways... I hope this is of interest to some of you.  Anyone who wants 
> the P12th template I use can email me and I will send it to them. You can 
> create your own using tunelab 97 only, but the curve once created can be 
> used in any version of Tunelab
>
> Cheers
> RicB
>
>
>
>