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I was taught that the fundamental was the first harmonic and that the second harmonic was the first partial.....
Have I remembered that right?

Greetings,
For clarity, piano techs have usually numbered the "overtone series" beginning with 1 for the fundamental. The fundamental can't be an overtone, and overtones and harmonics are often mixed, interchangeably. Designating the fundamental as the first 'partial' allows us to compute combinations of intervals more easily and avoids the semantic confusion of overtones and harmonics. A guitar player will usually call the first overtone the "harmonic" in that touching the string without fretting at the 12th fret produces the first harmonic.
hence confusion.
Regards,

That's kinda how I remembered it as well. Until I checked up, for the new "Electronic Tuning" page of my website.

As I understand it now in relation to vibrating strings:

HARMONICS are integer multiples of the fundamental frequency. The first integer is 1, so the first harmonic is the fundamental frequency multiplied by 1, which is the fundamental frequency. Harmonics are theoretical numbers.

PARTIALS are the actual frequencies produced, rather than the theoretical harmonics. The First partial is also the Fundamental. The second partial will be near, but not exactly, the value of the second harmonic, etc.

OVERTONES are the partial frequencies ABOVE the fundamental. The First Overtone is the Second Partial. It is possibly best to avoid talking of Overtones at all, in relation to piano technology.

Ah, I was typing at the same time as Ed!

Well most modern digitals use samples of real pianos so they absolutely have the same partials as the acoustic they were sampled from. Modelled pianos will be a bit different (as you can change the inharmonicity factor) but they can still be extremely close to real pianos.

From a theoretical perspective, this is false, because the overtone series is infinite, and piano samples are finite.

From a practical perspective, piano samples may contain all audible overtones. Frequencies beyond the Nyquist limit will be filtered out, as will harmonics at amplitudes below the dynamic range floor of the mics used when sampling. The latter perhaps could lead to audible differences, but I'm not sure. The advertised dynamic range specs of the best mics would suggest audible harmonics should be captured, but the issue is complex.

Having the same partials doesn't mean that a digital will function the same as an acoustic piano. With the digital pianos, the partials will just beat. With acoustic pianos, the partials get pulled together. Some tuners sense this as the tone getting "sucked in/together." That effect doesn't happen on the digital piano.

If you think our ears have infinite bandwidth you're sorely mistaken. I'll grant you the non-linear mixing effect of the human ear drum could potentially introduce intermodulation artifacts from ultrasonic partials but I suspect these are below the noise floor of the ear anyway.



Good point about the Weinrich effect - but this occurs during tuning, no? Once a note is tuned, all the sympathetic locking is, well, locked in. I would posit that in a blind trial of a piano tuned in ET and then retuned in software to a WT would be indistinguishable from the same piano tuned to exactly the same WT first - with both then played back through the same audio chain.

Partials are the components you get when decomposing the waveform into simple wave components, each of a single frequency. You need both frequency (term in the Fourier series) and amplitude (coefficient of the term in the Fourier series) to describe a partial.

There can be many more partials than just the principal and harmonics of a single wave vibrating in a plane. For instance, piano notes with 2 or 3 strings experience interference between the strings, and sympathetic resonance of undamped strings, which gives rise to a set of partials significantly more complex than just the harmonic series of a single vibrating string.

Good points, thank you.

It's been a long time since I read his lectures on piano acoustics. I'd have to go reread them to see how they apply.

So in one respect, yes sympathetic locking occurs at the time of tuning. There is a difference if you resonate a single note alone while tuning, vs. resonating other intervals together while tuning the note. It all will produce different results. But, even after it is set, there is still a "pull" on each note. So a C, if used as a root (of a chord), 3rd, 5th, 7th, 9th, etc. on an acoustic piano will get pulled in different directions when measured. C doesn't just stay in a fixed place and "beat" like a digital piano. There are literal shifts that take place based on what is resonating. This can be measured. Ideally, the tuner will tune the piano in such as way there is maximum flexibility in this respect. That allows the piano to sound more in tune with itself, but it also allows it sing more. For those that are familiar with the "bell-like resonance" of the golden age of pianos and tuning, this is what is going on.

Thanks Peter, that's this one isn't it? Oddly I can't find it on rollingball.com.


That's what I was expecting most people to say :-)


Is that Young's first or second temperament? And now I'm not sure if that's your preference or EBVT is!


Right, and I know some others prefer ET too. I wonder if he tried it or just imagined how bad it would be!


I like that approach! If you don't ask, you get WT. Next time, if they don't specify, maybe try La Monte Young's "The Well-Tuned Piano" :-)


Interesting. Maybe it's because guitars are often poorly tempered! Some slight differences between instruments probably makes it sounds more.. human.

truetemperament.com make squiggly fret WT guitar necks. Reviewers/bloggers think it's ET with better intonation, which it is (straight frets don't quite work as each string bends sharp a different amount when fretted).

But it's also a WT inspired by Bradley Lehman's Bach temperament. This used to be on their website (and can be found via archive.org), but now they're more vague about it. My hunch is explaining WT was confusing to customers. They still list the offsets from ET on their How to tune page though.

There's also evidence that EVH and Frusciante tuned the B string down to get pure major thirds (though in Frusciante's case it's not clear if it was intentional).


I'm a complete newbie, and the first two pieces I decided to try.. one had 6 flats and the other 5 sharps!


