Talk:Piano key frequencies

Tenor C
Keyboard instrumentalists call C3 Tenor C, not C5. We generaly use these terms: Bass C (C2), Tenor C (c3), Middle C (c4), Soprano C (c5). This is due to the range of our instrument and not based around the range of vocalists (as C5 for Tenor C would be). Most early keyboard instruments didn't extend much past C2 and C6. This can still be observed by looking at the keyboard of the modern organ. -Z. (05/15/08)

About the table
This table needs to be wikified. I'll try to get to it later. Not much time on line these days. Merry Christmas! Quinobi 13:56, 25 Dec 2004 (UTC)


 * This piano is upside down. High notes are low, and low ones high. If you turn your head left so the black keys are above the note names (as is natural), the high notes are on the left, the exact opposite of a piano. --Wahoofive 17:23, 18 Mar 2005 (UTC)


 * Well, if you look at how the frequencies are derived from the Twelfth root of two schema, you logically start at the 'bottom' or lowest frequency, which is A0 (or is it A1?) on a modern piano.Quinobi 09:26, 28 Apr 2005 (UTC)
 * This could be solved by placing the notes to the right of the Scientific Name/Frequency. —Preceding unsigned comment added by 65.110.231.134 (talk) 23:49, 17 September 2007 (UTC)
 * I don't see how that follows. The frequences are derived from A440, which is more or less in the middle. Anyway, somebody already changed it. &mdash;Wahoofive (Talk) 16:05, 28 Apr 2005 (UTC)
 * Take a look below at Octaves, Notes, Frequencies, and Appearance and let us know if you think that this needs any more work. hydnjo talk 19:43, 28 Apr 2005 (UTC)

VfD removal
Consensus was to keep, but under a new name (Piano key frequencies). There were a few votes to move, but not for that specific name: if anyone objects to that new name, feel free to bring it up here.

Here is the archived discussion: Votes_for_deletion/Virtual_piano. Antandrus 21:24, 9 Apr 2005 (UTC)


 * Hey, good. I Like the new name. Thanks. Quinobi 09:16, 28 Apr 2005 (UTC)

Oops
It appears that this piano is one octave too high. Since it's not completely trivial to fix I'll do it when I have a few minutes (unless someone gets to it first). The lowest note is A0, not A1 (notice that the dashes are confusing --there is an A-1, but not on a piano) and the top note is C8. In the Yamaha system, common on MIDI synthesizers, Middle C is C3; this sometimes causes confusion. Antandrus 22:43, 25 Apr 2005 (UTC)


 * There isn't really a standard for octave numbering. Middle C is sometimes C3, sometimes C5, sometimes C4, depending on who is writing. Aternatively some use: CC C c c' etc... It really doesn't matter what you use as long as it's consistent and understandable. Rainwarrior 18:46, 1 April 2006 (UTC)

Octaves, Notes, Frequencies, and Appearance
The keys now go from A0 to C8 as they should and with their proper frequencies. Also, the high notes are at the top which seems more natural, and the black notes are defined with both sharp and flat notation (#/b) so as to avoid confusion. And finally, the width has been adjusted to make the keys appear more like the aspect ratio of a keyboard. Thank you to Antandrus for all the tedious editing and to all the others who have helped along the way. I hope this article is done, but if it's not, well then feel free. hydnjo talk 19:38, 28 Apr 2005 (UTC)
 * Looks good. I made a few tweaks, like adding missing slashes. I took the width parameter completely off the table; tell me if it looks significantly different (it changed the word wrapping a little). But articles on Wikipedia are never "done." &mdash;Wahoofive (talk) 20:41, 28 Apr 2005 (UTC)
 * Thanks again. It looks fine. I must have been editing the dual notation with the missing slashes during cocktail time. ;-)  hydnjo talk 11:51, 29 Apr 2005 (UTC)

Reverse Frequency Formula
I didn't know where to put this but here is a formula I had just worked out to get the note index based on a frequency (or at least close to it considering rounding). It was very useful in my application to index it this way so it may be useful for others to have it clearly typed out.


