Talk:Piano acoustics

Merge from Railsback curve
I am suggesting we merge Railsback curve into this article, since currently it does not explain much that is not already described in more detail at Railsback curve. Eventually other acoustic properties of the piano might be added as well. - Rainwarrior 23:20, 9 June 2006 (UTC)

I would be wary of merging - it seems to me that acoustic properties of the piano should be kept in Piano acoustics (and fleshed out with piano-acoustics related material currently at Railsback curve, and matters relating to the construction of the curve and the concept of stretched octaves being favourable due to non-ideal acoustic properties should be kept in a Railsback curve article (with both articles linked to each other). The concept of a Railsback curve is presumably applied to other instruments too - the harp and pipe organ, for example. Does anyone know if the name 'Railsback curve' is specific to piano tuning?. Chrisjohnson 13:15, 11 June 2006 (UTC)


 * It is definitely specific to the piano, but the effect does apply to a few other inharmonic instruments; not so much the harp as it has less tension and less sustain, and not at all the pipe organ (pipes are not appreciably inharmonic). - Rainwarrior 17:55, 11 June 2006 (UTC)

Railsback curve was merged into Piano acoustics by Opus33 on 18:55, 17 June 2006.

Talk merged from old Railsback curve article
(Sorry, I'm sure this is not the right way to merge, but at least the talk is now here.) Opus33 20:45, 17 June 2006 (UTC)

Railsback curve edit June 9, 2006
Reasons for my edit on June 9, 2006:


 * 1) Piano technicians are indeed conscious of this effect; understanding of it is essential to the proper tuning of the piano. Though this process has arisen out of a process which is intuitive, this does not mean that a piano tuner doesn't know what's happening.
 * 2) The paragraph beginning If inharmonicity is not taken into account... makes strange suggestions about tuning practice. What I mean is that inharmonicity needs to be taken into account in order to produce a tunning that ignores it. (This is related to the first issue about it being the intuitive approach.)
 * 3) The intensity of sound only really varies between zero and maximum when the two tones are equal in intensity. (I'm removing this little inaccuracy, and leaving the reader to find a more detailed description at the beat article.)
 * 4) Two basic causes: this is incorrect. The lower strings are not substituting the resonance effect; the primary cause is still string stiffness which is augmented by resonance more in the bass. There are more details to the strings of a piano, which I have grouped with a revision of the above under shape of the curve.

Rainwarrior 23:03, 9 June 2006 (UTC)


 * I'm also suggesting we merge this page with Piano acoustics, as the latter contains the same content in less detail, but has a more general title, giving it the possibiliy of containing more at some later point. - Rainwarrior 23:18, 9 June 2006 (UTC)


 * I'm basically happy with the changes. You're right; I shouldn't have suggested that technicians are generally unaware of the effect.  I did wonder if they were sometimes unaware of the named curve itself.


 * I'm not in principle opposed to a merge, but I'm concerned that people wouldn't be able to find the contents via the title "Railsback curve." I wasn't able to find out much about it through either a Wikipedia or a Google search, which is why I wrote the article in the first place.


 * Incidentally, with respect to stiffness-induced inharmonicity, I have a paper here which suggests that it accounts only for about 5 cents worth deviation in the lowest octaves, and that the rest is due primarily to resonances from the soundboard. I'm not sure the reference is kosher--do you recognize it?  L.I. Ortiz-Berenguer, F.J. Casajus-Quiros, M. Torres-Guijarro, J.A. Beracoechea, "Piano Transcription Using Pattern Recognition: Aspects on Parameter Extraction."  In Proceedings of the Seventh International Conference on Digital Audio Effects, pp. 212-16, 2004.  Am I misinterpreting this paper?  I was going to post this citation, but I thought I'd wait to see if this interpretation remained in the article. BrianTung 07:12, 10 June 2006 (UTC)


