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Re: Help with best octave sizes [Re: Mark Cerisano] #2406608
04/05/15 02:17 AM
04/05/15 02:17 AM
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Mark Cerisano I PM'd you the results of the survey as the web survey hangs on the submit, asking me to "add an email account"


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Re: Help with best octave sizes [Re: Mark Cerisano] #2406831
04/05/15 05:29 PM
04/05/15 05:29 PM
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Mark Cerisano Offline OP
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Kees,

Yes that's it.

Re pure 6:3. It only sounds like a pure 4:2/pure 6:3. In actuality, it can't be but we can't hear it.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2406895
04/05/15 11:07 PM
04/05/15 11:07 PM
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I may be interesting to mention how the octave spread relates to inharmonicity, at least from a theoretical point of view.

I use the following definition of the IH constant "B", which I think is a different "B" than the one you use, it's just a matter of convention. From tunelab manual:

IH(n) = B x (C[n] - 1)

(Comment: IH(n) is the amount of cents that partial n is sharp.)

where C[n] is given by the lookup table
n C[n]
--------------
1 1.000
2 4.000
3 8.450
4 13.18
5 19.72
6 27.27
7 35.53
8 46.25
etc.

On all piano's I have data on B(A4) = 2*B(A3), roughly (about 15% accurate).

So if that holds the octave spread (the cents difference between A3 tuned as 4:2 and tuned as 6:3 to A4) will depend only on B(A4).
Working it out I get that a good rule of thumb is:

Octave spread = 2.5 * B(A4).

Range of B(A4) on piano's I have data on is 0.6-1.8.

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2406899
04/05/15 11:39 PM
04/05/15 11:39 PM
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Mark Cerisano Offline OP
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Am I correct in calculating that your final formula indicates a octave spread of
2.5*0.6 to 2.5*1.8 which is 1.5 to 4.5?

If so, it does not follow my findings.

Assuming the human ear cannot hear beat speed differences less than 3% (according to my limited study) and considering the fact that I have tuned octaves where I cannot hear a difference between M3M10 and m3M6, that implies that the differences are less than 3% and the cents value of that spread is less than 0.5.

Also, octave spread, intuitively, should vary with some function of the difference between B(A3) and B(A4). Your formula suggests octave spread depends only on B(A4). That doesn't make sense because with a constant B(A4), changing B(A3) will alter the octave spread because the difference between A3(4) and A3(6) will change while A4(4) - A4(2) remains unchanged. But octave spread depends on delta 4:2 and delta 6:3, therefore octave spread changes.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
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Re: Help with best octave sizes [Re: Mark Cerisano] #2406904
04/05/15 11:56 PM
04/05/15 11:56 PM
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Vancouver, Canada
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Originally Posted by Mark Cerisano, RPT
Am I correct in calculating that your final formula indicates a octave spread of
2.5*0.6 to 2.5*1.8 which is 1.5 to 4.5?

If so, it does not follow my findings.

Assuming the human ear cannot hear beat speed differences less than 3% (according to my limited study) and considering the fact that I have tuned octaves where I cannot hear a difference between M3M10 and m3M6, that implies that the differences are less than 3% and the cents value of that spread is less than 0.5.

Also, octave spread, intuitively, should vary with some function of the difference between B(A3) and B(A4). Your formula suggests octave spread depends only on B(A4). That doesn't make sense because with a constant B(A4), changing B(A3) will alter the octave spread because the difference between A3(4) and A3(6) will change while A4(4) - A4(2) remains unchanged. But octave spread depends on delta 4:2 and delta 6:3, therefore octave spread changes.

Yes ospread depends on B(A3) and B(A4) but I find that in practice B(A4) = B(A3)/2, so then it depends only on B(A4).

Your 3% accuracy of beat speed discrimination is highly optimistic, as you used sine waves, rather than more complex actual piano tones. Assuming the actual beat speed discrimination is 9% instead, I think the numbers work out.

What range of octave spread in cents have you measured?

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2406915
04/06/15 01:26 AM
04/06/15 01:26 AM
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If there is less iH at A3 than at A4, shouldn't B(A4) approx = B(A3) * 2?