 * Symboliclly: 12/log2(log(F) - Log(440*2^(-49/12))) = Note Index
 * Decimals: 39.863137*(log(F) - 1.41424686) = Note Index
 * It should be noted that both should be put on the page, since decimal points are important and the more accurate the better —Preceding unsigned comment added by Bamaboy1217 (talk • contribs) 21:26, 7 August 2009 (UTC)

Article Title
The article is not at all about Piano keys. It should be titled “Frequencies in the Diatonic Equal-tempered Scale” or something like that. — Chris Capoccia T&#8260;C 13:29, 27 July 2006 (UTC) (Changed Diatonic to Equal-tempered. Rainwarrior is right about the name of the scale   — Chris Capoccia  T&#8260;C 19:32, 27 July 2006 (UTC))

In what way is it not about piano keys? The primary datum in each row is the piano key, followed by the note name and frequency. Very useful, I found this article when I googled 'piano frequencies' and I found what I was looking for here. HighInBC 14:06, 27 July 2006 (UTC)

Because all kinds of instruments make these tones, not just pianos. Pianos were not even the first instrument to make these tones. These tones make up the Diatonic scale Equal-tempered scale, and are not restricted to any one instrument. — Chris Capoccia T&#8260;C 15:23, 27 July 2006 (UTC) (Changed Diatonic to Equal-tempered. Rainwarrior is right about the name of the scale   — Chris Capoccia  T&#8260;C 19:32, 27 July 2006 (UTC))

I did not know that, I thought pianos used a subtle variation to that scale. HighInBC 15:58, 27 July 2006 (UTC)


 * "Diatonic" would be the wrong name for this. The diatonic scale has 7 notes to the octave, not 12, and no fixed tuning (there are many ways to make a diatonic scale). This is twelve tone equal temperament. - Rainwarrior 18:10, 27 July 2006 (UTC)

From the VfD of this article:


 * The "scientific" or "just" scale uses evenly spaced notes (frequency ratio of the twelfth root of two), but the standard musical scale is slightly different.

Not sure how relevent this is to the tipic at hand. HighInBC 16:00, 27 July 2006 (UTC)


 * We certainly shouldn't have the word "just" there. It's already got a very distinct meaning in tuning theory that is not that. (See just intonation). - Rainwarrior 18:10, 27 July 2006 (UTC)


 * Equal tempered chromatic scale frequencies? I can think of titles that are more precise, but they tend to be much longer.  Ideas?  Antandrus  (talk) 16:19, 27 July 2006 (UTC)


 * This set of frequencies seems much more applicable to a synthesizer controlled by a piano sized keyboard. Someone pointed out above that a piano is slightly different than equal temperament, which it is (see Piano acoustics or Piano tuning). Basically the only thing truly "piano" about this is the 88 keys. In fact, didn't this page used to be called "Virtual piano"? "Frequencies of equal temperament" might be a better title. - 18:05, 27 July 2006 (UTC)

I probably never would have found this article if it was called "Frequencies of equal temperament". I was looking for the frequencies of piano keys, and that is what I found when I got here. I think the name apt as it is. HighInBC 19:04, 27 July 2006 (UTC)

That objection would be handled if the article was retitled "Frequencies of equal temperament", and crossreferences added for "Piano key frequencies" (along with guitar, bass, etc.) Swiss Frank (talk) 17:19, 15 July 2018 (UTC)

MIT calls their list Frequencies for equal-tempered scale. — Chris Capoccia T&#8260;C 19:32, 27 July 2006 (UTC)

As that list has more notes on it than a piano has keys, perhaps it is an apt name for their list. Ours has only frequencies for piano keys, thus the name seems proper as is. HighInBC 18:34, 19 September 2006 (UTC)

octave numbers, middle C and A440
On listening to the OGG file of 440Hz (double checked on a software signal generator), i noticed that that note is actually an A 2 octaves higher than the open A string of the guitar, (which everyone says is supposed to be A440 / A4, but perhaps they set it by the strings's 4th harmonic).

