Just intonation whistles - how?

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Just intonation whistles - how?

Post by benhall.1 »

Several apologies first: firstly, sorry if this is too anal/intellectual; secondly, I know Carey Parks makes one, so I could have just asked him direct (but I thought there was a chance that some other people might be interested, as I am); and finally, there may have been threads on this before, but I can't find one that quite asks this:

I know that there are whistles made "in Just Intonation". As I say, Carey makes one, and I've seen others elsewhere. But this concept has always puzzled me, and I'm just reading stuff about tuning systems, and now I'm even more confused. I would assume that a JI whistle would have to be tuned to be 'in tune' from a JI point of view in one key only. Using a D whistle, compared with ET, the F# would be flat, the G would be sharp, the A flat and the B would be flat. I haven't got the brain power to work out the rest. But, just from this, wouldn't that mean that, as soon as you tried to play in another key - even in another mode, say, like E dor, you wouldn't be in tune in JI any more?

In other words, doesn't JI mean that you have to be able to adjust the tuning of any given note depending on its context, and that therefore you can't have a truly JI whistle? Or any fixed pitch instrument?

[BTW, I'm really not trying to be smart. Quite the opposite. My brain is in a bit of a fug on this one. :-? ]
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Re: Just intonation whistles - how?

Post by MTGuru »

benhall.1 wrote:wouldn't that mean that, as soon as you tried to play in another key - even in another mode, say, like E dor, you wouldn't be in tune in JI any more?
Yep, sort of. JI is root specific, so cross-keys played on a different root will be off. Now if you work out the intervals and ratios, you find that closely related keys around the circle of 5ths still have a lot of consonance, particularly for diatonic stuff like ITM. But yes, some of the intervals will be off. I was crazy enough to try to spreadsheet this at one point long past.

The thing is ... is doesn't matter. If the pipes are JI in D, and the whistle is JI in D, and the fiddle is playing JI in D, and the flute is playing some God-awful embouchure-twisting flute intonation ... :-) ... then you're all off in the exact same way when you're playing outside of D. Voilà. It's just part of the characteristic sound.

Now bring ET instruments into the mix - banjos and boxes and concertinas - and in theory you've got a clash. But it's a clash that's 100 years old now, and I think might also be considered part of the characteristic sound. Howard Goodall talked about this in his "Big Bangs" series on Western music history, in the context of Romanian and Balkan music. When ET accordions invaded a tradition dominated by pitch-malleable strings and winds, the ensuing clash came to be regarded as tolerable, and even desirable.

Ultimately, I think a certain degree of chaos around the performance of ITM - including intonational fuzziness - is part of its charm. And in playing it myself, I'm happy to leave over-concern with music theory issues to the armchair musicologists. :wink:
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Re: Just intonation whistles - how?

Post by chris_coreline »

at the risk of getting singed, at the session last night i overherd a conversation which went somthing like this:

'i think im out of tune, well.. i wouldent busk with it, but its good enough for folk'

which opens up an old can of worms, to which i will only add that cent-perfect tuning is for pop music and modern jazz. this music is from the soul, and the soul should never be perfect.
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Re: Just intonation whistles - how?

Post by david_h »

If you are after a long discussion try an old one: viewtopic.php?f=1&t=69080 :D
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Re: Just intonation whistles - how?

Post by hans »

edit: as Dave suggests
Last edited by hans on Thu Jan 21, 2010 4:11 am, edited 2 times in total.
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Re: Just intonation whistles - how?

Post by david_h »

But the horse died :wink: :D
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Re: Just intonation whistles - how?

Post by s1m0n »

AFAIK, most sets of pipes are already in JI, because all notes have to be in tune with (= harmonics of) the drone or they sound like crap. Back when we were both learning whistle, a pipe-obsessed friend began making his first set of SSPs (out of copper tube & acrylic, I think) using plans he'd found online. He built and tuned the chanter, learned the fingering and began playing it, only to discover when he got to the drones that the fact that he'd tuned to ET was a big problem. Henceforth, his chanter had sticky tape across the edges of the holes every time I saw it.
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Re: Just intonation whistles - how?

Post by talasiga »

benhall.1 wrote:Several apologies first: firstly, sorry if this is too anal/intellectual; secondly, I know Carey Parks makes one, so I could have just asked him direct (but I thought there was a chance that some other people might be interested, as I am); and finally, there may have been threads on this before, but I can't find one that quite asks this:

I know that there are whistles made "in Just Intonation". As I say, Carey makes one, and I've seen others elsewhere. But this concept has always puzzled me, and I'm just reading stuff about tuning systems, and now I'm even more confused. I would assume that a JI whistle would have to be tuned to be 'in tune' from a JI point of view in one key only. Using a D whistle, compared with ET, the F# would be flat, the G would be sharp, the A flat and the B would be flat. I haven't got the brain power to work out the rest. But, just from this, wouldn't that mean that, as soon as you tried to play in another key - even in another mode, say, like E dor, you wouldn't be in tune in JI any more?

In other words, doesn't JI mean that you have to be able to adjust the tuning of any given note depending on its context, and that therefore you can't have a truly JI whistle? Or any fixed pitch instrument?