Chris Leslie ARPT
Piano technician
http://www.chrisleslie.com.au
Re: Help with best octave sizes [Re: Chris Leslie] #2406934
04/06/15 02:56 AM
04/06/15 02:56 AM
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DoelKees Offline

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Originally Posted by Chris Leslie
If there is less iH at A3 than at A4, shouldn't B(A4) approx = B(A3) * 2?

Thanks for catching the typo.

Kees

Re: Help with best octave sizes [Re: DoelKees] #2407025
04/06/15 09:36 AM
04/06/15 09:36 AM
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Mark Cerisano Offline OP
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Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT
Am I correct in calculating that your final formula indicates a octave spread of
2.5*0.6 to 2.5*1.8 which is 1.5 to 4.5?

If so, it does not follow my findings.

Assuming the human ear cannot hear beat speed differences less than 3% (according to my limited study) and considering the fact that I have tuned octaves where I cannot hear a difference between M3M10 and m3M6, that implies that the differences are less than 3% and the cents value of that spread is less than 0.5.

Also, octave spread, intuitively, should vary with some function of the difference between B(A3) and B(A4). Your formula suggests octave spread depends only on B(A4). That doesn't make sense because with a constant B(A4), changing B(A3) will alter the octave spread because the difference between A3(4) and A3(6) will change while A4(4) - A4(2) remains unchanged. But octave spread depends on delta 4:2 and delta 6:3, therefore octave spread changes.

Yes ospread depends on B(A3) and B(A4) but I find that in practice B(A4) = B(A3)/2, so then it depends only on B(A4).

Your 3% accuracy of beat speed discrimination is highly optimistic, as you used sine waves, rather than more complex actual piano tones. Assuming the actual beat speed discrimination is 9% instead, I think the numbers work out.

What range of octave spread in cents have you measured?

Kees


Using this method:

1. Record M3M10 and m3M6
2. Filter waveforms and measure bps using beats/time in Audacity or Ocenaudio.
3. Choose a partial frequence close to A3(2) for the 4:2 octave and A3(3) for the 6:3 octave.
4. Use the bps of each test to approximate the partial frequency of each octave.
5. Calculate the cents of the difference between each partial pair.
6. Use the geometrical relationship of the 4:2 and the 6:3 to calculate the octave spread.
(It is interesting, and validating, to note that, mathematically, no matter what size the octave is, the octave spread allows calculates out the same.)

With that system, I have measured numerous octaves and their tests, and the range is:

0.08 to 5.00


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2407129
04/06/15 02:43 PM
04/06/15 02:43 PM
Joined: May 2010
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Vancouver, Canada
DoelKees Offline

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Originally Posted by Mark Cerisano, RPT
Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT
Am I correct in calculating that your final formula indicates a octave spread of
2.5*0.6 to 2.5*1.8 which is 1.5 to 4.5?

If so, it does not follow my findings.

Assuming the human ear cannot hear beat speed differences less than 3% (according to my limited study) and considering the fact that I have tuned octaves where I cannot hear a difference between M3M10 and m3M6, that implies that the differences are less than 3% and the cents value of that spread is less than 0.5.

Also, octave spread, intuitively, should vary with some function of the difference between B(A3) and B(A4). Your formula suggests octave spread depends only on B(A4). That doesn't make sense because with a constant B(A4), changing B(A3) will alter the octave spread because the difference between A3(4) and A3(6) will change while A4(4) - A4(2) remains unchanged. But octave spread depends on delta 4:2 and delta 6:3, therefore octave spread changes.

Yes ospread depends on B(A3) and B(A4) but I find that in practice B(A4) = B(A3)/2, so then it depends only on B(A4).

Your 3% accuracy of beat speed discrimination is highly optimistic, as you used sine waves, rather than more complex actual piano tones. Assuming the actual beat speed discrimination is 9% instead, I think the numbers work out.

What range of octave spread in cents have you measured?

Kees


Using this method:

1. Record M3M10 and m3M6
2. Filter waveforms and measure bps using beats/time in Audacity or Ocenaudio.
3. Choose a partial frequence close to A3(2) for the 4:2 octave and A3(3) for the 6:3 octave.
4. Use the bps of each test to approximate the partial frequency of each octave.
5. Calculate the cents of the difference between each partial pair.
6. Use the geometrical relationship of the 4:2 and the 6:3 to calculate the octave spread.
(It is interesting, and validating, to note that, mathematically, no matter what size the octave is, the octave spread allows calculates out the same.)

