The idea for this thread came from a discussion in the Teachers Forum about key signatures. J S Bach wrote in all keys for a well-tempered instrument. (I realise that this is not the same as our modern day equal temperament but it is close enough for this thread to take off.) I would be interested to hear other people’s thoughts on the need for using the more remote keys. Each key has a different characteristic of course and these can be used to good effect. Modulations may be executed without the need for awkward enharmonic changes before suitable pivot chords can be employed, and so on. It has been suggested that there is no need for, for example, the key of C flat Major when B major will sound the same on a piano. Would anyone care to contribute?

I was thinking something remarkably similar when I posted this on that other discussion....

I've seen G# minor used as the ii chord for F# major. But that could well have been on alto sax which has 3 more sharps than concert pitch instruments.

We heard a piece at Stalybridge last weekend with a key signature of six flats.with an additional F flat added in aroud bar twelve, This was "La Fille aux Cheveux Lin" by Debussy.
I have been working on a composition recently which begins in the key of A flat major and then modulates to the tonic minor albeit briefly. I would not make much harmonic sense for it to move from A flat major to G sharp minor, even though the sound would be the same.

The Harp Interlude in Bemjamin Britten's Ceremony of carols is written in Cb major.

I've found that loads of pieces have 6 flats (Debussy seems particularly fond of them, although i would have to disagree, c flat is pointless). I don't think i've ever seen anything with 6 sharps though.

It is indeed, and it gives it a different tonality from the key of B major, which Britten used to great effect.

On a slightly different point though, would anyone care to suggest a suitable pivot chord to use when writing a modulation from the home key of C flat major to the submediant major? Modulations are not simply made from the tonic key to its most closely related keys of the dominant, the subdominant and the relative minor. If a piece begins in C flat major then a simple modulation to A flat major is possible. What would you do if it were written in the key of B major?

Just the other day I had to do some on the spot sight-reading for a singer. The piece modulated to G# minor and I had problems with feeling and visualising the chord V under my fingers - D# Fx A# - especially as it was also an arpeggio in inversion! She left the music with me to give me a chance to practise. When the pressure was off I could have kicked myself - all I had to do was 'imagine' the chord as Eb major - Eb G Bb! Now easy!



All I would do would be to modulate to G# minor and do an immediate enharmonic switch to the Ab tonic major by adding one of those key signature changes mid-piece - like you get in Dip Quick Studies! I'm not sure a simple pivot chord would be possible as the Ab major chord is not in common with both keys. Even a switch to Gb Major still gives Ab as a minor chord. It's all great revision this and to really engage with all this stuff. I shall spend the evening now finding all the keys which have an Ab major chord in!

P.S. Just found a couple of examples where composers have used the remote keys to be able to modulate effectively from keys with 5 and 6 flats, but where in practice, the pianist would probably 'imagine' an easier enharmonic equivalent.

Brahms op117 no 2 Intermezzo in Bb minor (bar 21). The chord is Ebb Gb Bbb My teacher (at the time) said 'okay - think of it as D major'.

Schubert Four Impromptus Op 90 no 3 (starting 16 bars from the end - how did I get hold of an edition without bar numbers)! I think this is fascinating and I have only just noticed it. Schubert wrote the piece in Gb major but there is a footnote which says 3 bars have been notated in C major with accidentals (the key signature of 6 flats is omitted for this line) so that Schubert can make chromatic alterations to the chords which he couldn't do otherwise. One of them is the same as Brahms above. The other is Abb Cbb Ebb = G Bb D.

A better edition might explain more about the composition process. I'd better stop before I write a thesis

That isn't too surprising since the harp with all the pedals up plays in Cb. I don't think it worries harpists too much. They are used to strange-looking chords and progressions to minimise setting the pedals.

An interesting subject. I have tried playing Claire de Lune in both C and D and it doesn't sound the same, not just to me but other people who know the piece well. Perhaps the tone of Db gets set in their minds, or the problems with piano tuning to equal temperament introduces discrepancies that give it a particular sound.

kai

I'm sure this is just me being stupid, but aren't they the same thing?

I thought that the whole point was that each key has different characteristics only if the temperament is Not equal? In Equal temperament this is abolished.


