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Hi Kees,

I now have an interesting workspace here at the conservatory. The concert hall hosts a Steinway D, a Fazioli 278, a Graf fortepiano (1827) and a cembalo.

I plan to experiment a bit with using the same temperament on these different instruments, and see how the music played on them comes out. I would like to include your "transposed/corrected" version of the bach-lehman temperament, and I know that you wrote instructions for setting it aurally earlier here on PW, but for some reason I can't find them now when I search through earlier postings.

Would you be so kind as to lay it down for me once more?

Regards,
Patrick

@pppat:

Greetings:

The info you need is in the thread started by PianoKeys135
Bach's WTC & temperament/tuning
#1543202-10/25/10 02:33pm

Kees answered at 10/25/10 9:26pm
Re: Bach's WTC & Temperament/ tuning[Re:pianokeys135]
#1543506

Sorry, not computer savy enough for a direct link.

-H.W.

PS- I can type it for you, no? e-mail?
I have it bookmarked.

Here it is:

CLICK: Bach's WTC & Temperament / Tuning

Thanks, Herr Weiss, for the clue!

--Andy

Verbatim by Kees:

Here's my interpretation(which is not exactly Lehmans)

First of all it represents the Circle of Fifths, and the loops represent fifths. Triple loops are the narrowest fifths, double loops medium narrow, and single loops the purest, perhaps even beatless.

Where C is, is indicated. Now we can read it in two directions. The correct direction is from right to left(so F on top, then C(where indicated), then G etc, till you end up at A# at the bottom. If you try it the other direction the resulting temperament makes no sense. We now have a qualitative spec for the Fifths except the last one A#F.
There are some cryptic curls. Lehman assumes it means a fifth, which is 2 cent(1/12)WIDE. I think it means it can be anything you want as long as it is not too much offensive, or it is a puzzle. I personally like it to be narrow like the ones next to it, which(keeping F fixed) improves the M3BbD.

To tune it aurally I have the following method.

0.Start with A3

1. Tune F3A3 purer than in ET, according to taste. Three beats per sec according to Lehman, but 4 or 5 is also possible, giving a much milder Well-Temperament.

2.Tune F3C4 and A3D4 temporarily pure(tune C4D4)

3. Tune G3 so that G3D4 beats 1.5 as fast as G3C4.

4. Tune C4 so that G3C4 beats 1.5 as fast as F3C4.

5. Tune D4 so that A3D4 beats 1.5 as fast as G3D4.

6. Tune A3E4 as narrow as G3D4, beating about the same(tune E4)

7. Tune E4B3 B3F#3 F#3C#4 beatless(the 3 single loops)(tune B3,
F#3,C#4).

8.Tune G#3C34 and F3A#3 temporarily pure(tuneG#3,A#3).

9.Tune D#4 so that A#3D#4 beats 1.5 as fast as G#3D#4.

10.Tune G#3 so that G#3C#4 beats 1.5 as fast as G#3D#4.

11.Tune A#3 so that A#3D#4 beats 1.5. as fast as F3A#3.


-H.W.

Thank you Cinnamonbear for your help.
I decided to type it and study at the same time, haha.
Everyday I get better in doing stuff in the Internet but I'm not quite there yet. You are faster than me, haha.

Good Night,

-H.W.

It's just my librarian side showing.

As to relative speed, there is safety in the slow lane! One sees more when one slows down, right? I'm supposing that you noticed a few things and thought some thoughts while you were typing.

So now, in this thread, we have the expedient answer (thanks to your typing) AND ready access to the archive, thanks to your bookmark! It's all good!

I suggest finding out what Owen Jorgensen had to say about that temperament before worshiping it.

Hi Pat, I see you have it already. Let me know how it goes and what you think.

Cheers,
Kees

Indeed, but as far as I know it was not known when he was alive.

Robert Hill is the only musician (excluding me) that uses it as far as I know.

Kees

Thanks everybody!

I will try this temperament and get back with feedback. I will probably start with the beat speed of the first third a bit faster than 3 BPS, not to shake things up too much

By the way, the Fazioli 278 has VERY low inharmonicity. I think it is the closest to theoretical ET (12^2) I've ever encountered on a piano. It's kind of crazy, actually - when you tweak the fifth towards pure, there is not much twang in the 4th at all. It feels like the sweet spot (the balance between the fourth, fifth and octave) is very wide.

Kees,

Perhaps I am not thinking about the same temperament as is being discussed here. The temperament that Bradley Lehman presented as the decoding of those spirals did not receive rave reviews from Owen Jorgensen well before he passed away. Jorgensen wrote about it in the PTG Journal well before his passing but I don't know which year or month that was.

I don't even remember exactly what Jorgensen said about it except that there were some ET sized 5ths in it which (as I recall), Jorgensen said would not have happened.

No, this is not Bradley Lehmans temperament.

Problem with that temperament as far as I am concerned is that the worst key is E major, whereas in my version it is C# major which seems more reasonable.

Kees

Patrick,

That would be a great piano to try the method upon that I will present at the PTG Convention in July. I am waiting for a recording of a Jazz performance here in Madison to be released where I used it on a Kawai RX-3 which also has fairly low inharmonicity.

I hope you will be at the convention and be on hand to play the piano after it has been tuned. Tuning a variation of ET where 4ths & 5ths beat equally allows one to match partials when tuning octaves nearly perfectly. The slight discrepancies cancel themselves out nicely. It produces the most in-tune sound from the piano I have ever heard, especially with the complex harmonies of Jazz compositions.

You do lose the key signature and modulation effects of a Well Temperament or Mild Meantone temperament but what is gained in overall smoothness has to be heard to be believed! I retain that method now as the solution for those who dislike the effects of key signature modulation, whether that be in modern music or all the way back to Bach.

The wonderful thing about it is that the techniques are those that 17th and 18th Century tuners may have or could have used. It is all about a zero beat rather than confusing and disturbing rapid beats.

All of the attempts at ET by such theorists as Marpurg and Neidhardt (among others) were imperfect, theoretically. But what they did actually do remains to be studied and enjoyed for what they actually can do for keyboard tuning. I can only remind people that Johann Georg Neidhardt conceived of a very close approximation of the EBVT III nearly three hundred years before I did in 1724!

As they said when I was a young man in Los Angeles, "Be there or be square!" (To be "square" was not meant as a compliment)

Oh, OK then, never mind! LOL

Yes Bill,

I tuned an RX-3 a week ago, and it was also very low in inharmonicity. But this Fazioli in it's own ballpark!

I have planned all year to come to the convention this summer, but now two factors might have made it close to impossible. One is a recording gig that is set for the same week, and in which I play. The other factor is economy, the trip from over here being a bit costly.

I know that there is some financial help for CTE:s working the floors, but I have no further information about that.

Bill, is this "ET" tuning something you can do for the Weber and the M&H on your next visit?