Making sense out of cents

[sprechen]

I am restoring a 1923 Steirische 3 row in Bb/Eb/Ab. I have done some tuning on others but not on this box. Now i am confused (
could be my age 79)! It's badly out of tune and this is what is confusing to me, I am using Strobe by Peterson and when I measure an A4 reed I get the following results. 1) Concert A set to 440, +16 cents, Hz 498.5 2) Concert A set to 445, -4 cents, Hz 498.5 3) Concert A set to 450, -23 cents, Hz 498.5.

Since the reed is always at 498.5 Hz,( irregardless of where the concert pitch is set) why doesn't the app say the reed is a B4 instead of an A4 when set to A=440?

Also, what is the best way to determine what pitch was the box originally tuned to? After looking at lots of measurements and trying to do some averaging I think its about 450.

Thanks for any help

 

[Glug]

I've tried to work out the tuning on a couple of old accordions.
The methods I originally decided to use were to measure average frequency for each note and put it in a spread sheet.
Then estimate the A4 value using two methods:

1) Assume each note is perfectly tuned to determine A4 reference frequency. Plot distibution of resulting A4 frequencies. Most common may be actual tuning.

2) For each note plot cents tuning error based on A = 442 or 443 and guess original pitch from distribution.

But I think the best method is to use a statistical maths package to fit an exponential curve to the measured frequencies and just read off the A4 value: I use R (https://www.r-project.org/) and the basicTrendline package.

 

[dak]

I am restoring a 1923 Steirische 3 row in Bb/Eb/Ab. I have done some tuning on others but not on this box. Now i am confused (
could be my age 79)! It's badly out of tune and this is what is confusing to me, I am using Strobe by Peterson and when I measure an A4 reed I get the following results. 1) Concert A set to 440, +16 cents, Hz 498.5 2) Concert A set to 445, -4 cents, Hz 498.5 3) Concert A set to 450, -23 cents, Hz 498.5.

Since the reed is always at 498.5 Hz,( irregardless of where the concert pitch is set) why doesn't the app say the reed is a B4 instead of an A4 when set to A=440?

I presume it does but you interpret the display wrongly.

Also, what is the best way to determine what pitch was the box originally tuned to? After looking at lots of measurements and trying to do some averaging I think its about 450.

It is probably not the best idea to tune a diatonic/bisonoric instrument with a tuner for equal temperament. That is not what the original tuning will have been using.

 

[JeffJetton]

But I think the best method is to use a statistical maths package to fit an exponential curve to the measured frequencies and just read off the A4 value: I use R (https://www.r-project.org/) and the basicTrendline package.

You could probably do this in a spreadsheet too, if you didn't want to install R, although it would present its own set of hoops to jump through.

 

[debra]

I presume it does but you interpret the display wrongly.

It is probably not the best idea to tune a diatonic/bisonoric instrument with a tuner for equal temperament. That is not what the original tuning will have been using.

That is the most essential part of all the replies!
A diatonic instrument that doesn't have all notes in each bellows direction will likely not have equal temperament tuning. The tuning can take advantage of the missing notes to tune different notes in such a way that intervals (third, fourth, fifth) can deviate less from their ideal ratio than with equal temperament tuning.
As for the the reading of the tuner, something must be peculiar in the Peterson tuner. 498.5 Hz is indeed a B4, not an A4 with about +200 cents deviation...

 

[sprechen]

That is the most essential part of all the replies!
A diatonic instrument that doesn't have all notes in each bellows direction will likely not have equal temperament tuning. The tuning can take advantage of the missing notes to tune different notes in such a way that intervals (third, fourth, fifth) can deviate less from their ideal ratio than with equal temperament tuning.
As for the the reading of the tuner, something must be peculiar in the Peterson tuner. 498.5 Hz is indeed a B4, not an A4 with about +200 cents deviation...