. . . Which I played: For some weeks now I have been using the music only to check dynamics and phrasing and as a very superficial check for such things as the notes, and I had quite forgotten what key it was in.

However, I think that on an equal temperament instrument this sort of key is still usefully employed, for three reasons:

First, even Irving Berlin knew that writing a tune on the black notes only (penatatonic) almost invariably gives a good tune, almost regardless of the notes you actually use, so composing in a key with 5 or more sharps or flats tends to give better tunes (even if you don't stick to pentatonic).

Second, If you try playing "La Fille" in another key, the notes don't quite fall under the fingers so easily. Of course, it may be that I am biased on this having learned it in the key it is written in, but consider scales and arpeggios: It is much easier to learn and play a scale or arpeggio if at least one of the notes is not a white key (and at least one is): The C major scale, for example, is a nightmare as it has no landmarks at all. I think the same is true of pieces.

Thirdly, as has been mentioned, odd starting keys may make certain modulations possible (or at least easier to follow) that are not so obvious in simpler keys.

On a fixed pitch instrument like the piano, the same sound. But string players would used different fingerings as far as I know.

kai

As another forum has pointed out, the strings on a harp are tuned to the Cb major scale. A passage in Cb major is much easier to play than one in B major because there is no need to utilize any of the pedals.

In ANY modulation, the best pivot chords are the ones that take on a subdominant harmonic function in the context of the new key, i.e. chords that become II or IV in the new key. If a modulation to Ab major is desired, then the best pivot chords are the Db minor and Db major chords:
- Db minor chord = II in Cb major AND IVb3 in Ab major
- Db major chord = V/V in Cb major AND IV in Ab major

Another possibility--albeit more remote--is the Bb minor chord, which can be taken as VII#5 in Cb major and II in Ab major.

If the original key is written as B major instead of Cb major, then the same modulation would be notated as G# major.

But well-tempered isn't the same as equal-tempered and there were at least 6 different systems of well-temperament. Each key only has a different characteristic in well-temperament, not in equal temperament! The reason why we imagine different keys to have different characters on an equal tempered piano is probably because of association (keys like C, G and D and their related minors sounding more familiar because they're used more, or if we play the piano we began our playing career playing in those keys). Or we get used to hearing a particular piece played in the key it was written in, so if somebody plays it in a different key it sounds all weird, but not because the different key actually has a different character.

Also, please explain how Cb major is different in character to B major when played on an equal-tempered piano. Do you think anybody could tell the difference just by listening? If so, why?

Violinia, you have already posted some very similar comments on the thread in the Teachers Forum about minor key signatures and I have answered it there. You did not understand my answer and so I will repeat it here.
C flat and B will sound the same on a piano as they are the same of course. When modulations and chromatic harmonies are employed the need for the use of these keys will become apparent. I posed the question about modulations here and Organ Dummy answered it very cleverly, pointing out that a change of key from C flat major to the submediant major could be performed simply and easily but that if the modulation were from B major to the submediant major then the new key would become G sharp major!!!!! (There is no key of G sharp major by the way. It would need a key signature of six sharps and one double sharp.)
It is when modulations occur that these more remote keys have their place.
We know that you read a book about tuning systems and their effect upon harmonies recently as you wrote about it at length about a month ago. I do not see the need to repeat what was said then except to add that, in equal temperament nothing is really equal. It simply gives an almost acceptable tuning system whereby each note is almost in tune rather than only some as in most of the other tuning systems. Therefore each key will still retain some of its own character on a piano. With instruments with greater flexibilities the characteristics will be more apparent but are there on the piano too. To a lesser degree.
I have chosen not to answer any more of your posts on the other thread. I will now make the same choice here.

This is an interesting topis for discussion but I do not feel that passing comments as you did on the other thread about how "someone with my qualifications should know that" is adding anything useful to this one. It would be a shame for it to be closed.

OK I can see the point for when when modulations occur, but there's still nothing (in the rule-book) to stop you modulating to a flat key froma sharp key or vice versa.