[BTW, I'm really not trying to be smart. Quite the opposite. My brain is in a bit of a fug on this one. :-? ]
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Re: Just intonation whistles - how?

Post by hans »

Ben, I had to reread the Equal vrs. Just tuning topic first.
One problem with talking about JI is that there are different kinds of JI tuning, depending what interval ratios the tuner chooses. And the different kinds give different problems when we want to play in modes or want to play in a different key, like G major on a D whistle.

But I stick to the conclusion I got to at the end of that discussion, which is to use the Indian just intoned major scale with interval ratios of 1/1 9/8 5/4 4/3 3/2 27/16 15/8 to the tonic. This differs from the Western JI major scale in the sixth, being 27/16, not 5/3, or +6 cents sharp to ET, not -16 cents flat.

Code: Select all

Indian JI major scale
I     II     III      IV      V     VI       VII      VIII
1/1   9/8    5/4      4/3     3/2   27/16    15/8     2/1  ratio to root
   9/8   10/9   16/15    9/8     9/8     10/9    16/15     interval
0     +4     -14      -2      +2    +6       -12      0    cents from ET
If we add a minor seventh of 16/9 (for a Cnat on D whistle, -4 cents to ET), this will give us a just intoned G major scale on the D whistle, but with a different major third interval (different flavour of just intoned major third). Some of the relative modes on D come out fine: in particular Dorian and Mixolydian. Phrygian got a "wolf fourth", and Aeolian got a"wolf fifth". Wolf intervals are nasty and the note needs individual adjustment.

But the main thing with this Indian JI major scale is that the Dorian and Ionian both work. There is no problem with the E (for a D whistle).
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Re: Just intonation whistles - how?

Post by fiddlerwill »

As a piper, JI is a basic fact of life. Recently I was playing with a Pianist who could adjust his instrument to Just intonation and set the root note of the scale , plus the ability to tune up to the pipes(GHB) and we had a great session. Now the GHB play in 3 keys(generally), A mix, D major and Bm. Its also possible to play in A major, G major and Am without using the G#in A, or the C nat in Am and G.. |All the notes on the chanter are ( meant to be ) in tune with the drone.

In our experiments we found that a root note of A just gave a better feel that D to get the G nat in its correct place in relation to the drones.


The important thing in this instance is that the notes of the tune, relate to the notes of the drones. When the extant powerfully overtones and undertones are taken into account then what actually happens is chords. We therefor find that each note played relates to the fundamental Bass drone and to the tenor drones as well creating perfect intervals.
This is why the contention that chords are an addition, an extra, is mistaken. They are in fact, within a pipe based music such as ITM, a firmament upon which the tradition is built.


As far as whistles go, well Im certainly no expert, but if you take the drones as a basis, then the whole intonation issue makes more sense IMO .
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Re: Just intonation whistles - how?

Post by walrii »

MTGuru wrote:I was crazy enough to try to spreadsheet this at one point long past.
Some of us are still that crazy. The monster spreadsheet below compares a scale in Dmaj JT with an ET scale. This first block is the cents difference between the notes of the JT scale and the ET scale, plus is JT sharper than ET.

Dmaj scale just and equal temperment.
JT Ratio Note JT Ratio JT Cents ET Cents ∆ JT-ET
1/1 D 1.00 0 0 0
9/8 E 1.13 204 200 4
5/4 F# 1.25 386 400 -14
4/3 G 1.33 498 500 -2
3/2 A 1.50 702 700 2
5/3 B 1.67 884 900 -16
16/9 C 1.78 996 1000 -4
15/8 C# 1.88 1088 1100 -12
2/1 D 2.00 1200 1200 0

These next blocks show the difference between various modes in JT and how they differ from the Dmaj JT and ET scales above. In these blocks, plus is the mode scale in JT sharper than the ET or Dmaj JT scale.

Bmin ∆ET ∆Dmaj JT
D 16 16
E -2 -6
F# 2 16
G 14 16
A -4 -6
B 0 16
C 12 16
C# 4 16

Amix ∆ET ∆Dmaj JT
D -2 -2
E 2 -2
F# -16 -2
G -4 -2
A 0 -2
B 4 20
C 16 20
C# -14 -2

Edor ∆ET ∆Dmaj JT
D -4 -4
E 0 -4
F# 4 18
G 16 18
A -2 -4
B 2 18
C 14 18
C# -16 -4

Gmaj ∆ET ∆Dmaj JT
D 2 2
E -16 -20
F# -12 2
G 0 2
A 4 2
B -14 2
C -2 2
C# -17 -6

Emin ∆ET ∆Dmaj JT
D -4 -4
E 0 -4
F# 4 18
G 16 18
A -2 -4
B 2 18
C 14 18
C# -16 -4

Dmix ∆ET ∆Dmaj JT
D 0 0
E 4 0
F# -14 0
G -2 0
A 2 0
B -16 0
C -4 0
C# -12 0

Ador ∆ET ∆Dmaj JT
D -2 -2
E 2 -2
F# -16 -2
G -4 -2
A 0 -2
B 4 20
C 16 20
C# -14 -2

Let's see if anyone is crazy enough to check my math!
The thing is ... is doesn't matter. :wink:
Indeed. What falls out of all the above is if you have an ET whistle that will reliably blow +20 cents from its ET tuning on all notes, you can blow into tune with anything tuned JT.

