Yes, I think that you’re right there, Jerry. I’ve often wondered (and I’m not alone) if Generation et al intentionally tune the third and seventh slightly flat (as an accomodation between Just and TET). I don’t think that it is exactly set to Just intonation, but perhaps somewhere in between. However, I fully admit that you have probably tested WAY more Gens than I have and will submit to your experience.
Erik
Apologies on my “poor tuning” comments, Lorenzo, but your original statement on just tuning was pretty misleading – if you tune it properly, the just tuned piano will be the most in tune piano you’ve ever heard – but only in whatever key it was tuned to.
One of my high school friends is very big in the early music scene, and I recently went to one of his concerts. I don’t recall exactly what keyboard instrument it is they used – but before one of the pieces they retuned one of the notes on it so it would be properly in tune for that particular piece. (And tuned it back the original way after it the piece was done.) However, I’m not sure if they were using just tuning, mean-tone, or some other early scale.
I’ve mentioned several times the following book… well worth the read:
Temperament
Lorenzo,
I think we’re talking about two different phenemona here. I’m not familiar with the phenomenon of inharmonicity of ringing strings that requires a stretching of octaves in tuning pianos. I don’t dispute that it’s a real effect that must be compensated for.
What I’m talking about is the fact that when you start constructing keys based on a perfect harmonic interval within the original key, working your way up and down the cycle of fifths to produce keys with sequentially one more sharp or flat as you go from key to key, you don’t end up exact octaves apart between a note in one key and a note with the same name in another key. This requires another kind of “stretching of octaves” to produce scales with notes that can be used in multiple keys. The result of having to do this if you want an instrument playable in all keys, is the various tempering schemes, of which equal temperament has become the standard.
Best wishes,
Jerry
My whistles are tuned to Equal Temperment with +/- 5 cents at moderate pressure, 70 Degrees F.
The special modes, like Ahava-Rabba and others are normally equal temperment unless otherwise requested.
By the way, folks …
This is a terrific thread. It really helps (at least it helps me) to compare notes and share information about the tuning of different whistles.
Erik, I agree with you that most of the whistles that come with a flatter than equal tempered third tend to fall somewhere in between just and equal. But they do run consistently flatter than equal, while the rest of the notes are much closer (suggesting that it isn’t a mistake, since they could match an equal tempered third more closely if they wanted to), and some of them are definitely all the way down to just.
Best wishes,
Jerry
One of the reasons I prefer the Clarke original design is that it is “bendable” enough to play either ET or JI. It comes in handy when playing with a concertina, fiddle, then with mandolin.
I can play in tune with each as everything except bottom D seems to “blow” into tune with whatever.
I had to get Michael Burke to re-tune one my low whistles because the C nat and C sharp were too sharp to my ear and I couldn’t blow them down.
Yes, it was misleading colomon, I was referring to the piano as a whole, not just the C scale.
That’s a good link. Reading the whole thing…along towards the bottom, it verifies what I was saying about a “just” piano sounding off. It’s talking about why an organ isn’t tuned to “just.” And, it talks about why “just” doesn’t work for other keys in the 12 note scale. The octaves are always perfect, from one to the next, but not especially from one to the third and fourth above. As the article says, the octaves are progressively stretched (according to math and the machine), because the further the note gets from middle C, the less accurately the ear interprets the tone. A perfectly mathematically tuned C, four octaves above middle C will sound off to the natural human ear…it’s getting close to being out of our hearing range, so the strings are stretch to let the imperfect human ear think it’s in tune. There have been times when I have just stretched the upper 7-8 note out of hearing range, and no one could even tell. I only do that on painos with terrible sounding boards that offer false harmonics.
I’m not sure how to explain it any further, but if you set the temperment scale F to F, around middle C, and tune it imperfectly to itself (called the temerament scale), then all octaves perfectly to each other (involving the progressive stretch, both up and down) you have a perfectly professionally tuned piano that is tempered, or tolerably imperfect. Make any sense?
