Equal vrs. Just tuning

[MTGuru]

In theory, it's perfectly possible to fret a guitar etc. for JI using split frets.

Here's one example: http://users.rcn.com/dante.interport/justguitar.html

[pancelticpiper]

Yes of course if a banjo is tuned normally (to ET) and the uilleann chanter has its B tuned to the strict -16 JI interval it's going to sound pretty awful every time a B occurs. And unlike a violinist, a piper can't make his B 16 cents sharper on the fly by good musicianship. (Pushing harder on the bag to fix a flat note works with some notes but not with others... some notes actually go flatter if you blow harder.)

So a piper who is playing regularly with ET instruments can either 1) tune his chanter more or less to ET or 2) play out of tune with his mates.

Listen to any good uilleann player on an album or whatever and you'll hear their B spot-on in tune to ET when they're playing in an ET context.

The reason I'm focussing on B (the 6th) is because it's the most deviant JI>ET.

The 4th and 5th are nearly identical.

The 3rd is the next-worst and I have the F# on my uilleann chanter at the ET interval.

The 2nd, E, is an odd one on the uilleann chanter because it's nearly always sharp in the low register but flat in the high register. It's the bogey note of the pipes.

To hear what an ET uilleann chanter sounds like playing in an ET context here's me playing with a Pipe Organ....

http://www.youtube.com/watch?v=onGGxt19ksg

[DrPhill]

Thanks MTGuru and PancelticPiper, I am starting to get out of my depth now, but I have learnt a little more. Maybe next time this topic comes up I will absorb a little more. There seems to be no end to the amount of musical knowledge to learn, but I guess I should concentrate on one small corner for now.

The guitar was weird... The pipe playing was nice - I am not normally drawn to pipes (except the gurt big ones played solo outside on a mountain) but perhaps my tastes are changeing as I learn more about music.

I might have to get the dots and try that tune now. (Is no tune safe from my mauling?)

[peeplj]

A thread that got a bit more into the "whats and whys" of it: Just Intonation, Equal Temperment, and Irish Flutes

--James

[highwood]

Boy these threads can grow fast if take a day off!

A couple of observations about 'ET' instruments:

I knew a young woman at music school who shared duties tuning the harpsichord for concerts - it always sounded better (at least to my ears) when she tuned it (and retuned it at intermission), I asked her why one day, she tuned it to sound good in the key of the 'main' piece on that section of the concert - in other words she at least shaded it towards just tuning.

I've known guitarists (I'll admit I don't know much about tuning guitars) who after 'tuning' retune for a particular piece based on the chords they feel are most important - so tuning away from ET to make the chords they are about to play sound better and as close to JI without creating bad dissonances.

edit - this is getting too long - I'll make a second post on my thoughts about whistles

[highwood]

Some thoughts on whistles:

Tuning is very situational - I find that I find a particular note's tuning becomes most noticeable to me as a player when I play a tune which keeps going back that note. What might be easy enough to correct as it goes by quickly becomes a pain when repeated or perhaps my ear can deal with it being off briefly but if it keeps coming back it starts to grate.

I find it more satisfactory to blow notes up in pitch than to back off them to get them to come down, so I feel it is better to have a whistle in JI which one can blow into ET as needed. So the whistles I have made have been mostly JI - though I aim for A=440 and so D is 2 cents flat (in reality 2 cents is kind of splitting hairs) and G is 4 cents flat compared to an ET G which to me is definitely noticeable but not hard to raise as needed.

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.

Of course if the E octaves are not in tune with each other one can play games with that too.

This can also be expanded into the whole oxx ooo C thing too - but I'm not going to open that can right now. If you have both a D and a Bb generation check out B, C, C# on both whistles (with oxx ooo C) what do you notice?

And to maintain a sense of perspective try playing a whistle into a tuner, and also record the whistle and play that into a tuner (so that you don't have the feedback) - sometimes I think it amazing anything sounds in tune.

[highwood]

One more thought - maybe two...

