Intonation test results are in!

Thought I forgot, didn’t ya! Well, now that the semester is over, the project is over and break is here, I can hopefully answer the burning questions of those who participated in the test. First of all, a resounding THANK YOU!!! to all my guinea pigs! I got a total of 14 completed tests back that I used to tally the results. Of course a larger sample would be better but I saw some interesting patterns emerging even with such a small group. I apologize to anyone who sent in a request to take test who never recieved it. If anyone is curious and would like a copy of the test sent to them now, I can get it out within a day; if anyone who has already taken it would like to hear it again once I explain it, just let me know. But if you haven’t taken it and want to, read no further, for the secrets will be revealed!

So here’s the deal. You listened to 12 examples. Only 3 different possible intonations were represented in those examples, each one 4 times. Four of the examples used what is called “just intonation.” Just intonation is the only mathematically perfect way to tune an interval: in a justly tuned interval the ratio of the frequencies of the two notes is exactly 2:1, or 4:5. or 3:2, or whatever. As a classical player of a fixed-pitch instrument (the harp) I’m forever sitting around in orchestra while the conductor tries to get everyone else to tune this way. I don’t understand how it works in classical music--maybe Trevor can help here? but I understand from acoustics that to play everything strictlly in just intonation would sound pretty terrible since the ratios add up evenly to an octave. But anyway, a classical musician other than a pianist or harpist would be expected to prefer a justly tuned interval in this test since that would be how they’re taought to tune. I had to take an intonation class last year at school where just intonation was the only acceptable intonation, for example.

The second type of intonation represented in the test is equal temperament. Equal temperamentwas invented to solve the problems of just intonation by dividing the octave equally into twelve semitones, or half-steps. Pianos and harps are tuned this way in classical music. The major third in question in this test is noticeably sharper in equal temperament than in just intonation.

The third type of intonation used is one modern fiddle player’s personal preference, and is even sharper than equal temperament.

So, all of them can be considered “in tune” by one standard or another. My interest was to see if I could notice any patterns for preference in a random sampling of Irish music enthusiasts. Everyone’s responses were tremendously helpful, and some of you, I suspect, have better ears than you thought after taking it. So here are the answers to the test:

Special
Just
Equal
Equal
Just
Special
Equal
Special
Special
Just
Equal
Just

Several people consistently rated just as flat, equal as in tune, and the other one as sharp. The overall trend among the group reflects this as well:

61% of the responses for Just Intonation were FLAT
25% were IN TUNE
7% were UNSURE
7% were SHARP

64% of the responses for Equal Temperament were IN TUNE
14% were FLAT
13% were SHARP
9% were UNSURE

48% of the responses for the Extra Sharp Tuning were SHARP
45% were IN TUNE
5% were UNSURE
2% were FLAT

So, there seems to be a definite trend towards preferring equal temperament, though the sharp tuning is overall less objectionable than just intonation. There are a million directions one could go in researching this type of thing in Irish music, particularly relating to how people actually play and hear intervals in tunes, but this was an interesting start. I really wanted to analyze commercial recordings of well-known fiddlers to see where they fit on this spectrum, but have been having trouble getting the frequencies of isolated notes with any reliability. Preliminary results are summarized in this chart, although I must make the disclaimer that due to technical difficulties one should not take these results as conclusive:

Sharpest
|
|1/5 tone sharper than Equal Liz Carroll
|
|Equal Temperament | Martin Hayes
| Paddy Glackin
|Just Intonation Brendan Mulvihill
|
|1/4 tone flatter than Just Kevin Burke
|
Flattest

So that’s all the data. Any questions, I’ll do my best to answer them! And comments are obviously welcome!

Were any musicians injured by any of these tests?

Okay, I have a question or three. Looking at that bottom table of famous fiddlers can you explain further. Liz Carroll is playing which degrees of the scale sharper than equal? Are these the same degrees in all keys? Or is it instead certain named notes regardless of key. Ditto for Kevin Burke being flat.

It strikes me that most Irish fiddlers use a lot more open strings than classical players, so therefor have less control over the relative pitch of these four notes through the various keys.

Am I not correct in the belief that in just temperament, if the 5ths are in perfect tune the octaves will be slightly out, and vice versa - which is the reason for tuning fixed instruments in equal temperament?

I know we should just get on and play some tunes, but now you’ve got me pondering these vexed questions - not for the first time.

