Hi, I'm working on tuning my piano using a strobe software tuner and the 'sample stretch' is about 39 cents sharp at C8. I might buy the software, in which case I can adjust the stretch.

But I'm curious: on this setting of 39 cents stretch at C8, the tenths beat very fast and it does not sound good. Is there a method for reducing this? My only guess is that there might be some other temperament where the major thirds (and hence the tenths) are not as wide as they are on equal temperament (which is what I'm using now).

I guess I could experiment with the various temperaments that are loaded into the program but maybe somebody knows right away 'oh you should use the XYZ temperament'.

What is the tuning program you use? It would not seem correct that only one note would be stretched to that extent without the previous notes incrementally stretched from A4, A5, A6, etc, for that matter. What does your program say about stretching the bass notes?

This is where your skill in aural tuning comes into play. If it sounds wrong to you, then it probably is, and you have to make adjustments according to the quality of the sound, quality of the beats. It is your ear that ultimately decides the interplay of intervals, octaves, and unisons.

When I tune my piano, I ensure the temperament from F3 to A4 is correct - all intervals beat accordingly before thinking about octaves up and down the register, then any stretch as I move away from the central octaves. I use 3ds and 6ths as checks as work to ensure the 4ths and 5ths are where they should be inside that F3 to A4 temperament (setting the bearings). Example the third G3-B3 beats slightly faster than (F3-A3 < or = 7 bps). Then I check the 6th F3-D4 ensure they are equal to G3-B3. My sequence for checking is: inside 3ds then outside 6ths up the register - that the interval beats increase as I move up the register, but that the inside 3ds and outside 6ths are equal or imperceptively close. Once you get past A6, it becomes nearly impossibe to count beats in thirds or sixths, but if the bearings were set in your core temperament, the rest of the notes should be very close and you can avoid getting fast beats. There are so many tuning techniques, but this is the one I've been using with success on my piano and a few friend's pianos that have allowed me to tune them.

Even though you probably know all this, but it's good to get a reminder. I constantly read on tuning techniques and practice them so when it comes time to do the real thing, I have options.

Remember, a good temperament is useless if the ocatves and unisons are out of whack, so be sure to work on your pin-setting technique that helps to ensure the unisons don't get knocked out when you play loudly. Good pin setting technique will also help to prolong the life of your pin-block.

I highly recommend Reblitz' book as a reference for you as you learn to tune. I reference also, Bill Bremmer, who posts regularly and gives excellent technical advice regarding aural tuning.

Glen

Sorry, what you are asking is just impossible. If the overall stretch is held constant (39 cents at C8), then the only thing you can vary by picking a temperament is the distribution of beat rates for tenths. If you make some of them beat slower, then some other ones will have to beat faster by the same amount. There is no magic way to make them all slower without reducing the overall stretch. But that is often a main goal of an historical temperament - to shift the burden of the beat rate onto intervals that are rarely used (in certain key signatures).

Thanks for sharing your technique Glen, I had not considered that the major 3rd a whole step up (G3-B3) should beat the same as the major sixth (F3-D4), though I have been using sixths to check my work on fourths and major thirds. I have Reblitz's book and I have been working on pin-setting technique just today actually.

The notes *are* incrementally stretched, but the issue is that since major thirds are wide (top note sharp) already without a stretch, the stretching makes this interval beat faster than otherwise. That sounds okay for a major third mid-keyboard, but the stretching is greater the further you go up (all the incremental stretches add up). So the tenths beat really fast. It doesn't sound good but it's a systematic problem, since they all sound that way. I think my best option may be to buy the program so that I can reduce the stretch to something that sounds better on my piano. I really want to put some stretch in the piano since it sounds wonderful otherwise.

The software I'm using is called Piano Tuner 1.9 and is from Katsura software. It has a strobe function and multiple built-in temperaments. Also, you can program new temperaments. For example I already programmed Bremmer's equal beating temperament (but haven't used it yet). I think the software is reasonably priced at 100 dollars.

Yes, thanks, I should have thought of this. I had a slight hunch this was the case but I hadn't thought it through fully.

I think I found the issue (also posted on the other thread I started about the stretch tuning). The 'sample' stretch is pretty drastic in the mid-range, where other tables have a curve that is relatively flat in the middle:

I found normal stretch tables on two web pages for strobe tuners:

http://www.mts.net/~smythe/st-6.htm#tuning

And:

http://www.pianosupply.com/tuners/490st.html#appendixc

Piano Tuner lets you enter data directly and make your own stretch tuning, so I just typed in the data:

Hi Charles,
C8 should be the last of your concerns...

I've never seen such a stretch as the one you depict in first graph posting. That might be good for a lousy spinet but I can assure you that when I began my tuning journey, I did not even think to begin to stretch the notes inside of the these four octaves - F2 to F6 until I was happy with the temperament through that range. If your temperament is correct from F3 to A4, you'd be better off not worrying about stretching any notes until you are outside of F2 to F6 range until you know what to listen for. Keep the octaves pure up and down from your temperament bearings (F3-A4 in my case) to F6 and down to F2. Any stretch you do should be nearly imperceptable.

Usually, longer pianos (longer strings) require less stretch across the scale and shorter pianos (shorter strings) require more stretch across the scale.

This is a more realistic graph of a general stretch tuning.

Railsback Curve for general reference

Keep using Reblitz' book as a reference. Let your ear be your guide.

Glen

Charles:

It is easy to think of stretch as a thing a tuning has more or less of and iH as a thing that a piano has more of less of, but it isn’t so simple.

Inharmonicity is something each string has and the higher strings have much, much more. Also, the higher partials are affected by iH much, much more that lower partials. So, the end result of stretching an octave so that the 2:1 octave is beatless can result in the 3rds and 10ths beating slower, not faster than theoretical.

Thanks for posting the diagram of the “Sample Stretch.” It is disturbing to see a straight line. This shows that the selected stretch is not related to the iH, but to a fixed octave ratio that is larger than 2:1. The flat-lining of the cent deviation curves at the ends of the scale (also on the other Topic) is equally disturbing.