 * You can redesign bass string core and winding diameters, and unwound parts to change inharmonicity with good predictability without doing anything to the panel, it's a subject that has received a lot of attention since 1938, here's some literature that I found useful: Harvey Fletcher, (1964) "Normal Vibration Frequencies of a Stiff Piano String" JASA V.36, n.1 ; Firth, Ian (1986) "Overwrapped Strings: Design Guide" Journal of the Catgut Acoustical Society N. 45 ; Sanderson, Albert "Piano Scaling Formulas" Piano Technology Topics (handout) ; Roberts, David (1990) The Calculating Technician, Piano Technicians Guild Foundation. I don't remember any one of them mentioning "Railsback curve" and even inharmonicity curve is a little misleading because there usually are discontinuities for instance from string winding variations. Mireut 12:58, 10 June 2006 (UTC)


 * If I did a merge, Railsback curve would still redirect you to the acoustics page, where it would have its own prominent heading. For familiarity with the term, I'd seen many graphs of the curve but I didn't actually remember the Railsback name from it. (In response to Mireut below, yes, "inharmonicity curve" isn't the right term at all as it is discontinuous and shaped differently, though it would be a related curve, a derivative of the Railsback curve.) I haven't heard of this Oritz-Berenguer et. al., though its title intrigues me (music recognition algorithms are right up my line of interest), but the title suggests that this article is about research about computer tone recognition, rather than on piano acoustics itself, meaning that any information on piano acoustics in that article was probably gleaned from other sources. I had a good reference on the subject lying around here at one point, but I have temporarily misplaced it; intuitively I would point out that if the soundboard resonance was the main cause of inharmonicity in the bass, large grand pianos would not have much less inharmonicity than uprights, as they do. - Rainwarrior 15:38, 10 June 2006 (UTC)


 * Actually, the article is (perhaps surprisingly) at least half about the actual acoustics, and if I recall correctly, it gives every impression of adding original content in that area. I don't have it with me at the moment, but when I get back in the office, I'll check it again. BrianTung 21:00, 10 June 2006 (UTC)


 * I found it here. I'll take a look. - Rainwarrior 22:05, 10 June 2006 (UTC)


 * Ah, I think I understand. In the conclusion the article states that "lower partials are very affected by the soundboard and their use must be avoided", which I believe means that the bass frequencies are very hard to use for tone recognition, but then it follows that for notes with fundamentals in this range, higher partials can be used instead (because of how difficult it is to guess soundboard reasonance). So, my interperetation here is that in the lowest frequencies string inharmonicity is overcome by soundboard inharmonicity, but not at all frequencies output by the string. By and large, I think string inharmonicity is still the main factor (which plays out in the grand vs. upright psychoacoustical anecdote I related earlier). - Rainwarrior 22:40, 10 June 2006 (UTC)

Piano acoustics
There have been some changes to Piano acoustics recently (Railsback curve was merged in, and I did a little bit of rewriting); I know you have knowledge relating to piano wire issues, would you consider giving it a look over? - Rainwarrior 05:26, 18 June 2006 (UTC)


 * Some comments if you want to discuss or use them (or wait till I have more time to work on the article)


 * The strings of a piano vary in thickness, with bass strings thicker than treble.


 * String length varies in proportion much more visibly than thickness.


 * These differences in string thickness follow from well-understood acoustic properties of strings.


 * Presumably this refers to the following paragraph but it does not explain these very well. There at least has to be explanation about what length of string is meant.


 * Assuming that two strings were equally taut and thick, a string that is twice as long as another would vibrate with a pitch one octave lower than the other. However, if one were to use this principle to design a piano it would be impossible to fit the bass strings onto a frame of any reasonable size;


 * Robert Wornum used one size wire, including the wound strings core wires, in his equal tension design. (So far as I know it was unique to him, his contemporaries systematically did not use equal tension, you might find a couple papers here that examine about scaling practice,, suggesting the emphasis about equality of anything apart from quality is a relatively modern one.)


 * That link is broken, and I simply can't believe you could use one size wire for more than about two octaves. The term "equal tension" makes the notion especially troublesome, because you couldn't tune a single note without affecting its tension. Funfree (talk) 17:39, 26 May 2014 (UTC)


 * the lowest strings would travel so far in vibrating that they would strike one another.


 * Not an awfully limiting factor since Mathushek (1851) and Steinway (1859) strings usually fan out and you can fan the action like in old Chickering grands.


 * thick string vibrates more slowly than a thin string of identical length and tension;


 * And material since heavy is more important than thick.


 * In pianos, long strings are considered desirable.


 * A funny statement following a section about how long strings are impractical.