As for keys having individual characters on an equal-tempered piano, you've still chosen not to explain why you think this is so, when all the intervals are identical and the only possible difference can be the register. I find it a bit odd that you're refusing to enage on this one. And ahem - I meant that "someone with my qualifications should know that" remark as a humorous reposte, bearing in mind the "as a teacher I'd have thought you'd know that"-type remarks you'd made to me earlier.

Oh well never mind, you're probably not going to read this anyway but I don't quite understand why there needed to be all this hostility in the first place.

Can I join in?
I agree on this one and the only evidence I have to offer is what my ears tell me.
If I play a hymn written in E down a semitone it doesn't sound only lower.

It could be because of the effect of the absolute frequencies, the intermodulation (the sum and difference frequencies that result from mixing two or more frequencies) which will actually be different for different keys. For an extreme example, listen to a pefect fifth played middle-C to G, then the same fifth two octaves down. A very different sound though the second pair are just sub-harmonics of the first.

But think about it logically, sbhoa, and there can't be any reason why Eb should objectively sound any different to E except that it's a semitone lower. The only possible difference is a subjective one: if we play piano we have a different response to the flat keys because we learnt to play in them after learning to play in C and the first few sharp keys. So our brain starts to recognise and remember the different frequencies and we convince ourselves they have a different objective character. The keys would certainly have sounded different on a well-tempered piano and they certainly sound different on a guitar, but this is because on these instruments the intervals are actually different according to which key you're playing in. This won't apply on an equal-tempered piano, though.

Anyway, who decided on which keys (sharp or flat) were to be matched with which frequencies? Hey that's an intriguing subject! When was it decided that A should come in a 440 (or 442 in Europe)?

Aha! This Wikipedia article shows how arbitrary these pitches are:



I rest my case.

It is a fact that, as I wrote earlier, in an instrument tuned in equal temperament nothing is equal. There is no arrangement of intervals that will make any scale truly consonant. It is bound to contain intervals that are slightly out of tune according to mathematical tables and principles.

A piano has to be tempered to give it an acceptable arrangement of both just intervals and of wolf intervals. It is this arrangement of slightly detuned or tempered intervals that gives each key its own individual character. They are not as obvious as in an instrument tuned to a different tuning system but they are there. It matters not one hoot to which A the instrument is tuned. This arrangement of intervals will remain the same, or almost the same. There are times when a tuner will temper certain intervals to suit a particular instrument’s own quirks but the basic structure of the tuning system remains the same.

Piano tuning is far more of an art than a science. A mathematician may tell you that equal temperament gives each key a uniform quality. A musician will not. If this does not make sense to you we must agree to differ on this occasion.

er.....if the first statement is true, then the second cannot be!!

(No mathematician can say something is true when it can't be)

I've looked into the mathematics of this and the problem occurs when you "close the loop"...
and don't get back to where you started. It is interesting

I'm still baffled by what you're saying here and genuinely want to know what you mean.

The method of equal temperament used to tune the vast majority of pianos in the West is where the octaves are divided into 12 exactly equal semitones. This in turn creates identical tones, minor and major thirds, fourths, fifths and every other interval, so every key sounds the same interval-wise. In this system only the octaves are exact as fixed by nature, ie in a ratio of 2/1. All the other intervals are approximations of the intervals as they are meant to be in nature, and some are more acceptable to the ear than others. In equal temperament the fifths become slightly narrowed and the thirds become wide, but the point is, all the intervals are identical no matter what key you're in. In other words, once the semitones are identical, the keys cannot differ in character, ie with their arrangement of intervals.

So how, in a system where the semitones are all of an identical width, how can any key sound different in character to any other key, other than with regard to its register? 'Agreeing to differ' doesn't uncover the truth of this and surely it would be better to establish what equal temperament acually means. Ie does it mean the semitones are all of an equal width or doesn't it? For the record, Wikipedia says they are, as it does at

http://www.tonmeister.ca/main/textbook/node272.html

http://www.phy.mtu.edu/~suits/scales.html

http://www.answers.com/topic/equal-temperament

A string player will adjust his intonation according to the vibrations and 'beats' he hears, and will vary it according to whether he is playing alone, with a piano or with other string players or with anyone else. A pianist is subject to the skill of the piano tuner, and a highly skilled piano tuner will tune a modern piano into equal temperament where the semitones really are equal. A musician with an good ear will find some of those intervals uncomfortable because they don't resonate in tune with the 'harmonic series'. But no matter how acute the aural perception of the pianist is, he won't be able to hear harmonic differences in keys played on the piano if the semitones are equally placed apart.

