Equal vrs. Just tuning

[peeplj]

Equal temper wasn't meant to fix the out-of-tune overtones in the harmonic series.

Equal temper was one scheme--there were others, various forms of "well temper"--which allowed you to play in any key on a keyboard without having to retune the keyboard.

The strongest advantage of equal temper is also one of its strongest weaknesses: it makes the intervals in every key exactly the same.

Thus, it is absolutely true that the modern piano, for instance, is out of tune in every key, by an equal and deliberate amount--assuming, of course, that it is tuned in equal temper. It doesn't have to be; there is no reason why a piano couldn't be tuned with another tuning scheme.

--James

[benhall.1]

Yes, but even if you tuned a piano absolutely in tune in one key - say, C major - it would be out of tune in every other. Any other scheme would make the piano out of tune in every single key.

[peeplj]

Yes, but even if you tuned a piano absolutely in tune in one key - say, C major - it would be out of tune in every other. Any other scheme would make the piano out of tune in every single key.

No, even just intonation stays pretty decent in your "close-to-home" keys. There are also various "well tempers" that divide the comma out unequally so that each key retains some of its original flavor. I believe I'm correct in saying that Bach's "Well-Tempered Clavier" was written as a demonstration of these.

On woodwinds, these tuning schemes really aren't that much of a concern. You are going to have more significant tuning compromises over things like L1, which has to tune the cross-fingered C-natural, as well as serve as an octave vent for D, and over having the holes where the fingers can reach them (which really isn't where they should really be).

That said, some whistles come very close. Burkes are a good example.

--James

[benhall.1]

Yes, but even if you tuned a piano absolutely in tune in one key - say, C major - it would be out of tune in every other. Any other scheme would make the piano out of tune in every single key.

No, even just intonation stays pretty decent in your "close-to-home" keys. There are also various "well tempers" that divide the comma out unequally so that each key retains some of its original flavor. I believe I'm correct in saying that Bach's "Well-Tempered Clavier" was written as a demonstration of these.

Exactly. Each key had a different "flavour" [sorry, I've translated that into English for the benefit of English speakers ]. The reason they had a different flavour was because they were, technically, out of tune, esepcially as regards the thirds and sixths. At least, they were out of tune if you take just intonation as your measure of in-tuneness.

[DrPhill]

Oy, this is a huge topic.

Right as usual.......

[highwood]

OK, so my interest here has become very focused and practical. I want a D whistle which is tuned to sound particularly good in E dorian. Is this possible? Would this be an ordinary JI D whistle? Or if it would be different somehow, how would it be different and why?

Yes
Probably not - what is a 'ordinary JI D whistle'
off the top of my head I'm sure it has to do with mainly the pitch of the E

I will ponder this last part some

Bill

[hans]

On woodwinds, these tuning schemes really aren't that much of a concern. You are going to have more significant tuning compromises over things like L1, which has to tune the cross-fingered C-natural, as well as serve as an octave vent for D, and over having the holes where the fingers can reach them (which really isn't where they should really be).

That said, some whistles come very close. Burkes are a good example.

Forgive my ignorance, but why is L1 important for octave venting on a whistle?
And what do you mean by octave venting? A whistle is not like a recorder in this respect.
I know that OXX XXX gives a cleaner D' than XXX XXX, but is the hole location or size that important for this effect?

On the other hand the hole size for L1 is very important for a cross fingered C, and the location as well. Many designs fail here, and the C fingered with OXX OOO is often too sharp, apart from that it is always of a poor tone quality. A C thumb hole is really the answer for all these problems. I just added one on my Burke Alu Viper, and the C is now so much better, full and in-tune.

[Mitch]

The modes of any just-tuned instrument will be as "in-tune" as as the root Ionian.

If you ever hear a Bach peice on a just tempered keyboard compared with an equal tempered keyboard you will suddenly understand the man's genius. You just have to be there to understand this.

Pianos are both a masterpeice and a joke - the strings of each note are not tuned to the same pitch - what you are hearing is something like any instrument flushed through a cheap guitar chorus pedal. One string only is tuned to even temper - the art of the piano tuner is what to do with the strings either side.

Guitars suffer the worst of all tuning fates - they will never be in tune .. one could fudge something aproaching true harmony with a 12 string.

Verily - when the machines start-up (boxes, guitars and keyboards) the magic of the music gets lost.

On the bright side - when a whistle is played in company - it tends to resonate to the ambient temperament - that's the big bonus of having an instrument that can achieve pitch variations so far around the sweet point. The caveat is - play solo using your ear, play in company with a sense of harmony - don't force it

(Edited to say: I regard 0XX 000 as the "beginner's C-nat" . Once you learn how to close down the tube and control it, all those timbre issues go away. It's important to get into harmony with the physics of the pipe.)

[david_h]

... play solo using your ear, play in company with a sense of harmony - don't force it

Very succinct. I've written that one down in big writing.

