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Question on tuning in ET #2267209
04/26/14 01:42 AM
04/26/14 01:42 AM
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Phoenix, AZ
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Chloe J. Scott Offline OP
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This isn't another thread about ET vs. any other T, it's just a few technical questions about tuning.

1) When you are tuning in ET, are you trying to hit the theoretical frequencies calculated by the 12th root of 2? I actually ran a great big Excel spreadsheet to calculate the frequencies out to their 8th partials so I can see what they are (theoretically).

2) When tuning a 4th, which partials are you listening for?

As an engineer I'm not afraid of techno-speak or calculations so lay it on me.

Thanks for your help.

James

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Re: Question on tuning in ET [Re: Chloe J. Scott] #2267221
04/26/14 02:56 AM
04/26/14 02:56 AM
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Oakland
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BDB Offline
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1. No, I am trying to hit intervals so they sound like they are proper for equal temperament. Numbers are not involved at all.

2. Fundamentals. They beat against each other, according to their maxima and minima, and I am listening to the relationship of those beats, and comparing them with adjacent intervals.


Semipro Tech
Re: Question on tuning in ET [Re: Chloe J. Scott] #2267235
04/26/14 04:34 AM
04/26/14 04:34 AM
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Canberra, ACT, Australia
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Chris Leslie Offline
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Hi James

1) No. The 12th root of 2 frequencies are only theoretical. The only exception is the first note that we tune, usually A4=440Hz against some accurate source, and from there all other notes are tuned by progressively tuning intervals until the whole piano is done. With each interval, the note being tuned is played together with a previously tuned note or notes and a judgement is made about the intonation based on the beat rates of nearly coincident partials. The main complication arises because of the inharmonicity of the piano strings in which the actual partial frequencies become increased from theoretical. Because of this, the tuned notes above A4 automatically become higher in frequency than theoretical so that they sound harmonious with the increased frequency of the higher partials for the already tuned notes in the middle of the piano. Conversely, the tuned notes lower than A4 automatically become lower in frequency than theoretical so that their sharpened higher partials match the notes in the middle of the piano.

2) When tuning a 4th, we listen for the beating that happens when the nearly coincident 4th partial of the lower note, and the 3rd partial of the upper note, sound together. Traditionally, a judgement is made out the tuning based on the rate of the beating which is about 1 beat per second for an ET 4th with inharmonicity in the middle of the piano. In practice, many tuners use other techniques based on the relative beat speeds of rapidly beating intervals arising from a common note a M3rd below the lower note and a M6 below the upper note.


Chris Leslie
Piano technician
http://www.chrisleslie.com.au
Re: Question on tuning in ET [Re: Chloe J. Scott] #2267268
04/26/14 07:21 AM
04/26/14 07:21 AM
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Strong, Maine
David Jenson Offline
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1. The piano is a musical instrument. I tune for the best musical sound. I pay no attention to the mathematical theory. It's really useless in the real world of spinets, beat up old uprights, and small grands.

2. I have no idea, and amazingly it turns out that I don't really need to know what the partial is. It's just there.


David L. Jenson
Tuning - Repairs - Refurbishing
Jenson's Piano Service
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Re: Question on tuning in ET [Re: Chloe J. Scott] #2267272
04/26/14 07:39 AM
04/26/14 07:39 AM
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People only hear beats at coincident partials--which means technicians essentially tune by unison, no matter what interval they are playing.

You need to account for inharmonicity in your spreadsheet.

Also, you need to account for the number of audible partials heard. You can't hear the first few partials in the bass, and the descant only has a few audible partials.


Masters degree in piano technology, +factory(s) training, etc., blah, blah, yada, yada, yada...[uncensored break-out in song]..."it don't mean a thing, if you aint got that swing."
--Klavierbaukuenstler des Erwachens--
Email: klavierbaukuenstler@gmail.com
Re: Question on tuning in ET [Re: Chloe J. Scott] #2267275
04/26/14 08:02 AM
04/26/14 08:02 AM
Joined: Nov 2013
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Southwestern Ontario
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prout Offline
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Originally Posted by James Scott
This isn't another thread about ET vs. any other T, it's just a few technical questions about tuning.