With that system, I have measured numerous octaves and their tests, and the range is:

0.08 to 5.00

Actually my lower limit is 0.4 (which I posted earlier) not 1.5 as I said here. Mistake. So I think the numbers agree closely enough.

It's kinda cool that you can measure inharmonicity aurally like this, I always thought of it as something you need an ETD for.

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2407260
04/06/15 09:23 PM
04/06/15 09:23 PM
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Mark Cerisano Offline OP
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Yes. For me, it is very exciting.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: DoelKees] #2407432
04/07/15 09:54 AM
04/07/15 09:54 AM
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Originally Posted by DoelKees
...

Your 3% accuracy of beat speed discrimination is highly optimistic, as you used sine waves, rather than more complex actual piano tones. Assuming the actual beat speed discrimination is 9% instead, I think the numbers work out.

...


I suspect you are right, which means it is unlikely to tune progressive RBIs aurally. So then, might it be impractical to use a temperament sequence that requires us to hear them? This is mostly a philosophical question.


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Help with best octave sizes [Re: Mark Cerisano] #2407602
04/07/15 03:47 PM
04/07/15 03:47 PM
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Mark Cerisano Offline OP
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All I know is when I tune ET and measure it, I see errors that I can confirm aurally.

However, I need to be able to hear the errors aurally first, without measuring them with a machine. That is the goal.

There is still room for me to improve.

For what it's worth, the real reason for this attempt to improve the ET temperament has to do with the accuracy needed to tune the treble. That's where the rubber meets the road vis-a-vis inharmonicity. When we consider the Railsback curve, this is obvious. These errors in temperament are not a big deal, but the error in the temperament will be multiplied into the treble and that's where small errors become big errors and affect the quality of the tuning.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: UnrightTooner] #2407659
04/07/15 05:42 PM
04/07/15 05:42 PM
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Originally Posted by UnrightTooner
Originally Posted by DoelKees
...

Your 3% accuracy of beat speed discrimination is highly optimistic, as you used sine waves, rather than more complex actual piano tones. Assuming the actual beat speed discrimination is 9% instead, I think the numbers work out.

...


I suspect you are right, which means it is unlikely to tune progressive RBIs aurally. So then, might it be impractical to use a temperament sequence that requires us to hear them? This is mostly a philosophical question.

Answering in similar philosophical vein, in the natural sciences you can improve accuracy of measurements by independent repeats. Typically to improve accuracy by a factor 2 you have to take 4 measurements. So maybe if you check a note and you have 4 beatrate comparisons to check, each 10% accurate, you'll get a 3% accuracy.

This is just idle speculation to pass the time while my coffee is brewing.

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2407730
04/07/15 09:43 PM
04/07/15 09:43 PM
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Mark Cerisano Offline OP
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For your fun.

http://howtotunepianos.com/octave-tuning-app/

Just tune A3 until the octave sounds the best you can get it.

Email me the number at the bottom and I'll email you back the octave size and spread (which should be the same for all the octave sizes).

This was done by tuning A3A4 as best I could. Then using Audacity to record A3 and A4 and create multiple A3's, each 0.0588% apart which is 1 cent.

To get better resolution, I need to record two A3's, 0.5 cents apart and alternate between the two sets I create with Audacity. I may do that next.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2407744
04/07/15 10:57 PM
04/07/15 10:57 PM
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Originally Posted by Mark Cerisano, RPT
For your fun.

http://howtotunepianos.com/octave-tuning-app/

Just tune A3 until the octave sounds the best you can get it.

Email me the number at the bottom and I'll email you back the octave size and spread (which should be the same for all the octave sizes).

This was done by tuning A3A4 as best I could. Then using Audacity to record A3 and A4 and create multiple A3's, each 0.0588% apart which is 1 cent.

To get better resolution, I need to record two A3's, 0.5 cents apart and alternate between the two sets I create with Audacity. I may do that next.

Cool, was I the first to take the test? Sounds like I selected equal beating 4:2/6:3 and octave spread is 1 cent.

Kees

Re: Help with best octave sizes [Re: DoelKees] #2407787
04/08/15 01:14 AM
04/08/15 01:14 AM
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Mark Cerisano Offline OP
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Hi Kees,

Yes, you were the first. Thanks.