 * Piano design strives to fit the longest possible strings within a given case size;


 * Material strength is more important than case size, remember that the oblique uprights of 1830s already had bass strings as long as any overstrung ones in the same size case as a vertical strung one (and in 1830s rectangular and wing shapes weren't the only ones).


 * each--as a rough approximation--at a pitch which is a multiple of the fundamental.


 * "rough approximation of an integer multiple of the frequency of the fundamental" is still vague.


 * Inharmonicity is related to length: the longer the strings are, the more they approximate ideal theoretical strings, and the closer to ideal harmonic alignment the tuning of the piano becomes, see the Railsback curve effect below.


 * A Pythagorean scale makes inharmonicity quarter each lower octave but still makes a nice curve. I think about half is common from before it could be measured and predicted.


 * The most prized pianos are (all else being equal) those with the longest strings. The flagship model of Steinway, the Model D, is 8 feet, 11 3/4 inches long (274 cm.); and the longest Fazioli piano is 10 feet, 2 inches (308 cm.).


 * (The Steinway Model C is identical in design.) Funfree (talk) 17:43, 26 May 2014 (UTC)


 * "Most prized" is opinion and their cost also reflects the materials needed, the quantities that are produced and the sort of market they aim at.


 * The shortest strings used in pianos are found in cheap spinet models, which are smaller than most other pianos.


 * Possibly the shortest long strings (begs questions about expensive spinets and what other pianos are smaller still) - but loose tolerances and bad quality control ("cheap"), and also back scale, bridge design and placement will affect the sound of low tenor and bass notes.


 * The highest notes on a keyboard suffer greatly from inharmonicity, as it is difficult to use a longer, thinner, string without it being succeptible to breakage.


 * Better to have figures instead of "difficult"


 * The highest keys on lower quality pianos often produce no note at all, only an unpleasant percussive sound.


 * This has to do with bridge placement (and condition), terminations, and hammer striking points (and hammer condition) more than inharmonicity - struck metal bars don't just make noise.


 * With the Railsback merge there's way too much emphasis on one detail, I think other popular topics that should be mentioned are things like hammer behavior, missing modes, what a bridge does, duplexes and undamped treble strings, soundboards as transducers, soundboard size, and soundboard resonances, for a start. I think a few figures, maybe even a little math would not be out of place in an article about acoustics Mireut 16:21, 18 June 2006 (UTC)


 * Thanks! This will definitely help get the article in shape. My edits yesterday mostly only shuffled around the information that was already there, but a lot of it was bothering me. I had actually removed a malformed reference to Pythagorean scaling (I knew the effect from readings in violin construction, but I didn't remember it ever being called "Pythagorean" before), which I think should be restored. (Maybe Pythagorean scaling deserves its own small page as well? This is definitely a widespread issue in instrument building... I'll get to that if I can dig up my references.) If you don't get to it I will try to implement your suggestions, but I think you've got a lot more detailed knowledge of piano acoustics than I do, so you could do a more thorough job than I could. - Rainwarrior 16:49, 18 June 2006 (UTC)


 * Denzil Wraight. "Pythagoras and the Scale Design of Early Harpsichords in France, Germany, and Italy." http://www.harpsichord.org.uk/guests/dw/wraight.htm - Mireut 16:41, 17 October 2006 (UTC)


 * Another thought, that might help organize this stuff, is that Piano _physics_ would cover action and keys, materials, reasons for going out of tune, etc., as well as the topics already mentioned. - Mireut 20:11, 20 June 2006 (UTC)


 * That's a good idea. - Rainwarrior 03:21, 21 June 2006 (UTC)


 * This one gives an idea how I think the article should look like, but doesn't make much sense to add without the different sections too.