I found the problem! I did the same test with an app called Pano Tuner and indeed it was a B4. My mistake, the Strobe app has a transpose setting and it was set to 2. I was not aware of that setting. My bad!! So my diatonic box is indeed a C/F/Bb.

I'm new to this so I will stick to normal tuning and see how that sounds.
Thanks for the help

 

[sprechen]

After thinking about what dak and debra said, it would be foolish not to take the advice of experts! So when I get to tuning this box I will learn how to tune to NOT have equal temperaments. Is there a topic here explaining how to do that?

 

[debra]

After thinking about what dak and debra said, it would be foolish not to take the advice of experts! So when I get to tuning this box I will learn how to tune to NOT have equal temperaments. Is there a topic here explaining how to do that?

People have been studying tuning for centuries now, essentially, since (supposedly) Pythagoras discovered the problem with going up 8 octaves versus 12 quints (say from C up to a high C versus from C up to a high B#) should result in two different frequencies.
All the studies on tuning tried to hide the error somewhere, preferably in an interval that would never be played, considering the key music is written for. I don't know how you would go about doing it (but there may be masters here in the art of tuning as it evolved over the centuries).
However, if you intend to play together with other musicians who play chromatic instruments (like piano, accordion, organ, all tuned to equal temperament) then it may be best to just tune your box to the same standard.

 

[Glug]

You could probably do this in a spreadsheet too, if you didn't want to install R, although it would present its own set of hoops to jump through.

Ooooh, I didn't know spreadsheets had that built in.

I use OpenOffice calc - the Logest function does an exponential curve fit: https://wiki.documentfoundation.org/Documentation/Calc_Functions/LOGEST

 

[Giovanni]

Ooooh, I didn't know spreadsheets had that built in.

I use OpenOffice calc - the Logest function does an exponential curve fit: https://wiki.documentfoundation.org/Documentation/Calc_Functions/LOGEST

WoW you folks are indeed clever ........................I'm most impressed .....................but not much the wiser its all to much for my delicate dim brain .
thanks for you replies it is much appreciated

 

[sprechen]

I am getting closer to the tuning phase and have a couple of questions.

I have attached a zip file (Excel spreadsheet) of my measurements (cents and Hz) for the 'C' reed block. Can someone with math skills tell me if the tuning is indeed around A=450? Also, which side would be the root and the tremolo.

Why would the B side, from #7 through #11 be an octave off?

 

[debra]

I am getting closer to the tuning phase and have a couple of questions.

I have attached a zip file (Excel spreadsheet) of my measurements (cents and Hz) for the 'C' reed block. Can someone with math skills tell me if the tuning is indeed around A=450? Also, which side would be the root and the tremolo.

Why would the B side, from #7 through #11 be an octave off?

I have no idea why you made a table with A4=450 because nobody tunes to A=450. Depending on what you want a modern accordion should always be tuned with A4=440Hz or 442Hz. 450Hz is way too high and you could not play together with anyone else (except maybe bagpipes) with that tuning. When you use a single reed that should have a deviation of 0 cents and the tremolo reed typically has a positive deviation which, depending on taste, is between +8 and +24 cents (I like +12, standard Italian is +16, stronger musette is +24). When the tremolo at A4 is X the tremolo should go down as the frequency goes up, reaching about 0.7X by A5 and 0.5X by A6. Going down I aim for about 1.3X by A3 and below that tremolo goes down again because that's what our ears prefer.
The table you showed has deviations that are "all over the place" as you would expect on an accordion that hasn't been tuned for 50 years...

 

[sprechen]

I tried taking measurements at various standards and the deviations where so far off. So I tried to guess where the average might fall and came up with 450. I found through research that these old boxes varied all over the place, from the 430's to the 450's. It would not be uncommon for this old box to be tuned to 450. I don't know if I could retune it this far to 440 without getting into trouble.

Still learning and appreciate all the help!

 

[debra]

I tried taking measurements at various standards and the deviations where so far off. So I tried to guess where the average might fall and came up with 450. I found through research that these old boxes varied all over the place, from the 430's to the 450's. It would not be uncommon for this old box to be tuned to 450. I don't know if I could retune it this far to 440 without getting into trouble.