Octave spread is the same for all octave sizes and based on the few measurements I've taken, it is 1.25 cents which puts it as a medium octave which according to my hypothesis, sounds good as a wide 4:2, narrow 6:3.

Your octave tests as a pure 4:2 (0.3%/0.03 cents) and a narrow 6:3 (17.6%/1.23 cents).

Did you try all of the octaves?

(There are some bugs in it yet.)


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2407792
04/08/15 01:40 AM
04/08/15 01:40 AM
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Mark Cerisano Offline OP
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I thought the a3's were progressive but I'm getting some feedback that perhaps they are not. I.e. octave 8, 9, and 10 progress as ok, rolling, less rolling. I tuned a3a4 the best I could and then measured a3 and a4. That was octave 16, which strangely enough, measures very close to octave 8.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2407797
04/08/15 01:55 AM
04/08/15 01:55 AM
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DoelKees Offline

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Originally Posted by Mark Cerisano, RPT
Hi Kees,

Yes, you were the first. Thanks.

Octave spread is the same for all octave sizes and based on the few measurements I've taken, it is 1.25 cents which puts it as a medium octave which according to my hypothesis, sounds good as a wide 4:2, narrow 6:3.

Your octave tests as a pure 4:2 (0.3%/0.03 cents) and a narrow 6:3 (17.6%/1.23 cents).

Did you try all of the octaves?

(There are some bugs in it yet.)

I took the liberty of downloading the audio files and do a frequency analysis and found the octave spread is 1.1, close. But the 4:2 bps of my selection is 0.4 bps and the 6:3 bps is 0.3, according to my analysis.

Partial frequencies I got are
a4 = 440.127
880.866
1323.121

a3(one I selected) =
219.161
439.576
659.606
880.491
1101.407
1323.386
1545.818

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2407977
04/08/15 01:11 PM
04/08/15 01:11 PM
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Mark Cerisano Offline OP
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Could be a bug in which octave you are listen to and which number is posted on the page. Wordpress does funky things with JavaScript.

All I do is use a band pass filter on the waveform to visually create the beats. Then drag through so many beats and ocenaudio displays the time to 1/1000 of a second. Then a simple beats/time.

Our numbers seem way off. Can you send me the audio file you analyzed. We should be getting same numbers.

Btw, are you using a spectrograph? I can't figure out how you can get accurate measurements by looking at those wide colour bands. Maybe after lunch, you could post a brief procedure ;-)


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2407978
04/08/15 01:13 PM
04/08/15 01:13 PM
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Mark Cerisano Offline OP
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Oh, you must be using a FFT. Which one?


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2407988
04/08/15 01:40 PM
04/08/15 01:40 PM
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Originally Posted by Mark Cerisano, RPT
Oh, you must be using a FFT. Which one?

I use custom partial detection software, not really FFT. It was tested against prout's data set and analysis method a while ago and I think it's very reliable.

Files I used were kawai-a3-08.mp3 and kawai-a4.mp3.

Kees

Re: Help with best octave sizes [Re: DoelKees] #2408068
04/08/15 05:32 PM
04/08/15 05:32 PM
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Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT
Oh, you must be using a FFT. Which one?

I use custom partial detection software, not really FFT. It was tested against prout's data set and analysis method a while ago and I think it's very reliable.

Files I used were kawai-a3-08.mp3 and kawai-a4.mp3.

Kees


Kees, I am interested in how your custom partial detection software works. The partial detection software I publish here a few weeks ago also attemps a method not based on FFT but does produce a frequency spectrum by phase detection methods. This has been my ongoing project.

Could you PM me with your reply?


Chris Leslie ARPT
Piano technician
http://www.chrisleslie.com.au
Re: Help with best octave sizes [Re: Chris Leslie] #2408076
04/08/15 05:45 PM
04/08/15 05:45 PM
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Originally Posted by Chris Leslie
Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT
Oh, you must be using a FFT. Which one?

I use custom partial detection software, not really FFT. It was tested against prout's data set and analysis method a while ago and I think it's very reliable.

Files I used were kawai-a3-08.mp3 and kawai-a4.mp3.

Kees


Kees, I am interested in how your custom partial detection software works. The partial detection software I publish here a few weeks ago also attemps a method not based on FFT but does produce a frequency spectrum by phase detection methods. This has been my ongoing project.