As far as i can tell from listening, the open A string on the guitar (which must be A2=110Hz if its 2 octaves below A4=440Hz) is the A BELOW the piano's middle C (as i don't have a piano, my measure of middle C is C4 from the http://en.wikipedia.org/wiki/Image:Pitch_notation.png image played on guitar), making middle C = 130.8Hz = C3.

Something doesn't add up here. Can someone please explain this?--KX36 15:43, 25 March 2007 (UTC)


 * The guitar's A string is notated as the A below middle C, and the guitar is a transposing instrument playing an octave lower than written. So the open string A is actually 110Hz. Read the guitar article for further information. &mdash;Wahoofive (talk) 16:38, 25 March 2007 (UTC)

A 440 is the A above middle C. —Preceding unsigned comment added by Zbryanpianist (talk • contribs) 20:05, 15 May 2008 (UTC)

I've long had issues trying to cross between various instruments in terms of pitch (especially with the octave transposition on guitars and bases), so I took the liberty to add equivalent open strings of guitars and string quartet instruments. 75.68.171.194 (talk) 01:49, 1 August 2009 (UTC)

Helmholtz pitch names
Hi,

I've been bold and inserted the note names using the Helmholtz pitch notation for those who don't use the Scientific A0-C8 notation. If I have caused any errors, feel free to correct, or post on my talk page. I've also converted the unicode flats/sharps into music so they display in IE.

–MDCollins (talk) 16:09, 6 August 2007 (UTC)

Other instruments
Several other instruments have been added. Perhaps we should consider renaming the article into "Instrument Frequencies". &minus;Woodstone (talk) 12:11, 1 August 2009 (UTC)

I suggest "Musical Frequencies" with crossreferences for "piano frequencies," "bass frequencies," etc. Furthermore, pianos don't even use these frequencies most of the time due to stretch tuning. Finally, is there a good reason to come up with a novel numbering system when MIDI note numbers cover the range of plausible fundamental frequencies? Swiss Frank (talk) 17:19, 15 July 2018 (UTC)
 * Regarding your last question, just one thought. Would numbering the keys 21-108 (or 12-119 for an extended piano) cause any confusion for those who are not familiar with the MIDI system? Jtrevor99 (talk) 21:40, 15 July 2018 (UTC)
 * There is nothing novel about numbering the 88 keys on a standard piano 1–88. Not only is it obvious, but the numbering is written on the levers controlling the hammers. Now, indeed numbering the extra keys may not be standard, given how rare pianos that have them are. Perhaps we could add the MIDI numbers as a separate column. Double sharp (talk) 07:51, 17 July 2018 (UTC)

Frequency Equation
Hello, I derived the equation $$ f(n) = 440 \times 2^{\frac{n-49}{12}}\, $$ just fine, but I was wondering if it could be rewritten to look a little easier (and less arbitrary) if the constant out front is not 440, but instead $$ \frac{440}{\sqrt[12]{2^{49}}} \approx \frac{27.5}{\sqrt[12]{2^{1}}} \approx 25.95654 $$ where 27.5 is the first note on the piano. Not vitally important, but the equation is a bit simpler, though less memorable and less precise? Or just as $$ f(n) = 27.5 \times 2^{\frac{n-1}{12}}\, $$ which is neither messy nor forgettable. —Preceding unsigned comment added by Andye (talk • contribs) 22:02, 13 May 2011 (UTC)

The equation is more complicated than it needs to be:

$$ f(n) = 440 \times 2^{\frac{n-49}{12}}\, $$

The expression in the power can be broken down, resulting in

$$ f(n) = 25.9565436 \times 1.0594631^{n} $$

or maybe a modestly less accurate

$$ f(n) = 25.956 \times 1.0595^{n} $$

It's less button-pushing (for manual calculations) and fewer math operations (for computational efficiency).

