Dear Folks,
Does anyone out there know of any maker whose whistles are tuned using “just intonation”? (For an explanation of this term, a fairly simple one by Stephen Jones (StevieJ) can be found at: http://www.rogermillington.com/untempered.html )
It seems that a few claim “careful” or “exacting” tuning, but I can’t seem to find anyone who mentions what standard for tuning they use. Of course, maybe no one cares…must just be my piano technician roots showing…
Best,
David
Reyburn makes some with just intonation, though I couldn’t on my quick look just now at the site see any info about them. But I know he makes them. Just ordered one.
I believe Steve Jones reviewed these somewhere. Helpful, huh?
http://www.reyburnlowwhistles.com/
Carol
David I do make “Just intoned” instruments on custom order. Carols new Low F is in “Just” temperament. If you want to hear a sample of a “Just intoned” low D, go to the home page of my site and you will hear Tony Higgins playing one. 
Ronaldo
I’d be willing to bet money (large sums) that nearly every whistle on the planet is tuned to equal temperament. I think there are a lot of folks who “test” the tuning of a whistle by sitting in front of an electronic tuner. I personally don’t agree with that method, but that’s because I don’t like equal temperament.
I was taught to tune pianos with only one pitchfork, making everything “sound” right. Heh. I realize that’s not the ideal, either, but you then get colored keys . . . meaning Bb sounds different from C, and not just shifted downward.
I’ve got special-order just-intoned Reyburn low F and high D whistles. I have been meaning to do a lot of things (like send Carol’s to her!), and one of them is to record the same tune on the just-intoned whistle and the even-tempered whistle, both times with a drone . . . I think that would highlight the advantages of just intonation.
How about a meantone whistle, Renaldo? Could you do that?
Stuart
Dear Folks,
Aha! I knew someone had to have addressed the issue. A few years ago I got sick of the ugly notes coming out of all the whistles in my collection and made my own, in mean tone (I figured that would match most closely the 18th C music that ITM draws on so heavily). Lo and behold, not only did it fix the ugly pitches, but also cleared up the C nat. (oxxooo), and made the difference between C nat. and C# much more obvious!
Ronaldo, have you noticed any difference in performance in your Justly Intoned instruments? Maybe the other differences are only from careful (read: “not factory produced”) workmanship? Makes me wish I had Dale’s never-ending supply of high-end whistles to test and otherwise fool about with…
Best,
David
Since you usually use the whistle for only a few keys, it would be really great to have a non-tempered whistle. That would rule.
David I’d just like to point out that my long and somewhat hurried ramble to which you posted a link wasn’t intended as a discussion of “just intonation” as a mathematically defined tuning system, I don’t know enough about the subject for that.
I was merely bringing to people’s notice the fact that equal temperament is foreign to some of the older traditional fiddlers (and a good thing too - many modern fiddlers sound so bright and almost discordant by comparison).
I don’t think most cheap, i.e. Generation-style, whistles are tuned to equal temperament, but I doubt whether they match the mathematical definition of just temperament either. On their own, though, don’t they sound just right?
It’s all a vexing question. I never had tuning problems in my life as a fiddle player - you can always adjust, say when playing with pipes - but since I became a whistler I seem to be struggling with tuning issues all the time. Isn’t the clash of whistle slightly out of tune with other instruments (esp. another whistle) just the most aggravating thing? I think the fact that the whistle is in a higher octave makes the problem so much worse.
It seems to me that when I play, say, in a session with good wooden flute players, my Generations fit in pretty well. But in a band context, esp. when there are fiddlers with classical training, I often can’t use them.
So I wonder how a whistle intentionally and carefully tuned to “just intonation” would work with other instruments, particularly say, uillean pipes on the one hand, and keyboards, concertinas and equal-tempered fiddles on the other.
What I’ve observed in my tweaking experiments with hand-me-down Generation-type whistles is that many of them are not tuned to equal temperament. I say that with the caveat that Generations and Waltons in particular, are inconsistent from one whistle to another of the same model.
The one Acorn and two Feadogs I’ve examined appear to be fairly in-tune, in equal temperament, as are the Clarkes (old Sweetone Cs are out of tune, but that’s been corrected).
Many of the Generation-type whistles tend to have an F that’s significantly flat to the equally tempered F. That is more consistent with just intonation, where the third note is 13 cents flat compared to equal temperament. They also tend to have a B that’s significantly sharp compared to equal temperament. I don’t believe that has anything to do with just intonation, but I would need to check the math to see. In the key of G, it would place the note maybe 25 cents sharp of just intonation. Many of those whistles also have a bell note that’s significantly sharp, regardless of whether you’re talking about equal temperament or just intonation.
Bottom line: Some of the Generation-type whistles appear to have aspects of tuning that have been influenced by just intonation. However, many of them are so far out-of-tune in other ways that it would be incorrect to consider them faithfully tuned to either system (not counting those two or three brands I mentioned).
Best wishes,
Jerry
Define non-tempered . . . I can’t think of an non-tempered system.
I don’t ask this in a belligerent way, just trying to understand you!