Whew. Edited to add: Dang, the formatting didn't work when I copied the spreadsheet into the post. I'll have to fix that later.
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Re: Just intonation whistles - how?

Post by highland-piper »

I'm going to agree with and amplify on some of Will's comments above.

Without being too nit-picky about what constitutes a particular key, or mode -- in Highland piping we have have tunes in at least a few of them, yet our tuning is set. Our chanter is tuned to the drones, so it's based on A. But we play tunes in D and B minor and most of the other notes our chanters provide.

Here's an observation related directly to the original question: orchestral violinists play in a form of JI called "pythagorean tuning" -- it's part of the reason a composer will choose a given key for an orchestral work -- each key sounds different. They're only all equally boring on piano and guitar. (They also use a normal JI for harmony parts, but that's another topic entirely). I have a cousin who tunes his own pianos, and he doesn't tune them ET -- he only plays music in a limited number of keys so he tunes it how it sounds best (by ear).

Here's one method you could use for tuning a whistle -- Get two whistles (the same kind), and cover all the tone holes on one. So the one can only play a D. Now play that constant D along with the other whistle, and modify the notes as necessary to make them sound the best. Start out by "shading" the edge of the hole. If it sounds better, then shade some more. Continue doing so until it starts to sound worse, then back off. That's the correct pitch. Put some tape on the hole to make it play that pitch. If shading doesn't improve the tone, then either it's already tuned, or else it's too flat. Carve it out some to find out. If it was already tuned, then put some tape on. After you figure out where all the holes should be, modify the second whistle to be in tune with the first (thus avoiding needing to have tape on every single hole.

Or just open them all up to begin with and tape them all down and don't worry about the tape, kind of like my band chanter :D :thumbsup:
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Re: Just intonation whistles - how?

Post by hans »

@walrii: I do find those ∆Dmaj JT deviations from Just Major meaningless, as the important point is that the relative modes are in-tune with themselves, i.e. that there are good ratios. And the cent deviations look wrong to me.

If you start with a just tuning of 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 as you've done,
you got deviations to ET of 0 +4 -14 -2 +2 -16 -12 0 approximately (we agree on this :) ).
Now lets construct Dorian on the second note (E on a D major scale):
If we use ratios we divide all ratios by 9/8. We get starting from E:
1/1 10/9 32/27 4/3 40/27!!! (not 3/2 perfect fifth) 5/3 16/9 2/1
If we use cent deviations we subtract 4. We get starting from E:
0 -18 -6 -2 -20!!! -16 -4 0
This is quite different from your figures.
I highlighted the wolf fifth!!! The other ratios are acceptable.

If we use a just tuning of 1/1 9/8 5/4 4/3 3/2 27/16 15/8 2/1, as I outlined in my previous post, using a different just sixth interval (the Pythagorean Sixth),
then we get for Dorian
1/1 10/9 32/27 4/3 3/2 5/3 16/9 2/1
with a perfect Fifth.
But in the Aeolian mode we get the 27/20 wolf fifth, whereas with the standard Western Just intonation with 5/3 Sixth the Fifth in Aeolian is perfect.
So there is no just intonation scheme which will get all intervals in all main modes right.
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Re: Just intonation whistles - how?

Post by david_h »

I think I understand the pipers to be suggesting that the presence of a set of drones may over-ride some considerations that are important if the scale for melody alone was being optimised. Does playing an E-dorian melody over a Uillean pipe drone change how the scale should be optimised (say from what hans is suggesting) ? And if so is the character of that sufficiently distinctive that a whistle played solo should have the same scale, or is it then just a case of doing what sounds best in that situation. But since a whistle doesn't (I think) have as much energy in high harmonics as a pipe chanter reed can it get away with being a bit more 'off' from what would be best for the drone?

Could be that MTGuru's post gives the practical answer.
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Re: Just intonation whistles - how?

Post by highland-piper »

david_h wrote:I think I understand the pipers to be suggesting that the presence of a set of drones may over-ride some considerations that are important if the scale for melody alone was being optimised. D

If you have a set of harmonically rich drones, then the presence of the drones over-rides all other considerations if you're playing solo.

In practice, if you are playing a reel or a jig (without drones) then no one will hear a few cents one way or another on most notes. In fact, without drones (say a whistle or a fiddle) you can be pretty far out of tune before most people will notice.

But your classical violinist only has one C# for playing a solo melody line. It doesn't matter what key, a C# is a C# (see the videos on violinmasterclass.com for an explanation of how to find each note on a violin)

I'm saying that you can optimize for any scale, and the others will sound OK -- the difference between one scale and another will be color or flavor, and not objectionable.

Now if you're playing with others, there could be difficulties. If I have a D whistle that I tweeked for D, and you have on that's been tweeked for G, we might have some issues. But if either of us is playing with a guitar there won't be issues. It all just depends on what you're doing.
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