# Tell me about the missing black keys on a piano. **URL:** \ **Category:** Cafe Society\ **Created:** [January 22, 2009, 3:33pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464 "2009-01-22T15:33:35Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [January 22, 2009, 9:35pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/41 "2009-01-22T21:35:07Z")
> [@Musicat](#): > > Just to expand a little on my personal experience, I find that even if I haven’t touched a musical instrument for days, I can walk to a piano and sing the note I am about to play. Maybe that’s more of a long-term memory phenomena. Ditto. I can also get an A bang in tune to 440 without a reference point, through nothing more than practice, having had to do it numerous times a day for many years. Can’t tune any other notes, though, because, well, A is the only one you need 😛 ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [January 22, 2009, 9:38pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/42 "2009-01-22T21:38:16Z")
> [@GorillaMan](#): > > Absolute pitch of this nature wouldn’t, however, be enough to hear whether a particular note was exactly in tune with A440 even temperament, though! There may well be an innate skill which, having heard these pitches, provides an exact recall of them, but nobody until the most recent generations of musicians would have experienced this as a norm, and so would not have developed such a particular memory for one tuning system. I don’t disagree. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [January 22, 2009, 9:40pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/43 "2009-01-22T21:40:14Z")
> [@GorillaMan](#): > > Ditto. I can also get an A bang in tune to 440 without a reference point, through nothing more than practice, having had to do it numerous times a day for many years. Can’t tune any other notes, though, because, well, A is the only one you need 😛 Yeah, this learned skill is apparently is different (and a point I was trying to argue with the researcher, along with guitarists who always seem to know exactly where that E string should be tuned) than “true” absolute pitch. ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [January 22, 2009, 9:43pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/44 "2009-01-22T21:43:17Z")
[QUOTE=Musicat] This question sometimes causes controversy among musicians. Some claim that good string players play “pure” scales, not tempered ones, but my position is that if they did, they would clash severly with fixed, tempered tuning of pianos. Since they don’t, they don’t. [/QUOTE] It’s more variable than that, especially as (I’m sure my posts have made clear) I would argue that there’s no such thing as a pure scale! String players do vary intonation slightly away from equal temperament, for example bringing leading notes ever so slightly closer to the tonic on which they are resolving, and pushing minor thirds just that little bit lower. The difference in timbres with inflexible instruments, namely the piano, helps avoid a clash, although the degree to which these alterations are made does depend on the ensemble in question. It’s one reason for enharmonic modulations sometimes not sitting comfortable, at least until they’ve been played through a few times so that the necessary compensations are made (sometimes an entirely subconcious process). I would suggest it’s also a reason that players’ early encounters with entirely atonal music, and in particular serialism, give some difficulties with intonation. There’s also the related issue of the compromise between tuning resonant 3:2 fifths across strings, and adjusting towards equal temperament particularly to avoid a discordant interval between the violins’ E and the C of the violas & cellos. ---
**Author:** ![Muffin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/muffin/32/4341_2.png) [@Muffin](https://boards.straightdope.com/u/Muffin)\ **Post date:** [January 22, 2009, 9:50pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/45 "2009-01-22T21:50:53Z")
Hey, **Sapo** , here is a virtual keyboard: [Flash Piano - The Method Behind the Music](http://numbera.com/musictheory/piano.aspx#) Click on each key, starting at one end, and working one key at a time to the other end. You’ll notice the same tonal distance – a semitone – between each key, whether it is a white key or a black key. For example, if you start at F and work your way up through F#, G, G#, A, Bb, and B, you will be progressing up the keyboard one semitone at a time. To continue this sequence, just press the next key C – don’t worry that there is no black key there to press. As you can hear, no note is left out of the sequence despite there not being a black key between B and C. Now keep on trucking along up the keyboard and you will see that the same thing happens between E and F, which are a semitone apart despite being two white notes. Every key, be it white or black, is a semitone apart from the key immediately beside it, be that key white or black. If you want to get into the relationships between keys, google about on the term “music theory”. There are a lot of on-line music thory sites other than the one with the keyboard, so poke about until you find one that works for you. ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [January 22, 2009, 9:57pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/46 "2009-01-22T21:57:45Z")