One the subject of the D dorian. I can't find the spreadsheet where I worked things out. But I think the main problem is that playing in a just D scale the E-B fifth is too wide and tunes that come home to E via F# suffer from a wide last interval. The B and F# both being very flat relative to the E that is 8/9 of D. I wonder if the 10/9 E would work better.

[hans]

One the subject of the D dorian. I can't find the spreadsheet where I worked things out. But I think the main problem is that playing in a just D scale the E-B fifth is too wide and tunes that come home to E via F# suffer from a wide last interval. The B and F# both being very flat relative to the E that is 8/9 of D. I wonder if the 10/9 E would work better.

E 10/9 and B 5/3 gives a perfect 3/2 fifth (5/3 / 10/9 = 3/2). Try it with a bit of tape to reduce the hole6 size a bit. But you might not like it for the D major mode! As highwood pointed out earlier, a compromise between E 10/9 and E 9/8 may be called for, so the player can adjust to either easier (-8 cents from ET?):

The hard note to figure out what to do with is the E - if you go with making it sound like a fifth from the A (I'm assuming in tune octaves !?!?) it has to be 2 cents sharp to ET A=440, if you go with a sixth from G that would be -18 cents compared to ET A=440, you could work something with E dorian which if you make E-B a perfect 5th would again be -18 cents. I've tried various things and am still not sure which I like best, except that ET does not sound right to me and -18 cents is way too flat to sound right in with or after an A - I've been trying something in between so the player ( just me so far) can go up or down as needed.

PS: or indeed do not compromise and use tape to partly close hole 6 when wanting a perfect E 10/9. And as whistle designer: design for a hole 6 which is of maximal size for a comfortable stretch, which will aid half-holing (Eb) and a E 10/9 achieved by taping.

[peeplj]

Forgive my ignorance, but why is L1 important for octave venting on a whistle?
And what do you mean by octave venting? A whistle is not like a recorder in this respect.

Whistle makers design their whistles so that you may play the second D as either oxx|xxx or xxx|xxx.

Some players prefer one or the other, some switch freely between them (I do). They don't care how you play your D's, of course, but they do take care to provide you an instrument that will work either way.

--James

[hans]

Forgive my ignorance, but why is L1 important for octave venting on a whistle?
And what do you mean by octave venting? A whistle is not like a recorder in this respect.

Whistle makers design their whistles so that you may play the second D as either oxx|xxx or xxx|xxx.

Some players prefer one or the other, some switch freely between them (I do). They don't care how you play your D's, of course, but they do take care to provide you an instrument that will work either way.

Yes, i know about the alternative D fingerings, as i said. But what has it to do with precise location of the L1 hole? There is roughly a wave pressure node in the vicinity of L1, but not precisely at all. The L1 hole is to my knowledge not used to tune D or octave D. If you know better i would be delighted to know how it is used for such purpose!

[peeplj]

Forgive my ignorance, but why is L1 important for octave venting on a whistle?
And what do you mean by octave venting? A whistle is not like a recorder in this respect.

Whistle makers design their whistles so that you may play the second D as either oxx|xxx or xxx|xxx.

Some players prefer one or the other, some switch freely between them (I do). They don't care how you play your D's, of course, but they do take care to provide you an instrument that will work either way.

Yes, i know about the alternative D fingerings, as i said. But what has it to do with precise location of the L1 hole? There is roughly a wave pressure node in the vicinity of L1, but not precisely at all. The L1 hole is to my knowledge not used to tune D or octave D. If you know better i would be delighted to know how it is used for such purpose!

The location can be moved a bit. Generally, a smaller hole higher on the tube is equivalent to a larger hole lower on the tube, though sometimes moving a hole will make a larger change in one octave than in the other.

You are correct in that, on most whistles, small changes in L1 don't do much in the way of tuning the octave D. However; I've one whistle where xxx|xxx and oxx|xxx are several cents off from each other. This whistle doesn't get much play as a result, although in every other way it's a lovely whistle.

--James

[hans]

The location can be moved a bit. Generally, a smaller hole higher on the tube is equivalent to a larger hole lower on the tube, though sometimes moving a hole will make a larger change in one octave than in the other.

You are correct in that, on most whistles, small changes in L1 don't do much in the way of tuning the octave D. However; I've one whistle where xxx|xxx and oxx|xxx are several cents off from each other. This whistle doesn't get much play as a result, although in every other way it's a lovely whistle.

AFAIK L1 is not used for tuning octave D at all. What you describe are the general rules for tuning the C#, which is directly affected by location and size of L1.

[david_h]

If you have a tunable whistle the effect of varying the position of the venting hole can be experimented with. With the the second octave bell note down to Db I get the the 'C#' somewhere near B but there is little or no effect on the Db pitch from venting. By then the bell note octaves are 20+ cents different so we are well into "wasn't designed to be played this way" territory for the bore and fipple.