Some are much more sensitive to tuning - what sounds fine to many people will send some of us screaming from the room (well usually my upbringing stops me from being so rude but ...). I like to think that the many would notice if they heard the same music played in tune but I'm not sure.

An observation: a harp tuned by ear to JI rings and sounds more beautiful, more harmonious that when tuned in ET, this is not just when a chord is played, a plucked string starts other strings vibrating and when the harp is well tuned a single string sounds noticeably fuller (and better to my ears). Note I'm not a harp player (yet) - just made a couple and working on a couple more.

[DrPhill]

With apologies to those who just want to play the whistle, and believe me I want to get back there too......

Thanks James for that reference. Now that I have read more I am either more confused or have discovered something a little unsettling. I hope it is the former. Let me explain.

Octaves are very important harmonies. An octave interval represents a frequency doubling, so if we start at a frequency and go up an octave we get double the frequency. If we go up another octave we double that new frequency.

so the (relative) frequencies go 1, (2), (2*2), (2*2*2), ......
ie 1, 2, 4, 8, 16 etc. These are all whole numbers.

Perfect fifths are important harmonies. A perfect fifth interval represents an increase by half of the frequency. So to go up a perfect fifth the frequencies are 1, 3/2. To go up another perfect fifth we multiply the 3/2 by another 3/2 and get 9/4.

So the relative frequencies go 1, 3/2, (3/2 * 3/2), (3/2 * 3/2 * 3/2),.......
ie 1, 3/2, 9/4, 27/8, 81/16

Since these fractions will never be reducable none of them are whole numbers.

So if the octave ratios are all whole numbers and none of the perfect fifth ratios are whole numbers then there will never be a count of fifths that exactly matches a (different)count of octaves.

So the 'cycle of fifths', where a number of fifths matches (another) number of octaves, is based upon a mathematically provable falsehood.

The discrepency between the different tunings (eg equal and Just) is caused because both are inaccurate approximations to some mathematically 'correct' musical system.

Yes, I know there are good reasons for the approximations and juggling, (e.g. transpositions). But is my reasoning/understanding essentially correct?

[MTGuru]

But is my reasoning/understanding essentially correct?

Yes, it is! In fact, you've hit a key point squarely on the nose. Namely, that Just fifths and Just octaves are incommensurate (they don't match up).

The discrepancy is called a comma. And one of the tricks of temperament is to hide or spread the comma among the other scale notes without detuning them overly much, in order to preserve the perceived consonance of the important intervals (3rds, 5ths, etc.) in the keys you're playing in.

The science, mathematics, and magic of constructing the many, various temperament schemes is a black art indeed. There be dragons there along the road to madness ...

I know enough about this stuff to understand the basic math and principles involved. Beyond that, the details are serious overkill for the performing musician who just wants to tootle some chunes.

[DrPhill]

But is my reasoning/understanding essentially correct?

Yes, it is! In fact, you've hit a key point squarely on the nose. Namely, that Just fifths and Just octaves are incommensurate (they don't match up).

Thank you MTGuru. Now I know where the discrepancy lies I can ignore it.........

Beyond that, the details are serious overkill for the performing musician who just wants to tootle some chunes.

............and get back to tootlin', which is where I should be.


(key point indeed! )

[david_h]

How much of folks tendency to accumulate whistles is related to the issue raised by squidgirl on the first page ? Do slightly different intonation profiles mean some instruments suit some tunes (or the way we want to play them) better than others.

[benhall.1]

Good grief, David! I think that's one of the hardest questions I've seen related to this music.

But the answer's "Yes".

[david_h]

Ah, by 'some instruments' I meant, given the context of the forum rather than just this dicussion, 'some whistles'.

I was thinking of E-dorian in particular. No matter what oral contortions I try I usually can't get the dynamics I want on a whistle that I enjoy in D and G. Seems to be too much under- and over-blowing to sound right. I gave up and got a flute...

[walrii]

it is difficult to find a good fretted whistle, innit?

Actually, no. We call them "tone holes."

[Denny]

it is difficult to find a good fretted whistle, innit?

Actually, no. We call them "tone holes."

life