I know about the logical answer but my ears still tell me a different tale for whatever reason......

Sbhoa, it would sound different to my ears too, but think about it - familiarity causes our ears to become accustomed to music sounding a certain way. We can remember pitches as well as pieces of music - many people can, for example, sing a well-known tune to order in the exact key it was recorded in - including people who don't see themselves as musical. If say 'All My Loving' the well-known Beatles tune was played a semitone lower than its usual key, most people would prick up their ears and think: hmm, there's something funny going on here, even if they couldn't put their finger on what it was.

Please tell me why you think your experience of a hymn played a semitone lower than normal is because flat keys are qualitatively different to sharp keys (well, I assume this is what you're thinking), when it turns out that the keys are only arbitrarily fixed in the first place. Ie although nature fixed the harmonic series, it didn't fix the pitches - we did. Honestly, I'm genuinely interested if you still think this, because I used to think the same thing, ie I thought flat keys and sharp keys were qualitatively different and this was why I could hear them as different. I've since thought about it a lot more and realised this can't be so. For instance, I didn't always know that the pitches weren't even (roughly because they're slightly different in Europe) fixed until relatively recently, and had thought that flat and sharp keys were somehow 'natural' (to add a confusing word into the mix!).

I'm not disputing the logic and don't disagree with it.
I don't have an explanation but still hold to the fact that for my ears at least the difference between E and Eb major is more than just a drop in pitch. E major sounds brighter.
It is quite possible that the difference is as you suggest just a matter of familiarity but I'm not totally convinced in spite of the logic.

Perhaps you're right and there's an inherent difference in quality between flat keys and sharp keys even if you remove memory and association from the equation. But as the pitches were abitrarily fixed and agreed on by people, not forces in nature, I think the conclusion really has to be drawn that it's because of association. How else could it be? You'd have to go back and ask the people who decided on the pitches: why did you decide to put D there, Eb there, and E there? Does the sound of an Eb scale just there actually sound duller in itself than the scales starting a semitone above and below it? Why?!?

Personally, I think that as musicians, we're always super-aware as to whether we're playing in sharp or flat keys and this builds up an association when we listen to music and gives us the tools to guess (very often correctly) whether it's being played in a sharp or a flat key.

Pitches are totally unlike intervals, which really are fixed in nature and not (until equal temperament) by people. A fifth really is fixed in nature, which is why we know immediately when it's being played out of tune, ditto semitones, tones, minor and major thirds and all the other intervals. It's amazing stuff, and it certainly gives rise to the feeling that music was always 'meant' to be, and humans just 'discovered' it - because they were meant to. In the same way that we're meant to speak in languages because we have the tools from birth - all you need to speak a language is one other person. All you need to make music is a singing voice and we're all born with one of those.

But that's a whole other (philosophical) subject.

sbhoa - do you have perfect pitch?

I ask because I wondered if people with perfect pitch could hear a difference between sharp and flat keys that the rest of us can't hear. When listening to a piece, I couldn't tell you whether it was in a sharp or flat key, let alone what key it is in.

I have excellent relative pitch - always came top of my year in aural at uni. But I don't have perfect pitch and to me, E sounds the same as Eb, only a semitone higher.

No I don't but using the transpose button on a keyboard is very strange as I feel that I'm playing/reading one thing and hearing another and want to keep correcting myself.
I'm not sure that I could tell whether a piece is in a flat or sharp key either.
I just hear the difference when I know what I'm playing if that makes sense.

I agree with Violinia here, if the intervals are equal, and nothing but pitch differs (which most people can only judge relatively) then the keys must be the same and cannot have a different 'feel'.