1) When you are tuning in ET, are you trying to hit the theoretical frequencies calculated by the 12th root of 2? I actually ran a great big Excel spreadsheet to calculate the frequencies out to their 8th partials so I can see what they are (theoretically).

2) When tuning a 4th, which partials are you listening for?

As an engineer I'm not afraid of techno-speak or calculations so lay it on me.

Thanks for your help.

James

If you were tuning a pipe organ to ET, the answer is yes, since wind excited pipes have essentially no inharmonicity (i.e., all partials are exact integers of the fundamental).

A spreadsheet for piano ET, which includes, for each note, the inharmonicity constant, which is unique for each string, not just each note, and also includes an additional constant for bridge/soundboard anomalies, particularly in the bass region, could allow you to tune a piano in nearly perfect ET. It would still likely sound terrible, since our brains (ears) want to hear a musical sounding piano, and that requires stretching the octaves even beyond what would be calculated by the spreadsheet. The amount of stretch is a personal choice.

Re: Question on tuning in ET [Re: Chloe J. Scott] #2267288
04/26/14 08:42 AM
04/26/14 08:42 AM
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Montreal, Quebec, Canada
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Mark Cerisano Offline
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Hi James,

I am an engineer too, as well as quite a few other technicians. And a very many non-engineer technicians know more about the mathematics and physics of tuning than I and many other engineers do.

As for your questions, here are my comments:

We do not listen to the fundamental as one person said. It does not produce beats. Although Virgil Smith did talk about the "natural beat" when tuning the bass, but I don't know the physics for that for sure. I suspect something to do with difference tones.

As for not listening to partials, that is one person's approach. For me, I take it to the other extreme, with very much success and predictability. Listening to beats in order to tune precise pure 12ths, or pure 19ths, or pure 22nds, and decide where in the keyboard I change from one to the other, allows me a pallet of tone to choose from, and reproduce consistently. (With all the talk of ET versus UT, I am surprised that no one has mentioned the treble temperament. Pure 22nds throughout the piano, sound much much different than pure 19ths, for example.)

Music should not be math, from an emotional point of view, but it is. We can't get away from the fact that music is full of math, no matter how much we want it to be surreal. The math allows me to be musical and consistent at the same time.

In order for you to understand why the 12th root of 2 doesn't work on a piano. look up inharmonicity.

Best Regards,

Last edited by Mark Cerisano, RPT; 04/26/14 08:45 AM.

Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Question on tuning in ET [Re: prout] #2267319
04/26/14 10:13 AM
04/26/14 10:13 AM
Joined: Mar 2008
Posts: 9,230
France
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Olek Offline
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Originally Posted by prout
Originally Posted by James Scott
This isn't another thread about ET vs. any other T, it's just a few technical questions about tuning.

1) When you are tuning in ET, are you trying to hit the theoretical frequencies calculated by the 12th root of 2? I actually ran a great big Excel spreadsheet to calculate the frequencies out to their 8th partials so I can see what they are (theoretically).

2) When tuning a 4th, which partials are you listening for?

As an engineer I'm not afraid of techno-speak or calculations so lay it on me.

Thanks for your help.

James

If you were tuning a pipe organ to ET, the answer is yes, since wind excited pipes have essentially no inharmonicity (i.e., all partials are exact integers of the fundamental).

A spreadsheet for piano ET, which includes, for each note, the inharmonicity constant, which is unique for each string, not just each note, and also includes an additional constant for bridge/soundboard anomalies, particularly in the bass region, could allow you to tune a piano in nearly perfect ET. It would still likely sound terrible, since our brains (ears) want to hear a musical sounding piano, and that requires stretching the octaves even beyond what would be calculated by the spreadsheet. The amount of stretch is a personal choice.