> [@Muffin](#): > > Hey, **Sapo** , here is a virtual keyboard: [Flash Piano - The Method Behind the Music](http://numbera.com/musictheory/piano.aspx#) A very useful link, thanks! I now have a good answer the next time I hear “But I don’t have a piano at home” from a kid! 😃 ---
**Author:** ![Muffin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/muffin/32/4341_2.png) [@Muffin](https://boards.straightdope.com/u/Muffin)\ **Post date:** [January 22, 2009, 10:10pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/47 "2009-01-22T22:10:22Z")
If you click on the “Click here to put the piano in a new window” line, it will open a keyboard popup that you can move about on your screen, and still use even when you go to other websites: [http://numbera.com/musictheory/keyboardpop.html](http://numbera.com/musictheory/keyboardpop.html) ---
**Author:** ![Muffin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/muffin/32/4341_2.png) [@Muffin](https://boards.straightdope.com/u/Muffin)\ **Post date:** [January 22, 2009, 10:51pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/48 "2009-01-22T22:51:37Z")
> [@Yumblie](#): > > So if I’m reading this right, pianos can be tuned so that a note on one is slightly different than on another, depending on what ratios you use. Have a boo at the Railsback curve [Piano acoustics - Wikipedia](http://en.wikipedia.org/wiki/Piano_acoustics) and how stretched tuning [Pseudo-octave - Wikipedia](http://en.wikipedia.org/wiki/Stretched_octave) is used to keep the overtones from conflicting they way they do if a piano is just tuned by the numbers [Piano key frequencies - Wikipedia](http://en.wikipedia.org/wiki/Piano_key_frequencies) Also, what we hear and what we thing we hear are not always the same thing, for a lot of folks find tones in the higher registers to be flat, so tuners often tweak them a little on the sharp side to account for the difference in perception [Piano tuning - Wikipedia](http://en.wikipedia.org/wiki/Piano_tuning) ---
**Author:** ![Muffin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/muffin/32/4341_2.png) [@Muffin](https://boards.straightdope.com/u/Muffin)\ **Post date:** [January 22, 2009, 11:00pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/49 "2009-01-22T23:00:07Z")
> [@pulykamell](#): > > You don’t need perfect pitch to be tripped up by a badly tuned piano. When I trip and stub my toe on my piano, the result is a piercing, pained, and far from perfect 587.330 D. Tuning the piano does not seem to help much with this. ---
**Author:** ![Aspidistra](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aspidistra/32/3894_2.png) [@Aspidistra](https://boards.straightdope.com/u/Aspidistra)\ **Post date:** [January 22, 2009, 11:02pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/50 "2009-01-22T23:02:33Z")
> [@GorillaMan](#): > > It’s played entirely on the overtones of a single fundamental, and so is in no key. > > > [@Aspidistra](#): > > > > I do find it interesting that in a minor key, the very first harmonic to be ditched is the Major Third - the most “obvious” and nice-sounding harmonic in the whole scale (excepting the octave). I’m not sure what that means though. > > It means that an explanation for the ‘rightness’ we hear in our tonal system is not adequately explained by identifying major 3rds in the harmonic series. I actually went and fiddled with the numbers this morning and found that: [ul] [li]The simplest ratio after the octave (1:2) is actually the fifth (close to 3:2) not the Major 3rd[/li][li]The next three in the series are the fourth (4:3) then Major 3rd (5:4) then Minor 3rd (6:5)[/li][/ul] So apparently, I was completely talking out of my arse in the first place, and there’s actually _not_ that much difference, mathematically speaking, between a Major or Minor 3rd ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [January 22, 2009, 11:20pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/51 "2009-01-22T23:20:49Z")