This might be the key to it: maybe the people who compose in the first place, influenced by music they've played in the past, will tend to chose a certain key for a bright piece because it naturally sits in that key from their past experience. For example, if C Minor has a reputation as a 'tragic' key (even if this is through personal experience alone), a composer may feel because of that their piece fits well in that key. Many composers themselves had perfect pitch so they may even have done this subconsciously, it pops into their head in that key. Interestingly YAP played a piece to me the other day, and said guess how many flats this piece is in. The answer was 1 but we both felt that it was the sort of piece that would usually have at least five.

We therefore see C Minor as a 'tragic' key because tragic works tend to be written in that key, and this will continue to influence future generations. I too experience the thing that pieces I know sound 'wrong' if they're not played in the key I'm used to, despite not having absolute pitch. I wonder though, if the first time we heard a piece it was played in the wrong key (by someone else and we weren't told this) would we find the same thing?

Aha! Good question!

I've wondered that, sometimes. You know, some of this thread really goes over the top of my head. It's just too complex for me to handle! I think I need a 'Chords, Obscure Keys and Modulation for Dummies' guide. Nice, student-friendly vocabulary; breaking it down bit by bit into a concise, comprehendable form for people like me who can't understand all the big, scary words! Then I'd be at a level with all these academic swells in no time!

I don't have absolute pitch, but there are certain notes I can pitch, and I generally tend to sing a piece of music in the original key. However, this is not a musical skill. I read somewhere that it is more linked to linguistics than musical aptitude. I think that what you're suggesting is more of a musical aptitude thing than an innate ability to pitch. Sometimes I'll compose something and think something along the lines of, 'Ooh, I don't like this G Major - it sounds too bright. Let's change it to E flat to soften it up a bit'. But unless you were either so musically adept that you could interpret the composer's intentions, I think it'd be very difficult. And even then, it'd be a bit of a lottery to 'guess' what the composer was getting at.

But then, if the individual notes of a scale, or of an instrument, were not quite evenly tempered, a person very sensitive to pitch might be able to pick up a dischord. Or they could be psychic.

As far as I'm concerned, there's no way of 'guessing' the will of a composer. Of course, if they discovered from some old, secret crypt a big Dvorak tune in C major and aired it live on Classic FM for the first time, then you'd wonder if you'd heard it correctly, but that's Dvorak for you... I'll never understand his obsession with flats. Though I'm sure he's written some things in C major.

I'd hazard a guess that if we heard something in the wrong key repeatedly and then heard it in the right key (say, a semitone lower) we'd think it sounded wrong. But if we were acclimatised to sharp and flat keys already by having played a lot of music, we'd still have a propensity to recognise if it was in a sharp or flat key whether it was in the right or wrong key in the first place, if you see what I mean.

Funnily enough I used to play a private game where I'd listen to some music on the radio and then see if I could guess what key it was in. I'd often get it right, but haven't put it down to the sharp or flat keys having a unique character of their own for a long time, because the 'familiarity' explanation seems more likely given the evidence.

I will add more to this, although I had thought that I had explained it clearly when I first wrote it.

The art of piano tuning is not governed solely by mathematical formulae. There is a science behind it of course and tuners need to have a detailed knowledge of different tuning systems and a very keen ear for both variations of pitch and for what is pleasing from a musical viewpoint. It is far more of an art form than is generally thought, and simply tuning an instrument according to exact tones as laid down by the theoreticians who decided that in equal temperament should consist of twelve equally spaced semitones will keep an electronic tuner happy but will not satisfy a pianist.
An expert in aerodynamics will say that a bee should not be capable of flight as its wing capacity is too small for its body weight etc but any bee worth its wings will demonstrate that the expert is wrong! An artist will create a very different image from that seen by the human eye but the end result will be just as pleasing and in many cases far more so. Art and science do not always come up with the same answers and usually the practical solution is the better one. It is exactly the same with tuning a piano to the system of equal temperament. There are certain intervals that can and should be altered to give the most musical result. An instrument tuned to the exact settings of an electronic tuning device will have a dull uniformity throughout its range and it will not give a satisfactory result to anyone with a slightly musical ear, and therefore it is not done, at least not by a tuner who really knows understands the artistry behind the science.
As I have said before it is these slight differences that give a non-uniform pattern to the tunings in what is called equal temperament, but is in fact not equal in the hands of a skilled tuner. Therefore each key will have a slightly different pattern of tones and semitones from every other key and it is this that gives the individual characteristic to each scale and key. I have now put this into what I feel are very simple terms and I hope that what I have written will be comprehended.
Any pianist, and I use that term rather than "musician" as it is the equal temperament tuning to which we are referring in this thread now, will tell you that there are differences between one key and another and these are as a result of the physical difference between one key and another and not as a result of any other associations that we might have with that key or sound. A piece played in E flat major will sound less bright than one played in E major because of the differences in the pattern of slightly detuned ,or tempered, tones and semitones contained in it. I will say one more time that tuning an instrument is an art form based on scientific principles. I made the remark earlier on another thread that if there was no difference between one key and another apart from the difference in pitch we might just as well play every piano piece in the key of C major. This was not simply a facetious comment. I had intended it to provoke the "How Stupid" response which indeed it did. Because each key has its own feel and mood, because of the explanation that I have detailed here, this would be lost if the same music were to be played in the key of C.