“…in just temperament, if the 5ths are in perfect tune the octaves will be slightly out…”

If you were to tune a piano, say, using the cycle of 5ths, where all the 5ths are just, the octaves will come out wide.

Yes, in just temperament, by definition, the 5ths and octaves are always true, which is the fundamental reason why on a keyboard instrument if you go more than one sharp or flat away from the key of C the keys sound progressively more and more out of tune. (I’m not going to go into the maths of this - it will give everyone a headache, including me, but there are books on the subject). This is the baisc problem that J S Bach addressed when he wrote his 48 Preludes and Fugues in all the keys in order to show that a keyboard instrument could be tuned so that all the keys sound equally good - or bad, depending on your point of view of view 🙂.

In practice, slight adjustments are made even to the tuning of the piano. A skilled piano tuner will tune the top octave of the piano very slightly sharp so as to give it more brilliance - if it were tuned exactly an octave above the one below it would sound flat.

A singer or instrumentalist who is used to perfect 5ths and octaves can find it disconcerting when playing with a piano and will always have to make appropriate adjustments to their intonation if they’re not going to sound “out of tune”. The tuning of the piano is so ubiquitous now that almost every other system of tuning will sound slightly out of tune until you get used to it.

Trevor

BTW, I should have made it clear in the first sentence of my previous post that I was talking about a keyboard instrument tuned in just temperament.
Trevor

Hi!

Kris, I’ll see if I can answer your questions. For the table of fiddlers, I was specifically looking at how they tuned the initial major third in a D major scale (do-mi, or d-f#.) I looked at a minimum of six occurrences of that third within one tune, measured the frequency in herz, converted it to cents, and averaged the cents. In each case I measured an open D and an F#. I was only interested in the size of the major third, not in how far apart the different tonics were--in other words, if people’s open D’s were tuned to different frequencies, I accounted for it mathematically so that I was only comparing the size of the major third itself. Then I placed each fiddler on the scale based on the average size of their major third in cents. All of the tracks I looked at were from commercial recordings, and all were solo unaccompanied fiddle. As I said before, the data is not conclusive both because I cannot guarantee the accuracy of the original measurement in herz (I have since got a few good leads on a better way to do this) and because it would be better to examine many more samples from each individual player. (Part of the problem with that is the relative dearth of unaccompanied tracks.)
Hope that helps--let me know if I can clarify anything further!

Trevor, thanks for helping me out with the questions about just intonation. I have a question for you now: non-fixed instruments don’t play everything in just intonation. do they? How do you actually do it in orchestra? Is it mainly harmonic intervals that you tune justly? From what I remember from my intonation class, they implied that everyone except fixed-pitch instruments plays everything in just intonation, but the professor (and the textbook) from the class I did the project for insists that this would sound horrible. I think they didn’t explain it fully in class because everyone who was actually affected by it already had been doing it in orchestra for years. Whatever “it” is--but that’s what I’m asking you!

Thanks~

Thanks o.f. - that clears things up a bit. Now, a specific question re Kevin Burke - which recordings did you use? Early, like Sweeney’s Dream (lot’s of unaccompanied there) or later ones? Cause I heard somewhere (firm Will?) that at some point he changed the intonation of his 3rds…. Now, I’m just being a real anorak I know, but can’t help wondering.

Ostrichfeathers, if we’re doing a piano concerto the orchestra subconsciously adapts to the intonation of the piano. In any case, we always tune to the piano at the beginning. This can cause intonation problems for the windwind in particular as they warm up in the first few minutes, so it’s not unknown at the end of a long first movement for the orchestra to have a quick re-tune. In the old days, a piano tuner would be on hand to re-tune notes on the piano that had gone off during the first movement of the concerto.
Organ concertos, like the Poulenc concerto, can be a real can of worms. It’s not just the intonation of the instrument, which may not be quite on A440 (so worrying players cursed with perfect pitch), but the acoustics and layout of the church. The organist may be 50 or more feet away, getting eye-contact with the conductor by means of a mirror, the organ pipes are probably producing their sound even further away from the organist and the orchestra, and as like as not there’ll be a horrendous 4-second reverberation time (Bristol Cathedral is an example), and all this has to be brought into synch for the benefit of the audience - great fun!
While we’re on the subject of orchestras I am most reliably informed that the intonation of a professional orchestra (especially brass and woodwind) in the first few minutes of rehearsal isn’t really much better than that of a good amateur orchestra. It’s just that the professionals get their act together that much quicker (visions of jobs on the line, etc).
Trevor

Ostrichfeathers, would you please be able to resend me the test so that I can look at it again? I realised I didn’t save it onto disk.