Stuart
Non-tempered means that the intervals of the key are built on actual mathematical relationships between frequencies so that there’s an acoustical relationship between the various notes. On a non-tempered instrument, no compromises (tempering) have been made to allow one instrument to play in more than one key.
Here’s the text from an earlier post about this:
Just intonation is what was played when individual instruments were only capable of playing a single key. C was different in the key of C than in other keys, for example.
Then different kinds of tempering of music were tried until everyone settled on the present system of equal temperament, which means that every interval in the chromatic scale is the same and all keys are constrained to use only notes from that 12-note selection. That allowed one instrument to play in any desired key, but it sacrifices some of the beauty of the music, since harmonies became approximate, rather than mathematically exact.
Singers and players of fretless instruments, like violins, know for example, that there’s a sweeter and more right on sounding major third that’s about 13 cents lower than the standard, equal tempered third.
That’s the just intonation third, and it’s the third a choir singer will sing when there’s a chord that contains it because that’s the third (and not the piano’s equal tempered third) that will make the chord resonate perfectly among the different voices.
Here are the ratios (applicable to any key) of just intonation listed against the notes of the C major scale. The ratios are based on the frequency of the tonic, and the rest of the frequencies for all the notes of the scale are calculated from there. You’ll notice that the frequency analyser tuning software that Serp told us about has an option for just intonation.
C 1/1
D 9/8
E 5/4
F 4/3
G 3/2
A 5/3
B 15/8
C 2/1
Here’s a thread that discussed it in more detail:
http://chiffboard.mati.ca/viewtopic.php?mode=viewtopic&topic=8508&forum=1&start=0
Best wishes,
Jerry
Steve,
I wasn’t implying that you were an expert; I just thought that your first few paragraphs explained it as simply as possible–always a good thing when this discussion arises.
Jerry,
I, too, have noticed that Generations tend toward just intonation without finishing the job properly. And just such a verminous C Sweetone was the final straw in my decision to build my own.
I simply find it interesting that so few instrument makers and repairers know anything about ancient alternate tunings. Especially when dealing with such specifically modal music as ITM. Choice would be a good thing, especially when spending more than $10 on your instrument (do I hear the siren song of WhOA in the distance?)
And I’m still interested in whether JI tuning would affect the technical performance of a woodwind, especially when it comes to cross-fingering.
Best,
David
David,
In the other thread I mentioned,
Ridseard wrote:
“FWIW, to my ear, the just temperament of the pipes does not clash with the equal temperament of (most) whistles, flutes, and fretted stringed instruments. If there is a slight tension between the intonations, it certainly does not detract from the authenticity of the sound or the enjoyment of the tunes, and that’s all that matters (at least to me).”
and Doc Jones wrote:
“Boy, I sure agree with that. My Just-tuned Reyburn sounds great with guitar, mandolin, etc.”
I don’t believe the question about cross-fingering came up. However, if you try to play the secondary major key on a just intonation whistle, the sixth will play significantly sharp.
For example, on a just intonation D whistle, attempting to play in G major will reveal a “wolf note” at the E. The rest of the notes will be pretty close, but the E in just intonation key of D is very different from the E in just intonation G.
However, I believe the modes, including relative minors, would work fine, since they’re built on the same series of related notes. (If I’m mistaken about this, please someone correct me.)
Best wishes,
Jerry
Jerry (et al.),
This ‘non-tempered’ scale you’re talking about is not actually not tempered, it’s got ‘just’ temperament. Just intonation and just temperament are equivalent. Also, just to make sure, I did a quick search and found that the term ‘non-tempered’ is used interchangeably with ‘just intonation.’
I suppose I have a theoretical problem with calling a just-intoned instrument non-tempered because you do in fact have to make some adjustments to make the instrument sound right; relying on purely mathematical relationships between the notes doesn’t sound right. This is the phenomenon called the ‘comma,’ which we can discuss at greater length if you like. The SHORT SHORT SHORT version is that when you start trying to do mathematical intervals past a single octave of notes, the purely mathematical intervals stop being in tune with one another. You have to shift the notes further apart than explicable by the mathematical intervals . . . so, I suppose, thinking of temperament as correction, the only truly non-tempered instrument would be one incapable of playing a whole octave (because even from low D to high D you start needing to shift).
I guess, writing this post, I can see why you’d call it non-tempered, and that it’s not incorrect to say that . . . I guess I personally think of it more as self-tempered or infinitely tempered, rather than non-tempered, because of the comma.
Stuart
Without looking into it further, it’s been my impression that the comma pertains to what happens when you try to apply a non-tempered or other than equal tempered system to more than one key at a time, following the cycle of fifths. I was not aware that there would be any error, or comma, if you stayed in a single key using just intonation.
Actually, E is the only note which will be off. On a whistle with perfect just intonation, E will be 9/4 times the frequency of low D, whereas just intonation for the key of G would require E to be 20/9 times the frequency of low D. The other notes (assuming you can produce a C natural at 16/9) fall precisely into place.
Thanks, Ridseard.
What about this comma issue with more than one octave in just intonation?