Still learning and appreciate all the help!

I'm afraid there isn't much you can do. 450Hz is way too far off to retune to something that is common today, except the standard tuning of bagpipes.
Last year we planned a concert with accordion orchestra and organ, only to find out the organ was tuned to 448Hz. That was just impossible and we have no idea why the organ was at 448Hz. But we just cancelled the concert...

 

[dak]

I'm afraid there isn't much you can do. 450Hz is way too far off to retune to something that is common today, except the standard tuning of bagpipes.
Last year we planned a concert with accordion orchestra and organ, only to find out the organ was tuned to 448Hz. That was just impossible and we have no idea why the organ was at 448Hz. But we just cancelled the concert...

Why wouldn't it be tuned to 448Hz? An organ can only be tuned higher (since like with an accordion, tuning some pipe types is a destructive process, and as opposed to an accordion, they don't have a reliable way of lowering the pitch), so every time it gets visited by a tuner, the frequency rises. After several decades, there may be a general tuning in store. That typically involves throwing the highest pipes away, building substitutes for the lowest ones (and any of those that cannot be made to be a semitone higher than with the last general tuning) while reusing some of the materials from pipes that need to be redone, and moving the pipes up. Some pipes will yield to trying to solder or patch up previously used tuning scrolls, but it's an iffish process, so the general direction is upwards. And some large pipes/types (like the wooden ones) have tuning mechanisms that are non-destructive. But the small metal pipes just don't tune reversably.

As a consequence, newly built organs tend to be lower than 440Hz, and as they grow older, they pass the 440Hz mark.

It is a question of money how far an organ is allowed to go up over the course of several tuning jobs before a general tuning gets scheduled. So pitch-rigid instruments like accordions should check before planning to play with an organ. Other wind instruments will also not be fond of significantly deviating pitches, but accordions cannot adapt at all.

 

[Tom]

Other wind instruments will also not be fond of significantly deviating pitches, but accordions cannot adapt at all.

Nice description Dak! My Fr4x accordion can be set from 415 - 466. Just sayin’.

 

[dak]

Nice description Dak! My Fr4x accordion can be set from 415 - 466. Just sayin’.

Well, you know the responses you get when pushing those buttons (the mark of a true accordion player), but I'll pretend to be in mute mode.

 

[sprechen]

Glug said:

I've tried to work out the tuning on a couple of old accordions.
The methods I originally decided to use were to measure average frequency for each note and put it in a spread sheet.
Then estimate the A4 value using two methods:

1) Assume each note is perfectly tuned to determine A4 reference frequency. Plot distibution of resulting A4 frequencies. Most common may be actual tuning.

2) For each note plot cents tuning error based on A = 442 or 443 and guess original pitch from distribution.

But I think the best method is to use a statistical maths package to fit an exponential curve to the measured frequencies and just read off the A4 value: I use R (https://www.r-project.org/) and the basicTrendline package.

In a previous reply I posted a zip file containing a spreadsheet with data I collected from the box I am working on. Help is needed with using this data to arrive at a best guess as to what was the original pitch that the box was tuned to. I need more help than 'put it in a spreadsheet'.

 

[Glug]

I took the A side push readings and fitted an exponential curve using R.




Then I used the curve coefficients and put them back in the spreadsheet:



And that shows the A4 equivalent is 449.01Hz.
That's a truly odd value, but it's what the data says.

 

[sprechen]

Thanks Glug..

I took sets of readings, tried to get an average of where the cents deviations were and then increased the A4 standard. When I got to A4=450 the + and - cents deviations averaged near zero and that's when I thought this box must be tuned near 450. Your calculation confirms that. If the y axis is Hz what is the x axis?

What formula do I need to plug into the spreadsheet to perform this calculation myself on other reed banks in this box.

Thanks Again!