A paino tuned “just” is just wrong, as discovered by Bach, although the octaves are the same, except there’s no stretch (mathematically speaking) in “just.” and any instrument tuned to “just” can probably be played with the piano (tolerably) in the middle octave, but when it goes to the second, you’ll not like it. Just would be right if we played in one key the human ear was right, but it ain’t, so we compromise and call it good. And it is as good as the human ear.
Ted, our senior uilleann piper expert from the UP forum just advised pipers not to try to tune to electronic tuning instruments because the playing note, due to pressure differences, will be different than the tuning note. It’s not stable enough for the subtle differences. And, on the whistle recorder, and flute, the instrument is tuned to each person’s embouchure, not to a machine. That’s why it’s good for some and not for other. Don’t tune individual notes to a machine. Tune one note maybe, the one in the middle most easy to repeat, then tune the rest of the whistle to that note while playing to a drone or other stable instrument. You’ll see pipers and flute players taping holes, filing, filling with clay or putty, it has to be individualized.
Hands-on experience with piano tuning will teach anyone that there’s almost an imperceptible difference between a tempered and just 4th (C-F) and 5th (C-G), but it will show up in the 6ths (C-A) and 3rds (C-E)…the tests for the piano tuner.
You’re right Jerry, it’s not out of tune with the piano or each other, at least to the imperfect human ear which we all nearly have. Just is always out of tune with tempered, technically, but I would challenge anyone to demonstrate the difference, hitting the two different notes in succession by voice, or with a bagpipe, etc, with the listener looking at his $5K tuning machine, lights rotating each way in thousandths p/second. 
Erik, a life of concern for details made me that way! 
Now I have an adversion to generalities. BTW, we just had an lady move down here from Alaska. She organized Irish music concerts, dances, etc., and played with a band. Her name is Laura Hall..do you know her?
Lorenzo,
I can sometimes (not always) hear the difference between just and equal tuning on the third but not on any other notes of a scale. (Actually, rereading your post, I think I may be hearing it on the sixth, as well. I haven’t investigated that, but I do often notice that something funny is going on around about the sixth on different whistles. I’ll have to take a closer look at that.) That makes sense, because they say the average human ear can’t distinguish notes within five cents of a pitch.
It’s my understanding, a just intonation third is 13 cents flat to an equal tempered third, so that should be audible. Since we routinely hear both (just on fretless stringed instruments and singing; equal on fretted and keyboard instruments), it’s likely that whether we’re hearing a just or equal third at any particular time, both will sound “right,” since they’re both familiar.
Singing chords and harmony, however, is different from simply singing a tune acappelo and hoping to get the intervals spot on. Because there’s a physical linkage between the sounds each part in a sung chord or harmony is making, you can adjust your pitches to spot on intervals with the other singers. This is similar to how you tune a guitar (you probably use the same technique with pianos) when you play two strings and adjust them so they blend together with no “beats.”
Again, the stretching phenomenon you’re describing isn’t anything to do with the difference between just and equal tuning. If you have to stretch the distances for an equal tempered piano, I’m pretty sure you would do the same thing for a just intonation keyboard, with the result that the intervals and harmonies of the just tuned keyboard would sound less dissonant, but you could only play in one key.
There’s a different stretching phenomenon that comes into play when you try to make an instrument play multiple keys, and that second, different, stretching phenomenon is what gives rise to tempered scales.
Best wishes,
Jerry
The name sounds familiar, but I’m not sure that I know her. Was she from Anchorage or Fairbanks? Was she with Acoustic Adventures or Celtic Confussion?
The stretch is the distance a longer string will sway back and forth in the air, thereby losing it’s correctness, producing an inaccurate pitch. Also, the octave stretch is called the progressive stretch up and down the keyboard…bringing (stretching) the strings and their octaves into accordance with the human ear.
Take a look at the two charts on this link…
http://www.phy.mtu.edu/~suits/scales.html
It also talks about the choral vs. the piano thing.
You’ll see the differences are not all the same. In fact, in the first chart it says “Fourth 4/3 = 1.3333 1.33483” Think how close that is. For all practical purposes, both are 1.33.