It is a balancing act - because the physics doesn't quite add up - there are slight differences in the intervals in the different keys - at least that is how I have always understood it.

Mmm, not so sure. If I play something on my Bb clarinet and then on my A, the two versions certainly sound different, but I'm not sure about wrong. Same if I play the same piece on the same instrument but transposed a semitone.

Yes!! By jove, she's got it.

I have just waded all through this technical stuff - my admiration for those who understand it knows no bounds - but I won't ask -I'll just read it all again until it sinks in!!!
I was never any good at either maths or physics!

Can I just say (in a very small voice) that I would like to see more easy pieces in difficult keys for younger learners. I mean really easy from other points of view. Does anyone know of any?

I have a very old book "Tunes in All Keys" which I use to help pupils understand tonality and get get feeling of a key but but the pieces are a bit naff.

No, neither of you are right.

I'm going to try and gloss over as much as I can and explain the mathematics behind intervals. Each single note we hear has a frequency, and the thing that makes different notes in different octaves sound higher or lower is that their frequencies are different. A frequency is a number of vibrations a second, measured in Hertz, and one can think of it in terms of vibrating strings: a big long string will vibrate slowly, producing a low note; a tiny string will vibrate quickly, producing a high note. The unit of frequency is Hertz, abbreviated to Hz.

So individual notes each have a frequency, and we can start talking about intervals. The sound of an interval is determined by the relationship between the frequencies of the two notes. Say we have two notes, one with frequency A and one with frequency B. As if by magic, the two notes will sound an octave apart if B is double A. For example, the A above middle C is 440Hz. The A above that will have double its frequency - 880Hz. Or, to get the A an octave below 440, we halve it to get 220. The really important thing though is that the characteristic sound of an interval is solely based on how many times bigger one frequency is than the other: the octave from 440-880 sounds like an octave, as does the one from 220-440, or from 110-220 and so on.

So, now we can define an octave: play two notes with one frequency double that of the other, and we have an octave . Also, if we fix A above middle C to 440Hz, we can tune all the As on a piano: double the frequency to go up octaves; halve the frequency to go down octaves. It'd be nice to know how to tune the notes in between the As though, too. In a given octave, there are 12 semitones; for instance:

A-A#, A#-B, B-C, C-C#, ... , G#-A'

How do we do semitones? We know for octaves, we use doubling: to move up an octave from a note, double its frequency. But how do we move up a semitone from a note? Furthermore, how can we ensure if we move up from a note by a semitone twelve times, we'll definitely 100% get to an octave above the original note?

The trick on a piano is to make all the semitones exactly the same size, and rig it so that moving up 12 semitones eventually results in doubling. The magic number is:

1.0594630943592952645618252949463

Or, more properly: the twelvth root of 2. For convenience, I'll call this number Larry.

To move up from a note by a semitone, multiply it's frequency by Larry. To move up a semitone from there, multiply its frequency by Larry. Eventually, we'll have moved up by twelve Larrys, and eureka - we're at double the frequency we started with .