 * The acoustics of a piano depends on a series of interrelated mechanical systems. Each note is furnished with a key and train of action levers used propelling the hammer against the strings corresponding to the note. A sounding length is established between a nut and soundboard bridge in one or more stretched strings fastened at both ends on rigid pins. The metal strings are arranged in order of their pitch, from the heavy and long low sounding bass strings on the left hand side to the light and short high pitched treble strings on the right, so that the nut and bridge can form continuous curves positioned in relation to the the points where the hammers are made to strike. The bridge controls the transfer of the vibrations to the soundboard whose large area produces sound more effectively than the strings alone. - Mireut 18:46, 25 June 2006 (UTC)

I'd like to hop in here as an amateur pianist and dilettante of knowledge. I loved this article! I had never heard of the Railsback effect, and found it most interesting. You guys are doing a great job - keep it up! Maurice Fox 16:05, 26 June 2006 (UTC)

Comments by Woodstone
In the statement about longer is better (less inharmonic), the key supposition is indeed for strings at the same frequency. Another question. I know that most modern eletronic pianos work with samples from real pianos in several frequency ranges. That seems to imply they have to be tuned with a Railsback curve as well. Does anyone know this for sure? And how about synthesized keyboards? Are they inharmonic on purpose? How can an acoustic piano play together with an electronic one? &minus;Woodstone 18:13, 28 June 2006 (UTC)


 * I moved your comment down here, it was hard to spot wedged in there at the top. Is your first sentence a question? (Yes, it is important that the two strings being compared for inharmonicity are at the same pitch. Is that your question?) Sampling keyboards differ, actually. Some do take the railsback curve into effect, some do not, but most good ones do (I've played a few cheap ones that have had rather terrible results in their piano samples). Synthesizers do not in general, and should not, unless they are inharmonic in a similar method to the piano (FM synthesis, for instance, is often inharmonic, but does not have the same effect on tuning because it is a different kind of inharmonic). Acoustic pianos playing with electronic instruments, or any instruments really is kind of a dodgy thing. Often the ensembles are big enough that the problem isn't noticeable, or sometimes the problem actually adds a charming kind of character to the performance. Some electronic keyboards are retunable and will let you enter a custom Railsback type curve in case you're playing with a piano, but in my experience very few people who own these expensive keyboards actually learn how to use this feature. - Rainwarrior 23:03, 28 June 2006 (UTC)

The first line was not a question, but meant as an approval of your change to my preceding edit. I had known about the Railsback curve for a long time, but reading the article just triggered my curiosity about the consequences for electronic instruments. Thanks for the clear answer. It might be appropriate to enter some of it into the article. It would also be useful to state some numbers about the deviation (in cents), because the scale in the graph is not readable. &minus;Woodstone 08:21, 29 June 2006 (UTC)


 * It's really tricky to give exact numbers... different types of strings, different lengths of strings, different pianos have different amounts of inharmonicity. The Railback Curve doesn't have a specific magnitude, just a general shape that will be slightly different depending on the particular piano. - Rainwarrior 05:04, 30 June 2006 (UTC)


 * http://www.goptools.com/gallery.htm Here you can see how some piano technicians look at piano scales, from Tremaine Parsons' PScale program, it looks the same as Sanderson's chart and the old Scale Designer program for Atari. I think they're all single iteration, but it balances with using one value for tensile strength. Mireut 21:23, 11 July 2006 (UTC)

Multiple strings
Most piano keys strike more than one string. Why is that and in what interval are those strings tuned? In octaves? DirkvdM 08:05, 12 September 2006 (UTC)


 * Hello, DirkvdM,


 * Question 1: Edwin Good (book cited in Piano) says it's to equalize loudness.  The bass notes would drown out the treble, if the treble notes didn't have multiple strings.  In fact, Good thinks the modern piano is deficient in this respect:  it requires players to use great force with the fingers of their right hand to "bring out the melody".  The Borgato piano firm is experimenting with using four, not three, strings in the treble; see Innovations in the piano.


 * Question 2: Unison, the very same note.  Octaves are for harpsichords and organs.   [Can anyone else confirm the following?  I believe it's supposed to be an exact unison.  No slight detuning, such as electronic musicians employ.]


