Whistle Temperament

No, I’m not talking about being calm and collected (as all whistle players are…)

I’ve been listening to some trad music, and to my ears it appears that fiddles and (especially) uilleann pipes seem to play in Just Temperament. Now the property of a whistle being ‘in tune with itself’ is often mentioned on this board, but what is the ‘right’ temperament for a whistle? As a diatonic instrument I would kind of expect that Just Temperament would be appropriate (Using the Just scale for D in a D whistle). Listening to my Susato and Feadog, they seem (to my ears) to be in Equal Temperament. Is this what modern whistle makers strive for, and are there any ‘Just’ whistles out there? Are some of the whistles that seem ‘out of tune’ actually in Just temperament, and we’re just so used to the Equal Temperament compromise (every scale is equally wrong!) that they sound wrong to us? And how come they seem bad to us, but they don’t seem to bother the uilleann pipers?

Any thoughts?

I’ve wondered about this myself. The equal tempered scale is a compromise enabling chromatic instruments to play in any key and be “almost” in tune, but now our ears have become accustomed to it. The Just temperament probably sounds more natural. I wonder which whistles are closest to Just temperament (certainly not Susato or Clarke).

I’m out of my depth in this discussion, and my once acute ear for pitch has been blunted by years of playing a butchered uilleann pipe chanter which had a lovely tone but the pitch of whose individual notes was all over the place.

People who know about these things observe that uilleann pipes are not - or should not be - in even temperament. The harmonics with the drones work better with a different temperament, the B and C in particular being slightly “flat”. Anyway, it’s part of the character of Irish music to slide up or down into notes, so maybe Irish musicians just don’t regard having a “true” whistle as such a big deal, especially given the price. On the other hand, I can appreciate the fact that makers of high-end instruments will strive for perfection.

[ This Message was edited by: Roger O’Keeffe on 2002-07-24 05:00 ]

Roger’s right… it’s a drone thing. I do know a pipemaker who made a chanter with equal temperment so the musician can fit in better with some musicial score he was working on with a symphony.

Although I understand the concept of Just vs. Equal, I don’t get what real difference it would make in such a small range as 2 octaves. Anyone care to spell it out? What would the difference in cents really be between the two scales in the range of a whistle? Seems like it would be pretty miniscule.

Cheers,
David

[ This Message was edited by: Feadan on 2002-07-24 09:06 ]

edited

On 2002-07-24 08:40, Feadan wrote:
Although I understand the concept of Just vs. Equal, I don’t get what > real > difference it would make in such a small range as 2 octaves. Anyone care to spell it out? What would the difference in cents really be between the two scales in the range of a whistle?

Cheers,
David

I don’t know if I remember this stuff all very clearly, but fwiw:

The issue is not melodic range, how many octaves up or down you play. The issue is harmonic range, that is how many keys you stray from the main or home key. Picture a circle of fifth* - the further you stray from your whistle’s key the more the difference between just and equal temprament matters. (There are many other tempraments, btw).

The way it works is that if you think about a the pitch of a note in Hz, like A=440, you can go up an octave by doubling that number, and you go down an octave by halving it: A’=880 etc. If you went up 12 fifth from a starting note, say C, you would arrive at a C again. (C → G → D → A → E → B → F# → G#/Ab → Eb → Bb → F → C) If you took that new C and divided the Hz in half as many times as you needed to get back to your original C (7 times, in fact), you would find that you would not have your original C, but something close to it. This divergance is called the Pythagorean Comma and it has puzzled philosophers, physicians and musicians throughout the ages.

In the eighteenth century somebody took the Pythagorian Comma and divided it evenly over all the fifth, making each one of them unpure, if you will. The effect was that the fifths would be in sync with the octaves, and that a piano tuned in this way could play in any key it wanted, as far removed from C (the white keys) as it wanted. That was called Equal Temprament and was popularized by JS Bach (who was into this sort of thing) in his Well-Tempered Clavier, which as you remember has a prelude and fuge in each of the 12 different keys, major and minor. Our ears have become so accustomed to Equal temprament that we don’t hear it as “dirty” or “off” anymore. Quite the reverse.

If you don’t do the equal temprament trick, you can’t really equate G# with Ab, and D# with E etc. So if you went up the ladder of fifth, you would end up at “B#”, and if you went down, you’d get a “D-flatflat”, both of which would note quite be C. The further you go from the key you started in, that is, the more accidentals (sharps or flats) you add, the more pronounced the “error” becomes (and that’s what I mean by harmonic distance).

For chromatic insturments, the only way to go is equal temprament nowadays (except for fiddles, which are fretless, and can mess with the temprament, as good Irish musicians very often will do). For diatonic instruments or instruments with drones, like whistles or pipes, there is less need for equal temprament and maybe even a problem with it. (Brass instruments, btw, notice this effect because they are built on the series of overtones–which is pure and not “equal”-- and therefore the players will have to compensate for equal temprament.)

I have never been able to figure out whether tin whistles were originally made in tempraments other than equal, such as the just temprament, or if their tuning has simply never been considered all that important.

Finally, I think that with mass popularity the trend in Irish Trad is to move away from the older, pipes-based tempraments toward mainstream equal temprament, which today sounds more “in tune” to most listeners. (I am sure piano accordions are no help.) That is part of why the high-end makers go for equal temprament, I’d guess.