So now we know how to tune a piano: set A to 440, set the other As off that by doubling, and fill in the gaps by multiplying by Larry. But what does this have to do with keys? Well, a piece can only sound different if played in a different key if the frequency relationships between the notes in the scale change if we change key. But they don't. A fifth from C to G is will sound like the interval we make by going up 7 Larrys from a starting note. A fifth from C# to G# will also sound like that. We can do that for any pair of notes: if we transpose the piece up by a semitone, all the intervals are the same as there are the same number of semitones and hence the same number of Larrys between the notes in the piece.

I'm not getting into temperament here as it's not relevant, not with a modern piano; all I will say is that the method described above (using Larry for each semitone) is what is known as Equal Temperament. Any modern piano is tuned using this method, and have been for in excess of 100 years. All electronic instruments - keyboards, digital pianos - are tuned using the method described above. The last time I got a piano tuner in, he used an electronic tuner; again, set to follow the rules given above. Now and again, a piano will be tuned using a non-equal temperament (varying the Larrys used depending on which semitone on the keyboard we're looking at) but that is very much not the norm.

I hope that clears a few misconceptions up .

Edit: quick mathmo summary, given Carol Piano has a maths degree .

The frequency of a note on a piano is 440 * (Larry ^ number of semitones from A above middle C to the note in question). I.e., it's exponential, and thus we have the constant ratio property and the divisor for any two equally-spaced notes is the same.

Not ANY pianist.

Unless you mean differences in difficulty. Yes, some keys are more difficult than others to play in. But that isn't what I thought you were talking about.

Petrat, thanks for the detailed explanation, which I've read through and considered. One question still remains, though. Are you saying that what is known as equal temperament isn't really equal temperament?

Equal temperament means the semitones are exactly equidistant, so consequently the intervals become exactly the same no matter what key you're playing in. ET was invented to solve the problem of well-temperament, which meant the intervals in some keys worked better than in other keys. The whole problem arises in the first place because 12 perfect fifths (as in nature: no beats) piled on top of each other causes you to arrive in a place slightly higher than 12 octaves. Narrow the fifths and you end up with a note that's exactly 12 octaves above your starting note.

Either modern pianos are tuned to ET or they're not. If they're not, then they're tuned to some sort of well-temperament where each key sounds slightly different and some work better than others.

I have found plenty of information confirming that a truly skilled modern piano tuner knows exactly how to tune in perfectly equal temperament, with the 12 semitones matching an octave divided into 12 equal parts.

You are saying this isn't so, and that piano tuning is an art whereby the tuner is in fact doing something different to that, which to my mind would be resulting in a sort of well-temperament. So which are you saying it is?

You mean 7 octaves not 12 but otherwise I agree with your post

Thank you!
(though I can't remember a thing about it... (the maths degree, that is ))

Busy doing other things eh?

Let's not go there though, after all...this is a family forum

Thanks for the explanation above YAP

No, it's 12 because if you pile fifth on top of fifth until you get back to where you started, you have to go through all 12 keys, ie C,G,D,A,E,B,F#,C#,Ab,Eb,Bb,F - and then you're back to C. Only for some bizarre (and highly inconvenient) reason this C is higher than it should be, hence the problem, hence the apparent solution - equal temperament. Make all the fifths slightly narrower and you end up with a C that's exactly 12 octaves above the first one. Make all the semitones exactly equal too, so that F# and Gb are exactly the same note (when they shouldn't be) etc etc.

Very Douglas Adams .

The important thing, as Violinia is well aware, is that the fifths are all slightly narrower by exactly the same amount. This means the 'compromise' is identical in all keys, and the precise colours of the intervals is the same in all keys. Anything else just isn't equal temperament, and unless one is playing a harpsichord or anacrusis's piano (tuned by her harpsichord-tuner husband), one is unlikely to come across anything else.