> [@Aspidistra](#): > > I actually went and fiddled with the numbers this morning and found that: > > [ul] > [li]The simplest ratio after the octave (1:2) is actually the fifth (close to 3:2) not the Major 3rd[/li][li]The next three in the series are the fourth (4:3) then Major 3rd (5:4) then Minor 3rd (6:5)[/li][/ul] > > So apparently, I was completely talking out of my arse in the first place, and there’s actually _not_ that much difference, mathematically speaking, between a Major or Minor 3rd OK, I was phrasing that rather misleadingly - yes, there’s something of an outline of a major triad with the 5:4 and 6:5 ratios - _but not of a minor triad_. That the latter is just as an important element of western tonality suggests that the overtone series really doesn’t serve as an explanation at all. Additionally, to preempt any suggestion that you could just swap the intervals around, they’d then be derived from two completely different fundamentals. ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [January 22, 2009, 11:23pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/52 "2009-01-22T23:23:04Z")
> [@Chronos](#): > > Most brass instruments are inherently not equal temperment, unless you constantly fiddle with the tuning valves (one exception, of course, is the trombone, which isn’t inherently any particular temperment). To make a truly equal-tempered horn, you’d need a separate set of tubing for each note, rather than just using various combinations of three sets. Yes, and if you have a good ear you can hear the effects of this. Two examples I can think of are a section of the Grand March from Aida and the first trumpet entry in 633 Squadron. In both cases the trumpets, which are non-equally-tempered instruments, are having to play in an awkward key, and some of the notes are slightly out of tune. ---
**Author:** ![Muffin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/muffin/32/4341_2.png) [@Muffin](https://boards.straightdope.com/u/Muffin)\ **Post date:** [January 22, 2009, 11:33pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/53 "2009-01-22T23:33:04Z")
> [@Chronos](#): > > (one exception, of course, is the trombone, which isn’t inherently any particular temperment) Sometimes sad, sometimes comical. What? ---
**Author:** ![Fish](https://avatars.discourse-cdn.com/v4/letter/f/bc8723/32.png) [@Fish](https://boards.straightdope.com/u/Fish)\ **Post date:** [January 22, 2009, 11:33pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/54 "2009-01-22T23:33:48Z")
> [@GorillaMan](#): > > Absolute pitch of this nature wouldn’t, however, be enough to hear whether a particular note was exactly in tune with A440 even temperament, though! I can do this. I used to work in a store that sold digital pianos and organs and each had the ability (which we would occasionally demonstrate) to tune the instrument up or down by 0.1 Hz. I could always tell by sitting down at the instrument and playing a few notes if it was off, even by the tiniest amount. ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [January 22, 2009, 11:42pm UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/55 "2009-01-22T23:42:45Z")
> [@Malacandra](#): > > Yes, and if you have a good ear you can hear the effects of this. Two examples I can think of are a section of the Grand March from Aida and the first trumpet entry in 633 Squadron. In both cases the trumpets, which are non-equally-tempered instruments, are having to play in an awkward key, and some of the notes are slightly out of tune. IIRC the Ride of the Valkyries is another example, with a key which gives a strident rather than triumphal sound to the brass. ---
**Author:** ![Aspidistra](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aspidistra/32/3894_2.png) [@Aspidistra](https://boards.straightdope.com/u/Aspidistra)\ **Post date:** [January 23, 2009, 12:04am UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/56 "2009-01-23T00:04:17Z")
> [@GorillaMan](#): > > OK, I was phrasing that rather misleadingly - yes, there’s something of an outline of a major triad with the 5:4 and 6:5 ratios - _but not of a minor triad_. That the latter is just as an important element of western tonality suggests that the overtone series really doesn’t serve as an explanation at all. Just to kick that back into layman’s terminology again… A major triad has the harmonic intervals 4:5:6. So that’s a nice, mathematically simple elegant ratio (score 1 for the “mathematical elegance” model of why we like what we like) A minor triad would be (_scribble scribble_) - uh - 10:12:15 ? Which is not mathematically elegant at all (score -1 for the “mathematical elegance” model). But I’m not sure that I agree that a minor triad is just as important an element of western music - most music seems to be written in a major key - it seems that people start making music in minor keys simply because they’ve exhausted all they want to do in a major key first? A diminished chord would be 5:6:8. Which is getting back into nice elegant ratios territory. And it seems to me just from casual listening/playing contemporary music that diminished chords are more common than minor chords … but bearing in mind that I know about two fifths of bugger all actual formal music theory, so I don’t have a handle on what’s considered to be “important” by serious musicians. Fascinating thread 🙂 ---