HTH

*) The circle of fifths, is just the fifth written in a circle, usually C at the 12 o’clock position. Notice that you need equal temprament to make the circle of fith really a circle, meaning that the twelfth fifth will equal the starting tone, seven octaves up.


/bloomfield


[ This Message was edited by: Bloomfield on 2002-07-24 10:55 ]

Bloomfield wrote

That was called Equal Temprament
and was popularized by JS Bach (who was into this sort of thing)
in his Well-Tempered Clavier


Just one correction. Equal Temperament is a product of 19th century. Then what temperament Bach had aimed his Well-Tempered Clavier for is a mystery with several theories. But that must had been a temperament suited for any contrapuntial music similar to Equal Temperament.

So, “Well-Tempered” means just “Well-Tempered” not “Equal”.




Regards,


Hiro Ringo

I’m not real sure exactly how much difference it’d make either, over the scale we’re talking about. I’m no expert on temperments, nor on music theory at all…but I find it an interesting read.

This](http://www.music.indiana.edu/som/piano_repair/temperaments/Syntonic_comma.html%22%3EThis) page talks a bit more about the math.
It appears to me that if your bell note is in tune, and ‘walked the scale’ by both methods (perfect fifths, and pure octave jumps) over about a two-and-a-third octave range, you’d end up off by about 22 cents by the time you get to the end. Luckily, that example coveres an even greater range than most whistles.

Near as what I can tell, how they spread around that 22 cent difference is what they call the ‘temperment’. Equal temperment evidently splits up that 22 cent difference among all the notes, so that they’re equally spaced from each other along the octaves, which would give us a couple cents per note? Is that right, or did I misunderstand something?

A couple cents isn’t much…easily able to be blown one way or the other on most decent instruments (as noted by Hiro).

Am I missing something here? To me, a couple-cent difference seems like much ado about nothing, considering the amount of pitch variation you can get with breath control.


On 2002-07-24 08:40, Feadan wrote:
Although I understand the concept of Just vs. Equal, I don’t get what > real > difference it would make in such a small range as 2 octaves. Anyone care to spell it out? What would the difference in cents really be between the two scales in the range of a whistle? Seems like it would be pretty miniscule.

Cheers,
David

[ This Message was edited by: Feadan on 2002-07-24 09:06 ]

I just ran a Google search and found the following site:
http://www.hlalapansi.demon.co.uk/Acoustics/MusicMaths/MusicMaths.html

They listed the difference between diatonic steps in “cents” for the two scales. I added them up and compared them below. If my logic isn’t terribly flawed then F#, C# and B are noticebly flat in the Just scale (or is sharp in the Equal scale?). I have noticed that most of my whistles registered flat on the F# when I use my tuner. So does that mean they aren’t “wrong” merely “different”?
Bill

Just

  • 204 182 112 204 182 204 112
    D E F# G A B C# D
    0 204 386 498 702 884 1088 1200
    Equal
  • 200 200 100 200 200 200 100
    D E F# G A B C# D
    0 200 400 500 700 900 1100 1200

Thanks Bill!

I knew that a couple of cents couldn’t be right, it just seemed like too much of a subtle difference.

Looks like the differences run between 4 and about 18 cents (which I would definitely find noticeable). Definitely a bigger difference.

(slightly OT, unless you plan to play along with any sort of Bagpipe)

The Way I understand Equal Temperament, is that each note is seperated by 100 Cents, or one Dollar. The Chromatic Scale consists of $12.

Some accountants (tuners) are more accurate than others. My CA30 is consistantly off by 1.5 HZ, which roughly corresponds to 6 Cents. (not even close to the advertized 1.5 cents)A good Human ear can detect something like a 1 cent difference, simply put this is where one would say “its OK and all, but something isnt just so, its a wee bit off”. For this and other reasons, to include the whistle tweaking i am doing, I only use Peterson Strobe Tuners. 1/10th cent accuracy, and I decide how much out of tune I would like to be.

A Bagpipe of any shape or form is definitly in Just temp. Every note is perfectly in Tune with the dominant Drone note. A piper will carve & tape Chanters, and adjust reeds until such time as each note matches a harmonic in the drone. It is a perfect and pure tuning. IF a Whistler or fiddler locks into what the bagpipe is playing, most likely they are falling in line with Just temp. as its the only place to go. Whether or not they know it, and whether or not their instrument is tuned that way.

An A440 GHB chanter (which I actually have)has the following cents offset values from Fairy tale dreamland equal temp. G -3.9, A +0, B +3.9, C# -13.7, D +19.6, E +2, F# -15.6, HG -3.9, HA +0. A Bb GHB chanter would have the same offsets, only bumped up a notch with the A#/Bb having the Zero cents offset. (The major discrepencies are on D and G from one chanter to the next)I am not exactly sure, but I think that D Small pipes would be about the same with a Zero ofset on the D, and all the other values shifted to fall in line.

With a human ear detecting 1 cent difference, equal temp Pipes would sound so horrible, that a really bad Piper wouldnt stand anywhere close to them, let alone “right next to them”, as in playing them.



[ This Message was edited by: rockymtnpiper on 2002-07-27 14:31 ]