The accuracy of the last one:

$$ f(4) = 32.707 \approx 32.70$$    (0.02% error)

$$ f(88) = 4199. \approx 4186$$   (0.31% error)

2602:306:CED0:6D20:1D56:84B9:7741:2E69 (talk) 02:44, 31 July 2012 (UTC)


 * The formula shows clearly how it is conceived: a 12-tone equal tuning with note 49 defined as 440 Hz. Why ruin a perfectly good formula by introducing arbitrary rounding? It is also easily modifiable, in case one would like to play for example an A 435 tuning, or if one would prefer to assign A440 to note 69, as in MIDI. &minus;Woodstone (talk) 06:34, 31 July 2012 (UTC)
 * Yes, the formula is not just there for plugging into a calculator or spreadsheet; it shows the mathematical basis for the series of frequencies. As Woodstone said, it allows for adjustment of parameters such as reference frequency and distance of the reference note from the bottom of the series. __ Just plain Bill (talk) 14:38, 31 July 2012 (UTC)

Extensions?
It would make sense to also include the notes from C0 to G♯0, as well as D♭8 to F8, as these notes appear on some pianos (although the standard range is undoubtedly still A0 to C8). Double sharp (talk) 08:02, 31 January 2014 (UTC)
 * I was about to write the same thing. The Hertz range for these pianos is 16.352 to 5587.65.  It wouldn't hurt to include them so long as it's clear they are not part of a standard keyboard. Jtrevor99 (talk) 03:56, 3 December 2016 (UTC)
 * Well, I went ahead and added them. We'll see what others think. Jtrevor99 (talk) 04:44, 3 December 2016 (UTC)
 * I'm glad you added them in another color. But it needs a legend to clarify for the user that these extensions are pretty rare. &mdash;Wahoofive (talk) 07:37, 3 December 2016 (UTC)
 * Good idea - done. Jtrevor99 (talk) 16:04, 3 December 2016 (UTC)
 * A question regarding the key numbers for the extended keys. It appears there is no official consensus for how to number keys 89-102. But, in order to fit the mathematical formula provided earlier in the article, the upper set would need to be numbered 89 to 93, and the lower set, -8 to 0. Should I change it? Jtrevor99 (talk) 15:26, 7 December 2016 (UTC)
 * Stuart & Sons is soon going to offer a 108-key piano going up to B8, so six more notes should be added. Double sharp (talk) 05:36, 1 March 2018 (UTC)
 * Added (although the piano is apparently not ready yet, it is planned to be in the first half of 2018; I would not change the range image at Piano until it comes out, of course). Double sharp (talk) 12:02, 1 March 2018 (UTC)

What do violin open strings have to do with this topic?
Why does the chart on this page show the open strings of various instrument unrelated to the piano? Cruft. &mdash;Wahoofive (talk) 07:37, 3 December 2016 (UTC)
 * I don't think they should either, but since they seem to have been around for a while, I have not yet gone further than cutting the non-standard strings (like a low C, F, and B♭ for the violin). What do others think? Double sharp (talk) 06:32, 1 March 2018 (UTC)
 * I'm indifferent. Perhaps if this page evolved into a more general "key frequencies" page, it would be useful. But since the topic is "piano key frequencies", it's probably unnecessary clutter. Jtrevor99 (talk) 18:15, 22 June 2018 (UTC)
 * I mildly favor keeping them. Tuning e.g. a violin in a room with a piano, one way is to tune each string to its corresponding piano key. "Unrelated to the piano" ignores its role accompanying such instruments. Just plain Bill (talk) 20:33, 22 June 2018 (UTC)