I do not agree that much with your last sentence.

The stretch is dictated by the iH and that one raise fast in the zone the ear hear less well so that reinforcement of pitch seem to correct the impression of justness that we hear.

Indeed those partials being high of the theoretical frequencies that could be created from the fundamental, allows for some margin, more or less tense octaves and intervals, but to me the octaves are still within the existing spectra, or the fast beating intervals begin to scream which is not much appreciated.

I would replace "our personal preferences" by something driven by the instrument and certainly also the way we are influenced by the room acoustics while tuning.

regards


Professional of the profession.
Foo Foo specialist
I wish to add some kind and sensitive phrase but nothing comes to mind.!
Re: Question on tuning in ET [Re: Olek] #2267328
04/26/14 10:37 AM
04/26/14 10:37 AM
Joined: Nov 2013
Posts: 4,468
Southwestern Ontario
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prout Offline
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Joined: Nov 2013
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Originally Posted by Olek
Originally Posted by prout
Originally Posted by James Scott
This isn't another thread about ET vs. any other T, it's just a few technical questions about tuning.

1) When you are tuning in ET, are you trying to hit the theoretical frequencies calculated by the 12th root of 2? I actually ran a great big Excel spreadsheet to calculate the frequencies out to their 8th partials so I can see what they are (theoretically).

2) When tuning a 4th, which partials are you listening for?

As an engineer I'm not afraid of techno-speak or calculations so lay it on me.

Thanks for your help.

James

If you were tuning a pipe organ to ET, the answer is yes, since wind excited pipes have essentially no inharmonicity (i.e., all partials are exact integers of the fundamental).

A spreadsheet for piano ET, which includes, for each note, the inharmonicity constant, which is unique for each string, not just each note, and also includes an additional constant for bridge/soundboard anomalies, particularly in the bass region, could allow you to tune a piano in nearly perfect ET. It would still likely sound terrible, since our brains (ears) want to hear a musical sounding piano, and that requires stretching the octaves even beyond what would be calculated by the spreadsheet. The amount of stretch is a personal choice.


I do not agree that much with your last sentence.

The stretch is dictated by the iH and that one raise fast in the zone the ear hear less well so that reinforcement of pitch seem to correct the impression of justness that we hear.

Indeed those partials being high of the theoretical frequencies that could be created from the fundamental, allows for some margin, more or less tense octaves and intervals, but to me the octaves are still within the existing spectra, or the fast beating intervals begin to scream which is not much appreciated.

I would replace "our personal preferences" by something driven by the instrument and certainly also the way we are influenced by the room acoustics while tuning.

regards


Yes, I see your point Isaac. When I said that I was thinking of the tendency of tuners to change the amount of treble stretch in a concert hall to make sure the sound reaches the back of the hall, as opposed to less stretch in a recording studio or small room. Also, the amount of bass stretch is mentioned by tuners here. Changing the stretch can make the bass richer as opposed to deeper. (I am stating these things from memory and may be incorrect. Please correct my statements as necessary.)

And I am sure you would mention, correctly, that the quality of the unison has a large effect on how the sound is perceived.

Re: Question on tuning in ET [Re: Chloe J. Scott] #2267524
04/26/14 08:55 PM
04/26/14 08:55 PM
Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
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Mark Cerisano Offline
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Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
I absolutely choose my own stretch.

Having said that, there was a time when I believed the tuner did not have a choice; an octave is an octave and there is only one size that sounds best.

Now, when tuning the treble, I choose which SBI to make pure; octave, 12th, 19th, or 22nd. This is a very small window, but the different stretches have a different colour. Pure 19ths have unique biting octaves and fourths, but very pleasant wide chords and lots of resonance in the mid range.

I do this all with the P4 window.

Does anybody else do this?


