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Hi Folks,

I've been doing some playing around with a tuning algorithm for setting the temperament octave, based on the actual frequencies of the partials for each note. I used a couple of different tools to measure the partials (they both produced very similar numbers, although not exactly the same), and then calculated an inharmonicity constant for each partial. There were a couple of strings that had a negative constant for one or two partials. This seemed odd to me, so looking at the actual frequencies of these particular partials, I could see that they were, in fact, slightly flat compared to the theoretical values (i.e. with no inharmonicity). I re-recorded the notes to make sure there wasn't something wonky with the recordings, and basically got the same results.

Does this seem right? I thought that inharmonicity resulted in partials being sharp of the theoretical values. Could some actually be flat or does this mean that my tools for measuring the frequencies are not accurate?

Why do you pose an either/or assumption? It could be both actual anomalies and aberrant measurement.

I genuinely think it sounds like a fun experiment you are doing. However, I disagree with the premise for developing a temperament. Let me explain...

First of all, is the unproven assumption that devices are capable of accurately detecting the richness of what Brian Capleton (author of the most complete and authoritative work on piano tuning) calls "the soundscape". No device yet made (to my knowledge) is able to detect and measure the complete richness of the soundscape. So, devices are set up to measure whatever they can and whatever the inventor thinks is relevant.

Secondly, the soundscape has yet to be fully defined -- much less any understanding of how the various elements of the soundscape interact as a whole or what the relative weight of those various elements may be as related to what people perceive to be in tune. We don't clearly know when partials are sharp, flat, or right on. I know that sometimes a given partial may not even be present on a given string. This all "comes out in the wash" so-to-speak if tuning is being done aurally but it becomes a problem if a tuning aid has been set to listen to that partial to make a determination of what the fundamental should be set at.

Let me be clear... I'm not against electronic tuning aids, In fact, I have two -- each of which at one time was sold at great price to piano technicians as the "latest and greatest" but which were subsequently cast off by their previous owners when the next iteration of "latest and greatest" came out. I just think that people who use them need to be aware of their limitations. And limitations do exist. My goodness, just a couple of days ago I ran into a situation where a tuning aid (one of the"big name" ones selling for $hundreds) told someone to tune a note an octave flat! It was an uncommon (but not unheard of) scenario, but still...

So, I hope you proceed. Improvement can only happen as people continue to develop ideas and technologies. At the same time, be skeptical about your assumptions.

Can anyone direct me to where I read the following. Standing waves can cause some partials to be termination reflected to waveform positions that overtake other partials.

In addition to the text there was a diagram illustrating the effect.

Ian

I have heard of this phenomenon before and at the moment, that is all that I can say about it but you are not the only person to have discovered it. Personally, I have never run across it.

Remembering that I had seen some discussion on the old PTG Pianotech some 20 years ago, I did a quick search and found a line of discussion. I copied something to reassure you that you are onto something:



I am not sure if the January 1991 article that was mentioned is accessible on the PTG site or not. I would also like to look into this because I seem to recall that Jim Coleman, Sr. had written about it.

The note B2 on Yamaha GH1 models is a particularly bad note, for example. It is size 18 plain wire where there clearly should be a wrapped string. The note is virtually untunable but aural tuning finds something that seems to be the best possible compromise. When that note is measured electronically after aural tuning however, it is always significantly sharp of where it would be expected to be to fit the scheme. This is possibly because of negative inharmonicity and that is what I seem to recall Jim Coleman, Sr. discussing on Pianotech about that particular note on those instruments.

I don't know if I would call it negative inharmonicity. A "wild partial" is how I think of it. Seems just about every piano I tune has notes where the various tests show contradictory errors, usually in wound strings. (I tune aurally) I usually go for the best 5th/octave, but check with the double octave and 12th.

Correct me if I am wrong, but I believe iH can be calculated from the frequencies of any 2 partials. Should be able to use an algorithm to determine if it is true negative iH or just a wild partial by comparing the iH value from a number of pairs.. But then what to do about it? Might depend on the strength of the partial whether it can be ignored or not.

Best of luck!

In theory iH can be calculated from any two partials, but in practice each pair may yield a different result.

Stride88, if you are calculting a temperament using measured partials could you tell us how you are going about this?. Are you doing it like an aural sequence from a starting note?

Bill,

I read this from a technical article not from a forum or blog. I'm sure I found it when searching for inharmonicity topics but have failed to find it again. Not a problem for me it was just that I thought if found it might be useful for this thread.

Ian

Thanks for the comments and interest.

First off, I want to let you know that I am not a piano tech. I am pursuing this only out of interest and so that I can possibly tune my own piano.




Chris - that is exactly what I am doing. I am following an aural tuners sequence, but instead of listening for beats I am doing a series of calculations and solving for the fundamental frequencies to give me the same beat rates. So in my algorithm, I just enter the partial frequencies for all the notes in the temperament octave, set the concert pitch, press a button, and voila, it calculates the fundamental frequency for each note.

The next step is to use a chromatic tuner and for each note, offset the A440 by an amount that will result in the correct frequency for the applicable note. This offset is also calculated in my program. I can then tune each note with the chromatic tuner.

I haven't actually tuned my piano yet using this method but it looks good on paper. Also, I know there is much more to tuning than setting the correct pitches. I've been reading a lot, researching, and talking to my own piano tech. I've been touching up unisons for years and I think I've got decent pin/string setting technique, so I'm going to give it a try .

Even if this works, it's obviously not very practical for a professional tuner, but I'm hoping it will give me decent results on my own piano.

Beemer, my post was directed at the original poster, not you. Sorry.

Negative IH would imply that all partial are lower than harmonic, which seems unlikely from a physics perspective.
More likely is a soundboard/bridge coupling or some interference from loose windings which would alter just 1 partial.

Kees

Though not particularly pertinent to this, I recall Dr. Al Sanderson talking about the Astin Weight piano: "I measured it...that thing had negative inharmonicity...that is one weird piano!"

Pwg