I don’t know her too well yet, here’s her web page that tells all.
http://community-2.webtv.net/LauraLeaHall/LauraHallsPersonal/
For those of you following Lorenzo’s link, note that the Tuning shift Wav file is not a comparison between Just and ET. It is a comparison of a Chord played in the wrong temperament… in this case, the errors compound. The difference between any one note are not so pronounced. Rather, the slight waver heard on the 3rd note and 6th note of the second sample are more akin to this discussion.
p.s. (I don’t think that Laura is the person I was thinking - we’ve likely never met)
That’s a great link, Lorenzo.
If anyone can come up with a similar chart that shows the differences between the notes of just intonation and equal tempered scales in cents, rather than in Hz, I would be most appreciative.
In the last MIDI file, if you listen carefully while the two scales are playing simultaneously, you can hear beats on the third and sixth, but not on the other notes (at least that’s what I hear).
I was taught to practice matching pitches singing by getting something that will create a fairly pure tone (I used the “clarinet” setting on my toy keyboard) and sing right against the speaker as it sounds the note. You can both hear and feel the beats when you’re a little off pitch, and you can feel the two sounds merge when you’re spot on.
As you get familiar with what that sounds/feels like, you get to where you can do the same thing in a chorus with the other voices. When everyone in the chorus is doing that, the sound and feeling of singing together turns magical.
Best wishes,
Jerry
Edited to add: It looks like Erik and I were typing simultaneously and heard the same things.
I’ve got that here somewhere, Jerry.
Until I find it, here’s another great site to chew on… I don’t think that Thomas posted this one: http://www.rdrop.com/~tblackb/music/temperament/
http://www.rdrop.com/users/tblackb/music/temperament/stoess.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/music/tempercn.html
http://www.justintonation.net/
http://sunsite.univie.ac.at/musicfun/tunexamples/
I could have sworn that I’ve got the cents difference around here somewhere… haven’t found it yet but I suspect that it’s in the rdrop site.
Erik
This thread has taken an interesting turn, but I’m afraid it’s been taken WAY further than I was looking for. I was simply curious to know what the active makers on this board use to tune their whistles as it was mentioned on the other board that they were tuned to Just temperment instead of equal. I thought they were all equal, and it sounds like at least one of our makers uses equal and not just as was stated on the uilleann board…
Ah! Here it is in cents, Jerry: http://www.rdrop.com/users/tblackb/music/temperament/t_Just.htm
Use the bottom graph and remember that the whistle only uses 7 notes. (For those that don’t understand the graph: use only these points: 1, 3, 5, 6, 8, 10, 12 for comparing to a diatonic instrument, ie. the whistle).
It looks like you’re right Jerry; the largest deviation appears to be around 13 on the 3rd and 6th. (as opposed to the 11 that I proposed earlier).
Sorry to swerve your thread, Brian. There are many makers that use equal temperament, but of the makers of which I’m aware only Renaldo offers it standard.
No appologies needed Erik. I’m just trying to sort the mysteries of the universe here…
That second link was a good one Erik, esp in the middle and towards the end.
Brian, I think it’s important for everyone who is either tuning, making, or playing whistles to understand all this. It’s all inseperable. You’d be surprised at how many I’ve run into who assume that some notes in the two scales are off by as much as a quarter step. Amazing!
I’d hate to play in a band if a whistle was tuned to “just” unless the players had a whistle for every key and could switch smoothly while in sets of 3 going from C to D then A.
Whoops…gotta run, late for a gig. I’ll read your latest later.
http://www.justintonation.net/sound/sequence_II.mp3
Lorenzo, here’s a clip that demonstrates that a piano can be tuned to just intonation. This particular just intonation (there can be virtually unlimited variations based on which fractional values you want to use for the intervals) is more exotic than the one we’re talking about, but you can certainly hear the effect.
http://www.newmusicbox.com/32/audio/harrison1.ram
(takes awhile to load) and
http://www.newmusicbox.com/32/audio/harrison2.ram
Here’s a page with info about the pianist:
http://www.michaelharrison.com/recordings.html