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Question on tuning in ET [Re: Mark Cerisano] #2267600
04/27/14 03:17 AM
04/27/14 03:17 AM
Joined: Mar 2014
Posts: 561
Northern CA
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Parks Offline
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Originally Posted by Mark Cerisano, RPT


Music should not be math, from an emotional point of view, but it is. We can't get away from the fact that music is full of math, no matter how much we want it to be surreal. The math allows me to be musical and consistent at the same time.


Oh Mark, and you chastised me for asking how to measure pure intervals in cents!!


Michael

"Genius is nothing more than an extraordinary capacity for patience."
Leonardo da Vinci
Re: Question on tuning in ET [Re: Chloe J. Scott] #2267608
04/27/14 04:47 AM
04/27/14 04:47 AM
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Montreal, Quebec, Canada
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Mark Cerisano Offline
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I'm sorry, I don't recall the post. If I did indeed chastise you, I am deeply sorry and apologize.

Last edited by Mark Cerisano, RPT; 04/27/14 04:49 AM.

Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Question on tuning in ET [Re: Chloe J. Scott] #2267621
04/27/14 06:05 AM
04/27/14 06:05 AM
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Posts: 9,230
France
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Olek Offline
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what surprised me is that you could not provide the formula for Hz to cents . It may be simple maths for an engineer. or at last the logical for it.

is it so difficult ?

Regards


Professional of the profession.
Foo Foo specialist
I wish to add some kind and sensitive phrase but nothing comes to mind.!
Re: Question on tuning in ET [Re: Olek] #2267649
04/27/14 08:33 AM
04/27/14 08:33 AM
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Montreal
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pyropaul Offline
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Originally Posted by Olek
what surprised me is that you could not provide the formula for Hz to cents . It may be simple maths for an engineer. or at last the logical for it.

is it so difficult ?

Regards


Here you go :Hertz<->Cents convertor - you can download the spreadsheet too. The formula is also given at the bottom of the page:

or c = 1200 log2 (f2 / f1)

There's lots of other useful conversions shown.


Paul.

Last edited by pyropaul; 04/27/14 08:35 AM. Reason: re-order for clarity
Re: Question on tuning in ET [Re: Olek] #2267667
04/27/14 10:11 AM
04/27/14 10:11 AM
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Mark Cerisano Offline
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Montreal, Quebec, Canada
Originally Posted by Olek
what surprised me is that you could not provide the formula for Hz to cents . It may be simple maths for an engineer. or at last the logical for it.

is it so difficult ?

Regards


Hi Isaac,

I recently wrote that some non-engineer technicians know more math about tuning than some engineers do. Thanks for proving my point ;-)


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Question on tuning in ET [Re: Chloe J. Scott] #2268703
04/29/14 02:18 PM
04/29/14 02:18 PM
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Re: Question on tuning in ET [Re: Chloe J. Scott] #2270828
05/04/14 05:37 AM
05/04/14 05:37 AM
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Hope the reading was helpful.

James, could you manage to include the effect of inharmonicity in your big excel sheet and satisfy the progressive M3rds, M6ths?

Re: Question on tuning in ET [Re: Chloe J. Scott] #2271744
05/06/14 06:05 AM
05/06/14 06:05 AM
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Olek Offline
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ET is compromising natural resonance of the piano, the point is to have it in the ear at the time the ET model is applied so not to dehumanize too much the end result !
In the end I believe that "tempering" means to keep the fast beating intervals to get too screaming.

Each new note tuned is judged vs the natural present consonance of the instrument, and adjusted so that is retained and can be retained higher/lower in the scale.

Doing so judging only by a theoretical model is taking something from the possible harmony.

That may imply that tuning with too much compromising for instance in intention to have some pure quadruple octave based on a very faint partial match, is useless.

Due to the "bandwidth" of acceptability (I do not really understand the principle but I see what is it about) , The strength of medium intervals and octaves seem to "attract" the "in tune" impression for the external octaves.


Last edited by Olek; 05/06/14 06:09 AM.

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I wish to add some kind and sensitive phrase but nothing comes to mind.!

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