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Yep, but remember to always practice stability. Nothing else works well without that.

You mean stability, as in setting the pins? Absolutely the hardest skill to master.

Yep!

So, you guys that did learn to tune with fourths and fifhts, how did you practise and how long did it take until you could set a working temperament?

I took lessons from a blind floor tuner. He had me read parts of Dr. White's book. At the second or third lesson he demonstrated how the temperament was set. Then I set a working temperament on the first try. Getting a good temperament took a couple more tries during practice. At the fifth lesson he said that there was nothing more he could teach me.

BUT, that did not prepare me for when I tried to tune a temperament across a break, like is common with spinets. I thought at the time that I wasn’t tempering the 4ths and 5ths correctly. It was a real blow to my self-confidence. I thought the warning about beatrates on spinets meant that the RBIs would beat slower or faster, but still be progressive. It was some things that I read on this great Forum that clued me into what really happens.

I can´t believe that you did that so fast, I think i tried tuning by fourths and fifths maybe 50 times and didn´t get it even once... I have been trying bills sequences now for a while and i think i´m starting to get deacent results now...

Touché!

Bill: what sequence to you use yourself? and how did you learn to tune in first place?

You asked, so I told you. Rather than tell you to go pound sand, I will consider how frustrated you must be and reply to your Topic about tight pinblocks. It really is OK. I understand. If the strings don’t stay at pitch, no temperament sequence will work very well. It is like trying to chain rolling logs on a moving truck.

Then I guess I won't bother telling about some really amazing things I have done, like herding bear.

This is another point I was making in another thread some time ago, the tuning pin system we have today doesn't have enough accuracy, because as you say, the speaking portion's tension changes, we can hear the difference in frequency and tempering, but the pin cannot be set that accurately.

You say that when a break in scaling occurs, the thirds will cause the fifths to be mushed around to fit. But the fifths and fourths are supposed to be mushed a little from ½ and 1 bps, they aren't supposed to beat exactly at that rates, plus the mushing effect of human error, you said humans can't tune consistently within 0,1 bps. Instead of doing the fourths and fifths in a row using one tuned note for another and then finding that F3-A3 beats faster than F#3-A#3, if you would make the thirds correct and let the fifths fall where they will, would you say the fifths and fourths are tempered wrong when let's say 1 cent is divided between four fourths and fifths, keeping in mind that they aren't all supposed to beat ½ or 1 bps? And if the end result is all intervals apparently sounding correct, isn't that the purpose?

today i actually set my first temperament within the range of 1 cent (partial2) by tuning fourths and fifhts. The key was to use the following formula:

contiguous 5ths ratio 2:3
5th and 4th top common note 2:3

5th and 4th bottom common note 3:4
contiguous 4ths ratio 3:4

D4 from A3 about 1 bps

G3 from D4 so that G3-D4 beats 2 times in the same time as A3-D4 beats 3 times.

C4 from G3 so that C4-G3 is a little faster than A3-D4 and G3-D4 beats 3 times in the same time as G3-C4 beats 4 times.

F3 from C4 so that F3-C4 beats 2 times when G3-C4 beats 3 times.
At this time i could check with the M3-M6 test (F3-A3 = 7bps F3-D4 8bps)
Then i tuned:

A#3 from F3 about 0,7 bps, checked so that F3-A#3 beats 4 times compared to F3-C4
At this time i could also check that F3-A3 , F3-D4 and A#3-D4 all are accelerating.

D#4 from, A#3. a bit faster than A3-D4.

G#3 from D#4 a little faster than G3-D4 and G#3-D#4 should beat 3 times compared to A#3-D#4. G#3-C4 should beat about 1 bps slower than A#3-D4.

C#4 from G#3. A3-C#4 should fit inbetween A#3-D4 and G#3-C4. C#4-G#3 should also fit in between G3-C4 and A3-D4.

F#3 from C#4 a little bit slower than G3-D4 but faster than F3-C4. F#3-A#3 should be 0,5 bps faster than F3-A3.
F#3-C#4 should beat 2 times compared to G#3-C#4 3 times.
again the M3-M6 test.

B3 from F#3. a little faster than F3-A#3. F#3-B3 should beat 4 times compared to F#3-C#4. at this time G3-B3 should fit inbetween F3-A3 and A3-C#4 and progress evenly.

The last note is E4 which is tuned from A3 and B3. B3-E4 should beat 3 times when E4-A3 beats 2. C4-E4 should also beat a little faster than B3-D#4. E4-B3 beats 4 times compared to F#3-B3.