 * Cheers, Opus33 16:00, 12 September 2006 (UTC)


 * Hahah, it's "supposed" to be an exact unison. It varies to taste though. In practice you can only get a unison so good, and the better you make it, the faster you'll notice it go out of tune. So it depends on how often you want to be tuning your piano. Also, there are frequent uses of the badly-detuned unisons when a "beer-hall" effect is desired (e.g. Berg's Wozzeck asks for a piano with detuned unisons). - Rainwarrior 16:37, 12 September 2006 (UTC)


 * Good's kind of right but presenting it that way turns it backwards, since wound strings were introduced after multiple strings per note. More strings also reflect the hammer better, so the effect of shifting hammers to strike fewer strings has more effect than just less sound. Mireut 18:57, 12 September 2006 (UTC)


 * If something to cite is wanted,


 * The usual assumption is that the function of triple stringing in the treble is to increase the volume in this normally weak register. But modern acoustic theory tells us that a third string only increases volume by about 10%. Perhaps the third string was really added to solve the problem of breaking strings, since a third string adds more resistance to upward motion of the hammer. Paul Poletti, Scale Analysis, 1997. p28 http://www.polettipiano.com/Media/scale.PDF


 * - Mireut 14:32, 26 October 2006 (UTC)


 * And in the Benade chapter I linked, "With any reasonably well-tuned piano, the perceived loudness at your ears ... should be roughly 40 percent higher when three strings are active than when only one is producing a sound" (§17.3, it also talks about their mistuning) - Mireut 14:06, 27 October 2006 (UTC)

Terminology
Piano technicians use many terms of cant, usually without giving much thought to any confusion they might engender outside the trade. The explanation of the Railsback curve uses "equal temperament" to refer to the "ideal" (another term of cant!) pitch frequencies generated by repeatedly multiplying and dividing 440 Hz by the twelfth root of two. (This gives A0 a frequency of exactly 27.5 Hz, A6 1760 Hz, etc.) But "equal temperament" is also used to indicate the temperament we almost always use, in which the (logarithms of the) frequencies of A#, B, C, C#, D, and so on (the chromatic scale), are equally spaced. The word "scale" is also used in more ways than one (in discussing temperaments and scaling), as are "note", "tone", "partial", "fundamental", "octave".... I don't mean to imply that it's technicians who are to blame, of course, since similar (and some of the same) ambiguities arise in the usage of scientists, musicians, and engineers. But this is one place where such ambiguities ought to be revealed, avoided, explained, cleared up, etc. I'd like to see the discussion of Railsback curve amended to avoid the implication that pianos are not tuned according to equal temperament. 4.234.48.120 22:43, 28 January 2007 (UTC)


 * But the implication and fact is that pianos are not tuned with equal temperament! &minus;Woodstone


 * Maybe stretched tuning would have been a better place to integrate Railsback curve, since temperament can be a little distinct from acoustics. - Mireut 19:40, 4 February 2007 (UTC)

Major physics input
I have made major rewrites to much of the article. I am a physicist, not a musician. Most of what I know about pianos I learned from Gabe Weinreich when I was a graduate student at U Michigan. He is one of the authors of the five lectures on pianos, and my addition of the section on multiple strings is based on my memory of his lecture. The section on fundamental frequencies is basic physics, and perhaps could be replaced with a link to the article on vibrating strings. The section on inharmonicity is physics-based, but I might not be doing a good job explaining my intuition.

I think that the merger with the Railsbuck curve is not smooth. Right now, it duplicates much of what is said in the rest of the article.

I would not have voted to merge the articles. The tuning system is only a small part of the acoustics of the piano, and the Railsback curve more appropriately belongs in the section on stretched tuning since it applies to all stretched systems. Basically any instrument in which there are multiple sound-producing elements, from the harmonica to the organ to the accordian to the guitar also suffer from stretched tuning, and they all have their own Railsback curves for the same fundamental physical reasons as the piano does: the idealization of an organ pipe as a thin tube of air breaks down because of its finite thickness.

David s graff 22:27, 7 February 2007 (UTC)


 * I noticed that Opus reverted my changes of piano acoustics. I didn't really feel like my additions were off topic, but I later found pages on vibrating strings that were somewhat similar to mine.  I started my rewrite because there seemed to be a few basic mistakes in what you wrote.

First of all, you confused "Thickness" with "Linear Mass Density". My nylon string guitar has thicker strings than my steel string guitar even though they are under much less tension because nylon is much lighter than steel. This effect also explains why gold-wrapped strings would sound better than aluminum wrapped strings.

Also, your discussion completely disregards another key variable in determining string tone, tension. A piano builder could always use strings of the same length and thickness but with different tensions. Your section only discusses two of the four variables which determine string frequency.

