I am using a software strobe tuner called Piano Tuner, and in the trial version the only octave stretch that it has gives me an octave of 524Hz and 1055Hz. This seems like a lot to me. The major thirds do not sound good to me on this tuning. This stretch means that that octave beats at 7bps if I'm figuring correctly. That sounds like a lot.

There was a thread last year on octave stretching but the details were given in cents. As I understand, 100 cents make a half step. There someone was talking about a stretch of 27 cents at C7. I'm not sure how to translate this to a difference in terms of Hz, given for example 524Hz as the lower note.

Any help appreciated.

Tell us more about the software "Piano Tuner".

In this section of the piano, I'd be surprised at a large stretch. I can't imagine tuning an octave and hearing 7 bps.

One way to listen for stretch is, after tuning an octave, to test for a fifth from the tuned note. It should be closer to pure for a good stretch.

Hop

Is 7Hz in one octave a big stretch?

Depends on what octave. In the 4th octave - 1 Hz is about 4 cents.
Or - A442 would be 8 cents sharp of A 440. This is looking at A4, the fundamental, not any of its partials.
100 cents between semitones is constant while Hz varies.

I also do a rough confirmation of octaves using a 5th - it keeps the stretch close enough.

The software is by 'Katsura' and is listed on the PTG website:

http://www.ptg.org/resources-software.php

It's called 'Piano Tuner' version 1.9. To buy it costs 99 dollars. In the trial version there is only one 'sample' stretch.

Charles:

Without inharmonicity, yes the 2:1 octave would beat at 7 bps. Strictly speaking, this octave is 1211.52 cents wide or stretched by 11.52 cents. But the beat rate for inharmonic tones will be different. The model piano in a database that I am working on right now has an iH of 1.14 for C5 and 2.86 for C6. Using 524 and 1055 Hz, respectively, gives a beat rate of 4.93 for a 2:1 octave, 3.67 for a 4:2 octave and a -10.22 for a 6:3 octave.

Is this too much? I wish I really knew. I am realizing through my studies that some strange things can happen to beat rates in this part of the piano. I have never used an ETD, and am working on reconciling what I hear with what the numbers say.

I went and took a look at the software. It seems similar to the peterson strobe, or any of the other "template" style tuning gear. From the picture of a sample stretch, it seems to only use the fundamental for tuning. There are ways around that, for sure.


To match the stretch options to the piano....? You've got to use some basic aural skills. It is misleading to follow just one partial match to hope for an appropriate stretch. So, (it's in one of my youtube videos about matching the box to the piano) use the tuning skills any musician has- tuning octaves or double or triple octaves without any other checks. You'll tune 5 or 6 single strings of "A"s for example via the machine. Now that you've got a "bookmark", you are free to move those notes a little up or down to see if there is a better placement to make those notes sound better together. Then, try and adjust the template to come as close to possible to those "ear" determined notes. It's about the best you can hope for using primitive piano tuning software...

Ron Koval
Chicagoland

Charles,

I've thought about this, and here's is what I think. The inharmonicity of the piano strings causes the partials to be sharper than those of a pure string or a mathematical progression. When tuning a higher note of a 2:1 octave, the beats at the higher note frequency should be zero. But the frequency of that higher note will be somewhat higher than twice the frequency of the lower note (which you would expect in the absence inharmonicity). When tuning a higher note of a 4:2 octave, the beats of a frequency one octave higher than the higher note being tuned will be zero. But tuning this way will tune the higher of the two notes sharper than the 2:1 octave (and much sharper than four times the lower note). While there will be frequency increases (kHz), the beats will be zero in the actual tuning.

Hop

OK thanks, and thanks to everyone for your posts. OK this makes some sense to me, but it seems like the beats will only be zero for a particular stretch that lines up perfectly with the sharpness of the partials. I am thinking that if I was getting 7bps then I was not tuning the octave correctly. I looked again at the software and the stretch is in the range of 30-40 cents by C7, so I do not think it is a phenomenally large stretch.

RonTuner,

I don't know where you got that stretch table. It didn't come with my version of the software. Maybe the version for Mac is not the same as PC?

I think I found the problem. I was able to find the sample stretch and it is really different from what you posted. Especially in the mid-range the stretch is drastic in comparison:



I wish I had read the 'just for testing' part before I spent two days on the thing! Oh well I learned plenty.

Yikes! That's a crazy graph!!!! I just found the other one on the website. I don't have a mac, so haven't used the software. I assume you are pursuing this software because you have a macbook?

Remember that ALL of the partial beats between intervals are heard in the mix. The goal is NOT to make one better than another, but to come to an agreeable mix of everything that is beating(or not) at the same time...

Ron Koval

30-40 cents is excessive for C7 but it would not be for C8. The inharmonicity between the first and second partial of C7 can easily be 30-40 cents. If C7 were tuned at +10 cents to match with lower notes for example, if there were 30 cents inharmonicity between the first and second partial of C7, C8 would form a beatless, 2:1 octave with C7 at +40 cents.

If you tune so that triple octaves are exactly in tune, C7 can end up being around +20 cents and C8 can easily end up being +50 cents. With that amount of stretch, you will hear some beating in the single octaves in the higher part of the 6th octave and throughout the 7th. That beating can get to the "rapid" point, 3-4 beats per second at the extreme high end of the 7th octave but it is usually not perceived by the musician as an unpleasantly "beating" octave. It sounds good, clean and crisp to most people.

You should always tune octaves for zero beats at the particular partial of interest. This means that if you are tuning octaves up, the higher note will only beat at zero for one of its partials, due to inharmonicity. A tuner exercises judgment as to which partial should be used (the higher the partial selected, the more the stretch of the tuning). The partial selected should vary depending upon where it is on the piano. Also, there are sometimes issues in particular pianos that cause a tuner to make other compromise judgments that don't exactly align with this procedure.


Hop