Could you PM me with your reply?

This has been discussed here several times in the past. Search pianoworld for "http://www.cs.ubc.ca/~kvdoel/publications/pres.16.6.pdf" and you'll see the threads.

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2408077
04/08/15 05:49 PM
04/08/15 05:49 PM
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Chris Leslie Offline
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Thanks. I'll see what I can understand from that.


Chris Leslie ARPT
Piano technician
http://www.chrisleslie.com.au
Re: Help with best octave sizes [Re: Chris Leslie] #2408152
04/08/15 09:40 PM
04/08/15 09:40 PM
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Originally Posted by Chris Leslie
Thanks. I'll see what I can understand from that.

We can take it offline if you want to know more. My email is my profile (My PM are turned off).

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2408187
04/08/15 11:33 PM
04/08/15 11:33 PM
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Mark Cerisano Offline OP
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Kees,

I am not crazy about using frequency detecting methods because I want to focus on using technology to help us tune better by ear. Frequency measuring software is counter productive because my ear will never be able to measure 440hz, but it can hear and compare beat speeds up to a point. That's why I prefer the filtering and counting beats technique.

But more to the point, JavaScript numbers arrays from zero and I did not advance the counter before displaying it. That means the octave you choose is a3-09. Try that. I think we should get better numbers with that.

Last edited by Mark Cerisano, RPT; 04/08/15 11:48 PM.

Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2408196
04/09/15 12:13 AM
04/09/15 12:13 AM
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Originally Posted by Mark Cerisano, RPT
Kees,

I am not crazy about using frequency detecting methods because I want to focus on using technology to help us tune better by ear. Frequency measuring software is counter productive because my ear will never be able to measure 440hz, but it can hear and compare beat speeds up to a point. That's why I prefer the filtering and counting beats technique.

But more to the point, JavaScript numbers arrays from zero and I did not advance the counter before displaying it. That means the octave you choose is a3-09. Try that. I think we should get better numbers with that.

That solves the discrepancy. For a3-9 I get 4:2 bps 0.13 and 6:3 1bps, 0.25 cent and 1.25 cent which is close enough to what you got.

You may not be crazy about measuring frequencies but if you can measure them you'll also know the beat rates. I agree if all you have is a (recording of) an interval the best method is to measure beat rates directly. This is definitely more accurate and ties in better with aural techniques.

Glad we solved this problem.

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2408263
04/09/15 04:54 AM
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I have not read the whole thread, but I guess it would be important to have data not just for large grand pianos but also for smaller grands and uprights.


Nordiska 120CA (Dongbei) upright from about 2004. Yamaha CP33 digital. Sennheiser HD 600.
Re: Help with best octave sizes [Re: Mark Cerisano] #2409086
04/11/15 06:23 AM
04/11/15 06:23 AM
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Mark

>http://howtotunepianos.com/octave-tuning-app/

I'm not a tuner

I prefer 6 or 7

Between 5 and 13 (maybe 15) sound 'ok' to me

I'm surprised how little tolerance there is between the "good" (6-7) and the "lower bound" (5) while there seems much more tolerance towards the upper bound 13

bad ---- ok - good ------ ok ----------- mmm ---- bad
1 2 3 4 - 5 -- 6 7 -- 8 9 10 11 12 13 14 15 16 17 18

BTW I hear a disturbing 'crack' at the start of the sound, like clipping. Maybe your samples are a bit clipped?




[Linked Image][Linked Image][Linked Image][Linked Image]
Re: Help with best octave sizes [Re: Mark Cerisano] #2409547
04/12/15 05:00 PM
04/12/15 05:00 PM
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Mark Cerisano Offline OP
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The clipping is the sound of the key being hit. I choose to keep it in.

Thanks for taking the test.

I assumed since Audacity did a simple percent alteration to the original waveform, that each A3 would be changed by a constant amount. Turns out that may not be true. From preliminary measurements, the octaves are not uniformly changing in size. More work to be done. 15 was the original octave tuned by myself by ear.

You should definitely hear a rolling in the 4:2 and 6:3 partials in the lower octaves, 6 and 7 especially. Have a listen again and focus your ear on A4 and E6.

Last edited by Mark Cerisano, RPT; 04/12/15 05:01 PM.

Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
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