Hi again,

Kris, I used Sweeney’s Dream--I can’t remember what track at the moment, but it’s written down somewhere. I’d be interested to compare the later recordings--Will, are you there? Know anything about those thirds? And I am a total geek and willing to discuss this sort of thing at sickening length so don’t worry about it if you have anything else to say!

Trevor, thanks! I know that anytime you have to play with a piano whether in chamber music or a concerto, you have to adjust to that, and it can be difficult. And I can only imagine the problems with an organ! What about when you’re not playing with a fixed pitch instrument though? What do you do then? Do you really play melodic intervals in just intonation all the time? I always assumed that you tune in just as much as possible, and instinctively correct it whenever necessary so it doesn’t sound bad, let the tonic drift where it may, when there’s no fixed pitch instrument around--but it must not drift too terribly usually, since although it sometimes that harpist’s nightmare where you enter 10 minutes into the piece and the pitch is has drifted somewhere in another galaxy than you tuned it to, this is (thankfully, in my experience at least) the exception rather than the rule.

Dow, I’ll send it to you again tomorrow.

later guys~

If we’re not playing with a fixed pitch instrument we play what seems right to the ear at the time. Bear in mind that the stringed instruments have open strings which should always be tuned exactly in 5ths, taking the orchestral oboe’s A as the reference, or a tuning fork or some such if there’s no oboe. So the open strings should stop you from wandering too far off course. In between movements, or complete works, many string players will do a quick unobtrusive tuning check and adjust accordingly (it takes only a few seconds). It’s not unusual to see a violin soloist in a concerto do a quick retune in a couple of bars rest in the middle of a movement, done so quietly you’ll never catch it.

It seems to me that among the few occasions today when you are likely to hear just intonation in action are the best unaccompanied choirs singing Palestrina or the like, and the best string quartets.

Putting on my Luddite hat (thanks, Zina!), my preference for tuning is my old tuning fork (hasn’t worn out yet, and still works even though the batteries haven’t been obtainable for years) for the A, and then I’ll rely on my ears for the other strings. I’d like to see more players, both fiddle and fretted, return to using and training their ears for accurate tuning rather than relying on the ubiquitous and expensive electronic yokes they now clamp to the pegbox. I’m sure these devices make one’s appreciation of intonation lazy.

Right, rant over for now! Happy Christmas!

Trevor

This has to be about the most useful interesting contribution to the site in a long time. What a fantastic bit of ‘research’. Does that make me an anorak as well?
I am not sure what tuning I use on the guitar but I tune the guitar listening to the intervals as they fall on the instrument - 3rds 4th or 5ths (Dropped D Tuning). Then I readjust so the 3rds in a C Chord don’t sound too bad. It is all about compromise. Furthermore this is complicated by the fact that if the open strings are in tune the 6th string will be out of tune if you move up to the 5th fret or higher. I cope with this by tuning the harmonics (12th fret) and then lowering the 6 string as far as I can without making it sound really off.

I thought it would be nice to arrange a duet (guitar fingerstyle) with a harp, but the tuning differences make it a little less than pleasing to my ears. I have never liked playing with a piano as there always seems to be too many dissonances. Even piano accompaniment of fiddle never seems to sit well on my ears for harmonic/tuning reasons.

Ostrichfeathers, would you please be able to send me the test so that I can run it past my ears.
Many thanks

Hi again,

I’ve got a few requests for the test in my inbox, and I just realized since I’m not home I can’t send out the file, since it’s on my computer. So if you’ll bear with me a couple days, I’ll see if I can get my roommate to send it to me and then I’ll forward it to all of you. Thanks for all the interest in my project!

I must’ve totally missed this while I was out in California for three months. Sounds fascinating! Are you going to do anymore of this sort of thing, Ostrich?

I have to say, the electronic tuners may make your ears lazy, but after trying to tune in an incredibly noisy pub on Sunday night (I finally had to tell the zouk player I was trying to tune to that I couldn’t hear him, and was my A sharp or flat?), I was ever so grateful that I can usually use my tuner.

You were out in California for 3 months and you didn’t even stop in and see us, Zina?

*snort* Jack, all those drugs must’ve really done you in all those years ago, huh?