My understanding has been that you can maintain just intonation across as many octaves as you like and it will always work, but Sturob has a different point of view.
Can you shed some light?
Best wishes,
Jerry
There will be always be a comma if you follow the cycle of fifths. This is completely irrespective of key. There is, in fact, is a divergence between the perfect mathematical relationship of the octave (2:1) and the fifth (3:2). What I call God’s mistake!
It only becomes noticeable over a span of several octaves, so on a whistle it wouldn’t matter. But if you formed a whistle consort (heaven forbid) with say contrabasses and sopraninos, and you tuned them to each other from bottom to top in just intonation, you’d surely run into a problem.
Perfect fifths and octaves don’t get on in the long run, or over the big span if you like. And since we can’t stand octaves being out of tune, the fifths have to be fudged… An example - the strings of the violin family are tuned in perfect fifths. In a quartet, everyone tunes to the leader’s (first violin’s) A. But, I am informed by a skilled quartet cellist (my sister) the cello’s bottom string has to be fudged - tuned up by almost a quarter tone - to ensure correct intonation with the violins.
It’s all very weird I know but remember that clever people have been looking for a solution since Pythagoras…
I think the question of temperament for whistlers is like hyphens for editors. If you take it seriously, you will quickly go insane.
Have a look at this page:
http://www.rdrop.com/~tblackb/music/temperament/ for a balanced view of the subject.
StevieJ,
Please read carefully. The cycle of fifths is irrelevant to what I’m talking about because I’m talking about an instrument that’s only played in one key.
This whole idea of a cycle of fifths where you can use the same instrument and the same sharps and flats across various keys is a fairly modern scheme involving compromises that don’t come into play at all with an instrument that’s only played in one key.
It’s my understanding that there’s never a comma with a just intonation instrument that’s only going to be played in one key, regardless of how many octaves the instrument spans.
Best wishes,
Jerry
[edit] I’ve gone to the link you’ve suggested, and I believe I see the problem. First, there are two ways the cycle of fifths is used. One, to describe the relationship between various keys as you add sharps or flats; and two, to attempt to produce a single scale based on notes related by intervals of pure fifths.
The assumption inherent in the comma debate as it pertains to a single scale, is that the only way to produce a scale that’s based on harmonic relationships is to use intervals of pure fifths.
Just intonation doesn’t try to do that at all, so there’s no comma. As far as I’m concerned, there’s no problem to be solved and no danger of driving myself crazy trying to solve anything.
Just intonation has both a third and a fifth that are in perfect harmony with the tonic, and all the other notes are in exact mathematical relationship with the tonic as well.
To my ear, that seems a much more logical way to tune an instrument that’s only going to be played in one key. That, incidentally, is how I was taught to sing, by a choir master who was also an accomplished violinist and understood the difference between intervals and chords with true harmonies, and the approximations and resultant lack of true harmonies created by equal temperament.
Here’s the problem. Let’s say you start with D and construct the circle of fifths until you get to D again. The problem is that with just intonation the frequency ratio between fifths is 3/2. If you go around the circle multiplying by 3/2 for each fifth, when you have gone full circle and reach D again, it will be some power of 3/2 times the frequency of the original D, but it wil be out of tune. Mathematically this is because the ratio between different octaves of the same note is some integer power of 2, but the integer powers of 3/2 can never be equal to an integer power of 2 (basically because 3 and 2 are prime numbers).
As long as you stick to octaves and don’t worry about the circle of fifths, there’s no theoretical problem, just an esthetic problem.
I can’t help but draw an interesting mathematical oddity from all this. If the circle of fifths worked the way it “should” work, the prime factorization theorem would be violated, and practically all of number theory would be destroyed. This in turn would invade and invalidate almost all of mathematics.
Jerry,
This is a great discussion! Wow!
The cycle of fifths doesn’t work for the octave; that’s the comma/‘God’s Mistake’ to which we’ve alluded. Even an instrument which can “only” play in one key (discounting all harmonic minors, blah blah blah) would need tempering if you got to a second octave, because the pure intervals are out of tune with themselves. I’m trying to find a good reference for this.
You mention the fact that interval tuning seems, “to your ear,” to be a much more logical way to tune an instrument that’s only going to play in one key . . . and you mentioned choir. With voice, you bring up an interesting phenomenon. Again, I’ll find you a good reference if you’re interested. Voice is unlike violin, even, in that an a capella choir is truly infintely tempered, and will sing intervals which don’t fit into ANY described tuning system. String players, like let’s say a group of violins, violas, and cellos, will play in tune with themselves and play at pitch (until their instruments start to detune, or something weird). Voices a capella tend to go flat because of the way the human ear adjusts the voice to be in tune. Choirs really only go sharp when they’re very excited AND some lead-type person goes sharp and everyone else adjusts.
Also, the point (to my mind) of the idea of comma is that the purely mathematical intervals are not in tune. Sure, you can tune an instrument to a purely mathematical interval system, but it won’t be in tune with itself. At the octaves, in particular. You can’t even go a to A to A’ with the “perfect intervals” and have them all be consonant.
Stuart