This was the first time i tried this sequense by comparing the interwalls against each other. The " fourths about 1 bps wide and fifths about 0,5 cents narrow" didn´t work for me. I noticed how much more accurattely i could tune when i have to compare different intervalls against each other. especially if the note beeing tuned is a common note. for instance C4-F3 to G3-C4 If they are equal beating C4 is too low. (this didn´t happen in this sequence).

One thing i did notice was that i didn´t get very much stretch with this method. how could i add a little bit stretch?

I don't know if i was just lucky today, but it seemed pretty easy. as i wrote earlier i have made over 50 attempts to tuned by fourths and fifths but now when i found out about the beating ratios beteween the different intervalls it got a lot easier.

As a jazzpiano player i find it relatively easy to play 3 beats over 2 or 4 over 3. i use that kind of polyrythmic ideas in my playing.

Feel free to critisize...

Martin

I tried a hybrid method today which worked out great for me. I tune F3 to A3 at 7 bps, making sure of the beatrate with a metronome. This is something I can do very accurately. Then I tune the 4ths and 5ths making up F3A3, first C4 to F3 then D4 to A3 then fit in G3 to make G3C4 and G3D4 be "correct". I can do this very accurately too. At this point I have F3 G3 A3 C4 and D4 solidly in place and just tune by 4ths and 5ths checking any RBI's that become available and if tests failed I listen to the 4ths and 5ths again and usually discover a problem.

With the contiguous M3 method I have problems placing C#4 as the A3C#4 and C#4F4 beats are sometimes very hard to hear.

I guess there'r many ways to skin a cat.

Kees

Do bother, it sounds very interesting.

I have played ney on top of Haleakalā mountain and got the almost extinct native ney-ney bird to reply to me.

Kees

In my opinion, this is the biggest mistake anyone can make. It is the reason why the rest f the temperament often does not work out, especially on short or irregularly scaled pianos.

I often read that with these, 4ths & 5ths sound good but the RBI's are irregular or not progressive (or digressive) across breaks, etc.

When I tutor someone, I tell them not to try to "count" or time beats with any measuring device whatsoever. The actual rate of the F3-A3 M3 depends on the inharmonicity and the size octave chosen. The contiguous thirds approach with two pairs of octaves will find that rate. If you find the F4-A4 M3 impossible to discern, the reason may well be that it is far too fast. If the F4-A4 M3 is too fast, then the F3-A3 M3 is too fast.

In theory you are right of course, but according to my calculations even on short pianos the error remains well under 1 cent and on nice grands it's more something like 0.2 cent.

Kees

Whatif you use a hybrid version where the F3-A3 is set by tuning the first set of contigous thirds?, then you would have a frame for tuning the rest of the notes, C4-G3-D4 between F3-A3 and F#-B3-E4 between A3 and C#4 and finally G#3-D#4-A#3 between C#4 and F4...

Martin

Kees,

I am not even thinking about theory! I am a seat-of-the-pants type guy. When I regulate, I never measure anything! I let the dimensions find themselves. So, why impose an arbitrary beat rate of which you can never be certain? Let the beat rate find itself!

If you have not had success with my descriptions, try investigating what Jack Stebbins RPT (long term primary instructor at the North Bennett Street School and three decade PTG tuning examiner) says in his material on "Let the piano tell you!"

There seems to be something very intelligent coming out of Finland these days! If you can get the series of contiguous thirds from A3 to A4 and verify that both octaves, F3-F4 and A3-A4 are at least similar in size, everything else will work, no matter how you go about it. Tune all the 4ths & 5ths you want after that until kingdom come and you will be able to correct yourself, now matter how you go about it.

I refuse to believe that people "cannot hear" the F4-A4 M3! If you say that you cannot, then you must do as I said, practice moving F4 against A4 until you can. Surely, you will be able to hear when you have a slow beat. Flatten F4 when you do hear it as you hear the speed increase to beyond the point of discernibility. You will hear it if you try.

There must always be an interaction and cross check between SBIs and RBIs in ET. Leaning too heavily on 4ths & 5ths will almost always result in Reverse Well, especially if you try to count 7 beats per second for the F3-A3 M3. That is a quick and easy recipe for Reverse Well.

Leaning too much on RBIs easily results in a Marpurg type quasi ET. The RBIs sound good but the 4ths & 5ths are all over the place.

Equal Temperament means exactly what it says: all intervals are tempered equally.

Well I find just about any recipe to set the ET temperament works for me, so I just like to play around with different methods.

What I like about setting the beat rate of F3A3 and taking it from there is that I can, if appropriate, set it to a low value (like 4bps), tune the 4ths and 5ths that span it proportionally, and then deal with the rest as I please to make up any unequal temperament I like.

Kees