Original Message:
Sent: 4/7/2026 12:52:00 PM
From: Geoff Sykes
Subject: RE: Top treble stretch? Inharmonicity . . . or our ears?
David --
In no way did I want to imply you are stupid. Fortunately your winking emojis tell me that you already understand that. Thanks. 😉
As we age everyone, especially men, suffers from hearing loss due to presbycusis. The loss of the tiny hairs in our ears that detect sounds. High frequency sounds are the first to go because the hair cells that detect them are nearest the opening of the ears and subsequently get damaged first. They are near the opening of the ears because high frequencies have much less power than lower frequencies and would diminish in power quite quickly as the sound wave travels in our ears.
Many years ago the Los Angeles PTG chapters held a meeting at the House Institute of Hearing. One of the things we learned was that hearing is so important to our survival that the brain really wants to hear everything it can. However, it doesn't really care what the frequency it's interpreting is. It just wants to hear the sound, any sound, as a warning. As a result, when hair cells die off, the brain starts using the hair cells closest to them as a backup. That means that if the hair cells for, say, A7, (3520Hz), die off the brain may start using the hair cells for 3521 or 3519 just so it can hear something. Anything. It doesn't care if it may sound flat or sharp. It just desperately wants to hear something in that area.
Not that many years ago, I attended a presentation on hearing perception at a PTG convention. I apologize for not remembering the name of the person who did the presentation. One of the things he demonstrated to us is that each of our ears hears things differently, even though the brain processes them as being the same. As an example he had a collection of tuning forks set out for us. All of them tested to be accurate at C4. When we held two of them up to our ears at the same time, one on each side, they both sounded the same and there were no beats. However, if we just took one of them and listened to it with one ear and then the other, there was a definite difference in tone. Everyone there experienced one ear as sharp and the other flat by comparison. But heard together, one on each ear, our brains interpreted them as the same.
Fletcher Munson demonstrates that high and low frequencies sound different at different loudness levels. At lower levels, bass sounds may be sharp while treble sounds may be flat. As you increase the loudness both of these extremes tend to flatten out.
I get the occasional call from a customer whose previous piano tuner was no longer available. And when I show up I can usually guess that the reason the previous tuner was no longer available is because they retired because they could no longer hear the high treble notes. And I discern this by finding the top treble notes being pulled extraordinarily sharp. Sometimes to the point that I'm surprised they weren't breaking.
All this to ask, when was the last time you had your hearing checked? 😉
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Geoff Sykes, RPT
Los Angeles CA
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Original Message:
Sent: 04-06-2026 18:39
From: David Pinnegar
Subject: Top treble stretch? Inharmonicity . . . or our ears?
Hi Geoff!
:-) Yes - of course I seem stupid ;-) but I'm not comparing these frequencies of the generator with notes on the piano which can be affected by inharmonicity. I'm listening to the raw frequencies generated by the tone generator and noting that my ears seem to want the frequencies to be higher than the 2:1 ratio of what we call octaves.
This leads to questioning whether tuning the top two octaves to the 2nd partial of the octave below or even 4th partial of the octave two octaves below is satisfying. Using my CTS5 ETD I'm using maximum stretch which takes my top octave tunings higher than the aural tuning from lower partials below, and still tend to find a flatness in the 6th octave in particular.
It's for this reason I'm personally finding the tone generator frequencies fascinating and potentially how my own hearing might be faulty.
Compared with A6 the generated frequency of A7 at 2:1 is flat to my ears. This is a hearing issue rather than a piano inharmonicity issue. Is it just my ears above 1500Hz or so or is it a general issue? If the latter it raises questions about assumptions we make in tuning the top two octaves.
Best wishes
David P
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David Pinnegar, B.Sc., A.R.C.S.
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+44 7868385643
Original Message:
Sent: 4/6/2026 6:01:00 PM
From: Geoff Sykes
Subject: RE: Top treble stretch? Inharmonicity . . . or our ears?
David --
The tone generator link is using simple x2 math for octaves. Mathematically the tone it is generating at A7, at 3520Hz, is exactly three x2 octaves above A4, at 440Hz. Therefore, using this tone generator, there are no beats when playing A4 and A7 together at the same time. If, however, you are comparing the A7 of the tone generator to the A7 on your piano, of course the tone generator is going to sound flat, and there are going to be beats. The A7 on your piano is at a higher frequency due to temperament, stretch, and inharmonicity.