Since there are four variables which can adjust tension, it can get confusing for the reader. I could have changed the title from "String Length and Thickness" to "String Length, Thickness, composition, and tension", but that seemed lame, so I changed it to "Fundamental Frequency"

I felt especially in discussions of inharmonicity that the reader would need to be familiar with the effects of tension and the difference between thickness and mass density. And since the physics is so basic (Basically, distance = rate x time) I thought it good to put in. I might say that we don't need the equation for wave velocity, but then we should still say that waves travel slower on more massive strings and faster on tenser strings.

This may all come from our different backgrounds, Opus is a musician and to me his comments include just barely enough physics to get by. I am a physicist, most of what I know about this really comes from the study of periodic stars (which actually obey basically the same equations as a trumpet, but can take days or years to oscillate) and I guess my comments include just barely encluded enough music to get by. Could you instead try to work in some of my ideas? David s graff 22:57, 7 February 2007 (UTC)

Hi there is just some contradictory information in this article regarding tension of the string

Inharmonicity and piano size "Basic strategies to REDUCE inharmonicity include decreasing the thickness or increasing the wavelength of the string, choosing a flexible material with a low bending force, and INCREASING the tension force so that it stays much bigger than the bending force."

Shape of the Curve "INCREASED tension, decreased length, or increased thickness all CONTRIBUTE to inharmonicity." Thanks, not sure which is right, great article.

Disappointing article
This article lacks precision of logic, terminology, wording, physics, music theory, and mathematics. The inharmonicity equation ought to appear, carefully explained, in the article on inharmonicity, and used in this article to demonstrate the pitch phenomena to which piano tuning must comply. The physics of string stiffness ought to be elucidated in one article or the other (or a third devoted to it), and the characteristic acoustics of struck strings ought, at least, to be mentioned, and linked to an article on the acoustics of stringed instruments -- plucked, bowed, and struck. D021317c 11:41, 4 October 2007 (UTC)


 * Go ahead and make the improvements you propose. &minus;Woodstone 12:54, 4 October 2007 (UTC)

Citation request
The above comment was hidden in the article in response to a request for a citation. 1+1=2 is not comparable in that it should be obvious to everyone, not just mathematicians. Wikipedia policy, however, requires that once a citation is requested it is required. Hyacinth (talk) 01:32, 6 October 2010 (UTC)
 * "That is obvious to every physicist. Would you demand a citation for "1+1=2"?"
 * OK, that was my hidden comment. For a scientific question like this, I would request a proof, not a citation. What is citation in humanities, that is proof in science. Anyway, I found a citation and added it inline. --Peter Buch (talk) 12:15, 27 October 2010 (UTC)

Railsback
I've been tuning pianos since a few years before I went to the Sims School of Piano Technology in Columbus, GA in 1970, where I got a very thorough education in piano tuning (along with lots of other stuff). But I've never heard of Railsback. This is not to say that he doesn't deserve a lot of credit, but I can't see that he contributed anything to the state of the art. There certainly ought to be a Wikipedia article about him! In any case, all this information about partials, the inadequacy of tuning to the mathematically-derived equal temperament frequencies based on the twelfth root of two, etc., MUST have been known well before the twentieth century, because you simply can't tune a piano without an understanding of inharmonicity and its consequences. So Railsback came at least a century after the technology became known. Moreover, in making pianos, it's essential to understand all this stuff in order to select the strings, their lengths, masses, and tensions, and the overall strength required for supporting the TONS of tension on the hardware. So this article isn't really (except for the brief mention of Railsback's contribution (not!) about piano tuning. What it is about is the mathematics of equal temperament. Note that there's nothing requiring that the octave be divided into twelve equal intervals (intervals are determined by the ratios between the frequencies of the two notes involved). In fact, doing so means that none of the intervals are pure, except for octaves. Bach's "The Well-Tempered Clavier" provides very nice music by which to test out the pleasantness of all the key signatures. Any tuner who could tune a piano to pass such a test would have to be doing something right, and using the frequencies mathematically derived here would definitely fail such a test badly.

Here's what I recommend: Change the name of the article to "Equal temperament". Funfree (talk) 17:33, 26 May 2014 (UTC)


 * The article does not claim that Railsback invented anything, just that he quantified what was piano tuners were already doing.