**Author:** ![fachverwirrt](https://avatars.discourse-cdn.com/v4/letter/f/94ad74/32.png) [@fachverwirrt](https://boards.straightdope.com/u/fachverwirrt)\ **Post date:** [January 23, 2009, 12:08am UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/57 "2009-01-23T00:08:32Z")
> [@Aspidistra](#): > > A diminished chord would be 5:6:8. Which is getting back into nice elegant ratios territory. And it seems to me just from casual listening/playing contemporary music that diminished chords are more common than minor chords … but bearing in mind that I know about two fifths of bugger all actual formal music theory, so I don’t have a handle on what’s considered to be “important” by serious musicians. > > Fascinating thread 🙂 5:6:8 is a first inversion major triad. 5:6:7 would be the diminished triad, but that involves the 7th partial, which nobody uses because it’s so flat. ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [January 23, 2009, 12:19am UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/58 "2009-01-23T00:19:53Z")
> [@Aspidistra](#): > > most music seems to be written in a major key - it seems that people start making music in minor keys simply because they’ve exhausted all they want to do in a major key first? Not at all! Pre-‘tonal’ music (I dislike using the term to mean ‘major/minor’ but it’s commonly employed in this way) has no less in common with familar minor keys than with major ones. In any case, what I’m emphasising is the equivalence we hear between major and minor _chords_ as well as keys. You can’t use C major as a key (rather than just a scale) without encountering chords of D minor and A minor. > [@](#): > > A diminished chord would be 5:6:8. Which is getting back into nice elegant ratios territory. And it seems to me just from casual listening/playing contemporary music that diminished chords are more common than minor chords … but bearing in mind that I know about two fifths of bugger all actual formal music theory, so I don’t have a handle on what’s considered to be “important” by serious musicians. You’re absolutely right that most music is not formed of simple consonant sounds. _Controlling_ how those which ‘sound right’ work alongside those which don’t is the function of keys, and only using major and minor triads in isolation would be very boring indeed! > [@](#): > > Fascinating thread 🙂 🙂 ---
**Author:** ![Aspidistra](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aspidistra/32/3894_2.png) [@Aspidistra](https://boards.straightdope.com/u/Aspidistra)\ **Post date:** [January 23, 2009, 12:37am UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/59 "2009-01-23T00:37:41Z")
> [@fachverwirrt](#): > > 5:6:8 is a first inversion major triad. 5:6:7 would be the diminished triad, but that involves the 7th partial, which nobody uses because it’s so flat. You’re right, I copied down the wrong column in my notebook. Need more caffeine. 5:6:7 is still a nice mathematical ratio though It seems to me that people do use diminished chords reasonably frequently in guitar tabs (which was what I was thinking of upthread). But I suspect that the guitar is not exactly an equal tempered instrument, so I don’t know if that makes a difference. ---
**Author:** ![Fish](https://avatars.discourse-cdn.com/v4/letter/f/bc8723/32.png) [@Fish](https://boards.straightdope.com/u/Fish)\ **Post date:** [January 23, 2009, 12:41am UTC](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464/60 "2009-01-23T00:41:16Z")
Incidentally, I seem to recall that there was an experimental piano made with alternating white and black keys, something like this: ```auto **C# D# F G A B** C D E F# G# A# ``` I can’t recall whether C was a white note or a black note, but you get the idea. It had a few advantages: it was much easier to transpose from one key to the next (you just move up to the next white key). There would only be two sets of fingering to learn — white-key and black-key fingering. Your hands wouldn’t need to be as big, because there were more keys per inch. It never caught on. Without labels on the keys it’d be hard to know where you were, especially if you took your hands off of the instrument to go up a few octaves. That is the greatest advantage of the current piano system. No, it isn’t symmetrical and it isn’t uniform white-black-white-black. Because of this, it’s much easier to see at a glance where you are. [Previous page](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464.md?page=2) [Next page](https://boards.straightdope.com/t/tell-me-about-the-missing-black-keys-on-a-piano/482464.md?page=4)