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Geoff Sykes, RPT
Los Angeles CA
Original Message:
Sent: 04-06-2026 08:59
From: David Pinnegar
Subject: Top treble stretch? Inharmonicity . . . or our ears?
Hi Paul and all for thoughts on this and for practical solutions.
However, the exercise I posed was independent of strings:
With https://www.szynalski.com/tone-generator/
Open the page in two tabs or windows in your browser.
Set one to sound 440
Set the other to 440
Now go right to the note selectorand with one page still generating A440 with the other go to A6. It's in tune.
Then go to A7 and for me it's flat. Go to A#7 and it's sharp. Go to A4 then go to A#7. A#7 is more in tune then than A7. Go back to A4. A8 then is flat. A#8 is happier.
People have mentioned beats but are the beats up there really important in the music as performed?
Is there is a disconnect between the received training of the technician and beats drummed into the aural tuning world and the music for which the instrument is to serve? When I'm listening to a performance involving top octaves, I'm not listening to the beats but to the notes and the music. Are chords really relevant in the top two octaves in what is performed?
Another cause of top octaves sounding flat is the Weinrich effect where the the three strings become flat compared to a single string "correctly" tuned.
Best wishes
David P
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David Pinnegar, B.Sc., A.R.C.S.
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+44 7868385643
Original Message:
Sent: 4/4/2026 9:40:00 PM
From: Paul McCloud
Subject: RE: Top treble stretch? Inharmonicity . . . or our ears?
"So is top treble tuning really about inharmonicity? Is it more about our own ears and perception of pitch, nothing to do with the piano?" Many years ago, we had a large gathering at a chapter meeting. The question was posed by the lecturer as he played an A chord in the treble section around A4, and then stopped. "Is this note sharp or flat?" as he played A6. He tuned the A6 up or down until everyone was more or less satisfied with it. When he played the chord and A6 simultaneously, it was obvious that A6 was way too sharp. There is a psycho-acoustic effect in our hearing that we like to hear a single note played by itself at a pitch that is much higher than what we like to hear when all the notes of a chord are played. Thus, we have found that more stretch in the treble seems to be a little more pleasing. If you sharpen everything too much, you can't play the chords up there. They beat profusely. But if you hit those high notes only occasionally, it sounds good. Does it have to do with inharmonicity? I'm sure it has something to do with it, but I'm not exactly sure why. We hear things musically in different contexts. Maybe some of you who are musicians, composers and arrangers could shed some more light on this.
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Paul McCloud, RPT
Accutone Piano Service
www.AccutonePianoService.com
pavadasa@gmail.com
Original Message:
Sent: 04-03-2026 10:51
From: David Pinnegar
Subject: Top treble stretch? Inharmonicity . . . or our ears?
Hi!
Happy Easter!
I'm preparing a seminar for the UK PTA and was fiddling around with online frequency generators. For fun
is really interesting.
Open the page in two tabs or windows in your browser.
Set one to sound 440
Set the other to 440 and use the > button to increase the frequency. Hear the beats. Go to the sine tab further along to change the upper frequency from sine to triangle. The 3rd harmonic comes in.
At 506 for instance it's horrible but 513 gives an undertone starting to appear, and at 520 it's sounding nice although I don't see why it should. We can hear the undertone going lower as we get to 528 and when we get to 550 the undertone is in tune and, importantly, gets louder.
Now go right to the note selector and press Db/C# which will take you to all ET notes. Press C#5 and hear the undertone shift to be out of tune. That's our standard industry-wide tuning.
Then there's another phenomenon of importance and this relates to stretch in particular.
With the one page still generating A440 with the other go to A6. It's in tune.
Go to A7 and it's flat. Go to A#7 and it's sharp. Go to A4 then go to A#7. A#7 is more in tune then than A7. Go back to A4. A8 then is flat. A#8 is happier.
So is top treble tuning really about inharmonicity? Is it more about our own ears and perception of pitch, nothing to do with the piano. This is why in the C6-C7 region I often feel that a tuning is flat even when one's tuned it properly to the 2nd partial and instead simply go for the maximum stretch setting on my machine - and why I feel that many ETD apps are simply too complicated and clever! Were I to tune the top octave properly to the 2nd partial of the lower octave, I'd regard it as flat. But that's where one can hear it audibly resonating rather than to the 4th partial of two octaves below, and duplex scales add muddle well to the equation.
Best wishes
David P
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David Pinnegar BSc ARCS
Hammerwood Park, East Grinstead, Sussex, UK
+44 1342 850594
"High Definition" Tuning
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