 * Of course he didn't invent anything. But why should this "curve" be named after him? It seems to me all he did was publish an article, publicly divulging what had probably been considered a trade secret among piano makers. Perhaps it should be called the Steinway curve, or the Cristofori curve. Funfree (talk) 19:39, 26 May 2014 (UTC)


 * I have to take it back. I said I'd never heard of Railsback, but actually, years ago, when I was experimenting with HTML, I tried to mark up an interesting article, which I posted |here here on the Internet. As you can see, Robert W. Young, at the very end of his 1952 article, credits Railsback thus: "Fifteen years ago Professor O. L. Railsback aroused interest of which this paper is evidence; when he started to use the first chromatic stroboscope to test piano tuning, he very soon found evidence of string inharmonicity." I'll probably find something about Railsback on the Acoustical Society of America's website. Funfree (talk) 19:56, 26 May 2014 (UTC)


 * I've started a new article, "Ora Railsback", but I really don't know what I'm doing, and hope somebody can help whip it into shape. Funfree (talk) 21:04, 26 May 2014 (UTC)

Main complaint
My main complaint is that piano acoustics is a vast field. "Scientific American" included a nice article about it in the 1950s. Rossing and Fletcher contributed a nice book, as did Harry F. Olson. But this article so far only discussed a rather trivial subject, and does so in a way that hasn't anything to do with pianos, except perhaps for the layout of the keyboard. To get into the acoustics of the piano, you have to begin with the acoustics of strings, and then differentiate the acoustics of struck strings from bowed or plucked strings, and then introduce some concepts of differential equations, then the various effects of the soundboard, which are really complicated, and then you might be ready to examine the differences between theory and real-world measurements. Tuning is a rather minor aspect of the subject, and what makes it difficult is not even addressed here; not that it should be. It should have a separate article. So should the influence of inharmonicity on piano tuning. So should varieties of tunings and their names. So should practical aspects of piano tuning. So should the history of piano making and technology. So should industries allied to piano manufacturing. So should biographies of famous contributors to piano history. So should the impact of World War I on the strength of piano wire. So should fallacies in the field of piano acousics (which are quite numerous), so should the selection of materials for pianomaking. But almost all of the information already here belongs in a separate article altogether. It's practically unrelated to pianos, or acoustics. It's more about playing around with a calculator. Funfree (talk) 19:39, 26 May 2014 (UTC)

The best equation
Albert E. Sanderson, in one of his earlier patents related to the Sanderson Accu-tuner, presented an equation right at the outset. This equation, which I studied for years, is unparalleled for giving the ideal frequencies of each of the partial tones for each of the 88 notes (and potentially more) on a piano. Unfortunately, I had to send off for a copy of the patent from the patent office to read it. But other people may succeed where I failed, about fifteen years ago. There really ought to be a Wikipedia article on Sanderson, for many reasons, and another on the equation and its analysis. You can't understand the Railsback curve without it. (By the way, there seem to be a couple of Wikipedians following me around and pestering me like gnats. Please ignore them.) Funfree (talk) 15:28, 1 June 2014 (UTC)

Harmonics, overtones, partials
In every source I have ever seen, all three of the above terms are specifically stated to mean *exactly and completely* the same thing, except with regard to whether the fundamental note qualifies as one of them. I think it would take a lot of *very* fine newer sources to dislodge that from my brain. Is it possible that there's a terminology mistake in this article so that something that isn't a partial has accidentally been called a partial? TooManyFingers (talk) 02:52, 24 August 2021 (UTC)

On closer inspection, it appears as if these words may be being opposed with each other based on using one word for the theoretical ideal expected sound and a different word for the sound that the string is actually producing. From my point of view it would be best to support that with sources from *outside* of piano tuning publications, since these are words used throughout the broader field of music. TooManyFingers (talk) 03:11, 24 August 2021 (UTC)


 * Harmonics are by definition multiples of a fundamental (first harmonic is the fundamental itself). Overtones and partials are other frequencies than the fundamental produced by an instrument. On strings and wind instruments most overtones are close to harmonics, since they produce sound in a close to one-dimensional medium. On percussion instruments, like bells and timpani, the sound producer is two-dimensional and overtones are much more complex. &minus;Woodstone (talk) 05:37, 24 August 2021 (UTC)