I think that clavinovas have a choice of temperaments, as does my keyboard with its choice of five different harpsichords. I know that my current tuner will tune to a tweaked version of equal temperament and my last tuner achieved very poor results on both of my instruments using an electronic tuner. As I have mentioned before the result obtained was dull and lifeless, although a robot might well have loved it!
I have also said before that tuning is an art and when the artistic side takes over from the mathematician;s one the results will be far more pleasing because the tuning will suit the instrument being tuned. By this I don't simply mean that a harpsichord will be tuned to one temperament, a harp to another and all pianos to what an electronic device would call equal temperament but that what needs to be tweaked will be tweaked! Some intervals will be adjusted slightly giving a non-uniformity throughout the rqange of keys that will give each key a certain characteristic, It is not just a simple matter of frequencies. Now I really am departing from this thread.

They do, but the default is equal. To double-check this, I've fed our clavinova into the computer to frequency-analyse the sound it produces for each note. A=440Hz, and the other notes are perfectly in tune according to a perfectly equal temperament - which is good to know, given digital pianos don't need tuning .



An electronic tuner does not equip a piano tuner with all the technical skills he needs to do a good job, however - there's far more to it than working from the bottom key up one at a time using the tuner to set the frequency.



An interesting hypothesis - essentially, you're saying that acoustic instruments have some special qualities which can be tweaked out of them by setting the strings to slightly the 'wrong' frequency. That's the only thing a tuner can do - any tweaking is restricted to changing the tension in a string with a tuning hammer, and if this is done a detectable change in frequency will be made.

To see whether this was the case, I frequency analysed professional piano recordings note-by-note. If any pianos are in tune, its those used for professional recordings. To be certain of my conclusions I used a few recordings of a few artists on a few different pianos. Again, as with the digital instrument, they had equal temperament - the piano tuner had done his job, as one might hope given the prices that Steinway-approved tuners charge. No mystical tweaking, no artistry - just a damned fine tuning job.

Anyway, even supposing a piano tuner did tune a piano to suit some keys - we'd have unequal temperament. Keys which weren't tweaked-for would sound nasty. As a general trend, early music has few sharps and flats and as the temperaments used became more and more equal, we see pieces using more and more remote keys. Bach's WTC was to prove a point as much as anything else, and even in the WTC he avoided certain fifths that sounded bad (recent work published in Early Music). Over the decades after the WTC, temperaments continued to become more equal until a truly equal temperament is used, all keys sounded equally good (or bad, depending which way one looks at it), composers used any key and any harmonies they wanted. The reason harpsichords cling onto non-equal temperaments is because the repertoire of the time sticks to few sharps/flats and avoids harmonies that would have sounded bad in the temperaments they used, so there's nothing to be lost and something to be gained by using non-equal temperament.



Aww . The above is left in case anyone else is interested, then .

I think, in my semi-ignorance that this is key - I have read in more than one place that due to perception, some of the notes on the piano are tuned mathematically out of tune to "sound right" to the human ear. I think it's the low notes - I forget if they are tuned sharper or flatter, but if tuned to the exact frequency they don't sound right. Plus like Petra says, things like wolf intervals etc which come into play if two notes are played together sometimes, and a good tuner will take this into account... it's also why a lot of tuners still tune by ear instead of using the electronic equipment which is now available.

I can't pretend I understand this - this is just what I have read in various places and been fascinated by. As such, if notes are tuned to take account of wolf notes, and take account of differences in perception, plus all the narrowing and widening of certain intervals to take into account the demands of equal temperament, it would explain differences in perception. I don't know but it's my understanding that a properly tuned acoustic piano ISN'T tuned in exact equal temperament


Just a theory on my part, but I have a friend who is exactly the same - she doesn't have perfect pitch by the usual definition - she can't pull a note out of the air, or tell you the pitch of a random note. However, she would be able to tell if you had transposed an electric piano, and finds it hard to look at the music if we sing, in choir, from music at one pitch when the piano has been transposed to another. My theory is that it's a sliding scale between tone-deaf - ie no pitch perception - and perfect pitch. I think that maybe it would be possible for her to learn perfect pitch, though I'm not sure and she hasn't tried. But certainly, even though I have a much better sense of relative pitch than she has, she can hear pitch in an absolute pitch way that I can't. Which I find very intriguing. Her older sister does have perfect pitch....





My shaky understanding is the same as Petra's - the good piano tuner for aim for an illusion of equal temperament, but not necessarily what a computer would consider equal temperament.