Theoretical piano key limit
I thought this was interesting, though probably does not fit the article - especially since, even if it's not original research, it's extrapolated. The theoretical limits for human hearing are as wide as 15-20000 Hz, depending on sources referenced. That would equate to 1 note below C0 (B -1??) to D#10...125 in total. Of course, you wouldn't end a keyboard on a sharp, so D10 or 124 keys is the practical limit. If there's any interest in adding this somewhere, let me know. Jtrevor99 (talk) 16:11, 22 June 2018 (UTC)
 * One should also consider the theoretical limits, as Stuart & Sons have done. One can of course keep making longer and thicker strings below C0, and in fact you would be able to hear the notes for a while (because even though the fundamentals are outside the limits for human hearing, their overtones can be heard), but the need to multiple-wrap the really low strings to keep their lengths manageable means that you quickly can't figure out what note it's supposed to be even if you can hear it perfectly well. Above B8, the strings are too likely to break. Double sharp (talk) 03:08, 23 June 2018 (UTC)
 * Interesting read; I'd been looking for an article like that, thanks. I will note that the range mentioned by the article is only for carbon-steel-based strings, which of course is what virtually all modern piano wire is made out of. I'd be interested to know if superalloys such as Inconel would allow the limit to go higher. Regardless, there's no reason to include this info in the article itself. Jtrevor99 (talk) —Preceding undated comment added 04:14, 23 June 2018 (UTC)
 * I'm rather dubious in any case about the musical value of such high notes, but I continue to think that it would have been nicer and more symmetrical to have a 109-key piano "from C to shining C". ^_^ Double sharp (talk) 05:38, 10 September 2018 (UTC)
 * P.S. If you ask me, I would already be very happy with 90 notes, just adding a low G and G-sharp: I sometimes feel the absence of those notes (there are quite a few pieces where you want to play them, but they are not there, such as Liszt's Harmonies du soir and Ravel's Piano Concerto and Scarbo) in a way that I don't really feel the need for more. Though I guess it would be more logical to complete the lowest 3-black-key group by having 92 notes down to the low F, which would allow Bartók's Piano Sonata to be played without alteration (not in my repertoire, though) – like a Bösendorfer 225. (Though I wish the low notes would sound clearer: in this video you can hear a big difference already from the A0, which my perfect pitch unhesitatingly calls out as an A, to the G♯0, which confuses my perfect pitch. Maybe it's because there is next to no competition for those notes? Already a 90-note keyboard with a very clear G0 and G♯0, like the A0 usually is, would be amazing!) Double sharp (talk) 07:36, 26 December 2019 (UTC)

Unreferenced message removal
I've recently added a few citations to this article. Given the article's short length, I think that six citations is enough to make it pretty well cited, but I'd like to see if there is a consensus to remove the message before doing so. InAndOutLand (talk) 18:50, 26 December 2019 (UTC)


 * I’d be in favor of removal per your additions. Stating “this article has no references” when it does is disingenuous. Thanks for the work. Jtrevor99 (talk) 03:49, 27 December 2019 (UTC)

Use 10log
The article gives an awkward formula using the 2log, instead of the current elog (ln) or 10log. So

n = 12 \, \log_2\left({\frac{f}{440 \,\text{Hz}}}\right) + 49 = $$

n = {\frac{12}{log_{10} 2}}\, \log_{10}\left({\frac{f}{440 \,\text{Hz}}}\right) + 49 = 39.86 \, \log_{10}\left({\frac{f}{440 \,\text{Hz}}}\right) + 49$$

I only put this last result in the text. Have a good day, Hansmuller (talk) 16:01, 1 March 2020 (UTC)
 * I oppose making this change. The "12" in the 2log formula makes clear that it is based on having 12 notes in one octave. There is nothing intuitive about 39.86, to allow the user to understand the origin of the formula. If anyone wishes to calculate the new values manually, they are welcome to make the conversion themselves - assuming their calculator does not have a 2log capability. Jtrevor99 (talk) 16:36, 2 March 2020 (UTC)  (EDIT: Never mind, I spoke too soon.  I see that you added the formula, instead of replacing it. That is fine. Jtrevor99 (talk) 16:38, 2 March 2020 (UTC))

Which keys are present on smaller pianos?
Some other piano sizes are 76-key, 61-key, 49-key, and more. Which notes are found on these pianos? Which notes are they to and from, which octaves, etc? I notice that the page currently has information for 88-key and 108-key keyboards, but not for smaller sizes. Aaronfranke (talk) 06:08, 27 December 2021 (UTC)


 * There are far too many variations on smaller keyboards/pianos to be able to represent them here. There is only one 88 key piano and one 108 key piano. Jtrevor99 (talk) 12:51, 27 December 2021 (UTC)

Two key numbering systems?
Having two different key numbering systems, as recently added by another editor, seems both unnecessary and confusing. I don’t believe there is anything official about the first column - since I was the one that added the extended keys and numbered them. I recommend collapsing back down to one set. Jtrevor99 (talk) 21:16, 24 May 2023 (UTC)