Yes that's what started me on this journey - sometimes picking up the guitar and feeling everything sounds bland. I'd be interested to know what these jazz pianists use, and whether they talk about it, or if it's their "secret sauce". I wonder what e.g. Nina Simone, Monk and the other greats used, and how much they understood about temperaments.


Is that similar to the unwell?


Absolutely. In 20 or 50 years time, maybe digital pianos will come with a different default, and that will then be what most people use.


Thank you, I'm familiar with larips.com but hadn't seen those articles before.


Isn't this true of ET as well? I think you're making a good point, but I'm not sure I understand it.


Maybe he's drawn to other aspects of the sound and tuning?


Um I think you just came to your own meaningful conclusion :-)

If you want to experiment though, I would go straight to pure/just intonation, meantone or quarter tones arabic-style. Get familiar with something really different. Try a 7/4 "harmonic 7th" like Michael Harrison for example.


Yes, I get the impression temperaments are not part of most people's musical education, and therefore many don't realise alternatives even exist.

I just entered the world of temperaments when my first tuning on my brand new August Forster 215 resulted in a different sound than I was accustomed - so much so that I had the piano retuned to a second temperament and am quite pleased now. Below are the tuner's notes:

First tuning -

Tuning style followed the pattern found: Sharp 4-2 tuning in bass, excessive stretch
In the 7th octave(6-3 bass and modified 4-1 tuning were used in the 7th octave used by me
double octave 4ths and 5ths in the middle of the piano)
Established pitch at 443 Hz(1st tuning)
Fine tuned to A=443 Hz(2nd tuning)

Second tuning-

Tuning style: OTS 3, 8/4 bass .5 cent treble octaves, 7th & 8th octaves: 2/1
Established pitch at 443 Hz(1st tuning)
Fine tuned to A=443 Hz(2nd tuning)

Which of the two styles above are more common?

blueviewlaguna, those are notes about how the octaves are stretched. That's different from temperament. A temperament is how the notes between the octaves are divided.

It seems like that information applies to a specific software. For example, I don't know what "OTS 3" stands for.

I don't think I said that, nor that our ears have infinite dynamic range, which I think is what you were trying to say. I don't think the tone of the SK-EX patch in my DP sounds identical to an SK-EX. There are audible differences. But as I said, from a practical perspective, piano samples may contain all audible overtones, but I'm not sure. Were you planning to offer any rigorous analysis to substantiate your claim that they are identical, even within the audible limits of human hearing?

Thanks for the clarification - I do recall my tech advising that he was changing from "favoring fifths" to "favoring thirds". The interesting part is that I had my previous Schimmel grand tuned by a different tech and I never took issue with how the tuning sounded.

Oh, well, that does sound like unequal temperament language! It sounds like they are moving from a well temperament to meantone temperament. But, meantone is very harsh in the extended key areas. Basically it doesn't work. I'd be surprised if that is really what they did.

Did you ask for an unequal temperament or anything special? Does the tuner know what kind of music you play?

No, that comment just relates to the stretch. The second tuning (referencing OTS) used Reyburn Cyber Tuner and the first tuning is cryptic enought to possibly be the notes from an aural tuning or perhaps Tunelab? If it was an aural tuning, then it is possible that the temperament was also skewed.

Ron Koval

Originally Posted by kpembrook
With UT, the partials don't line up the same way and as a result have a dissonance in the higher coincident partials.

Isn't this true of ET as well? I think you're making a good point, but I'm not sure I understand it.

****************

No. This is something that can be empirically observed. Actually, it's a function of the inharmonicity of piano wire which results in the the higher partials being sharp to whole number multiples (see ample discussion above about harmonics, partials and overtones). So, the widened thirds of ET put the higher partials "in tune" at the expense of a few beats at the fundamental or lower partials. The other tunings try for "purer" intervals but the "pure" in practice is at the fundamental or lower partial level, thus leaving the higher partials less consonant. So, the more "consonant" intervals a given tuning has the more those intervals will not be consonant at higher coincident partials. So, it's not about UT as a concept, per se. It's that the more untempered or less-tempered thirds there are, the more out-of-tune higher coincident partials there will be.

The way I learned setting the temperament from Travis's book doesn't involve counting beats. (Who can really count--or even estimate-- whether a particular third is 6.2 bps or 6.1, anyway?). I tune the thirds so that the upper partials "line up" and then the beat rates will be correct (or acceptable, or closely matching somebody's theory). The test is that 3 stacked thirds should equal an octave and that's what I get.

On a separate "note" (so-to-speak ), I'd like to bring back something I had mentioned before regarding the usage of electronic devices to "measure" what we are doing. I gained a helpful term from Brian Capleton's Theory and Practice of Piano Tuning (and I confess I haven't read all 680 pages yet). Capleton's term to describe "what we hear" is "soundscape". Electronic devices (at least not yet) do not measure the soundscape in its entirety but rather extract a single aspect of that soundscape and presents that information in some sort of display or definable quantity. The complex interactions and events of multiple-note chords (even basic two-note intervals) remains to be explored and described using scientific devices. (Not saying it can't happen -- just that it hasn't yet). My comment here is in regard to people incorrectly using what is reported by measuring devices as somehow "correct" and "true" when, in fact, they are still operating at more of a Middle Ages level in comparison to the richness perceived by the human ear even though we can't attach numerical quantities to our perceptions. Hearing is nonetheless valid.

Nice points. Capleton's book is quite something, isn't it. I really like your last two sentences above - we have yet to see a recital delivered to an audience of appreciative Electronic Tuning Devices.....