This is my first post to this forum. Although I don’t play the whistle, I am curious about tuning and temperament, so would love to gain any insights into the topic, and you guys seem to know a lot from reading many of the threads.
Most often I hear how equal temperament is a “compromise”, and that if it wasn’t for the necessary practicalities of modulation, and instrument design, Just intonation would be used all, or most of the time.
However, to me, equal tempered intervals sound ‘sweeter’ than Just intervals. This could well be because I, like many, have been conditioned to hear them, and I fully appreciate that I may eventually prefer JI intervals given enough time (I have unsucessfully tried for a week to condition myself solely to JI with no luck). On the other hand, the conditioning could work the other way, or indeed, both ways.
To cut to the root of the issue, my question is directed towards those who prefer Just intoned intervals over their equal tempered equivalents:
For those of you that prefer the pure (JI) major third over the ET version, do you prefer it in every way? In other words, is there any kind of way whatsoever that you prefer the ET version, or is the JI version better in every way?
For the record, although I prefer the equal tempered intervals in the sense that they sound ‘sweeter’ or more ‘on-tune’, I appreciate the fact that pure intervals can sound more at one with the fundamental to form a single timbre, and also can have a lovely ‘droning’ quality. However, I count this as a separate type of consonance to the ‘sweeter’, or more ‘on-tune’ consonance type I spoke of previously.
Well, all I can say that in my misspent youth, when I learned the guitar, I constantly thought that the steel-string ones I happened to play were crap, as they forever sounded out of tune. The nylon strung ones weren’t as bad. Much later, when exasperated, I delved into the problems much deeper, I learned that my ears were telling me exactly what happened. I actually heard equal temperament as hopelessly out of tune. It’s built in. The reasons have a hell of a lot to do with mathematics, and require about 5 volumes of very thick books to explain them If I started cluttering up this forum with that, I would be banned instantly. But the fact is that (I quote from memory) approximately 5% of people are acutely aware of the dissonant nature of equal temp, and it feels rather unpleasant. The effect is different depending on the type of instrument or voice used, and comes down to the overtone content of a given type, and from there down to maths again.If you are not bothered, give thanks to your stars, it can be a real pain.
Try listening to the soundsamples of Bach’s music using equal and non equal temperament for comparison on this site
I know which I think the sweeter of the two.
I couldn’t find the comparison samples on the website. It’s written somewhere that Dr. Bradley did the experiment comparing 5 Bach pieces and that the video recordings were too big (5 mega per minute) to be put on the internet and he just gives an email for info to ask about the samples.
Is there another link somewhere else on the website that I am missing?
I finally found the section of your web site that deals with intonation and intervals…
I must say, your “The 12 Golden Notes” is one of the best analysis I’ve seen on the subject. At the bottom of the page you have a survey with examples of Just vs. Equal Temperament. I love that “blind” test re the Triad Options!!! That’s exactly what I’ve been thinking–that the difference is so small, unless you know which you’re hearing in advance you may not be able to tell which is which.
I also like your samples of the fugue played on the harpsichord in JI and ET. You say you “knocked up this tune in about an hour.” So, that’s that you playing!? That fugue played with JI is a fine example of dissonance as the tune steps up from G# to Eb about ¾ of the way through the clip. To my ear, that chord progression sounds far better in ET, otherwise I’d probably like the Just version.
Great web site you’ve got there Dan! Tell us a little about yourself! Are you student or faculty? If student, is your major music, math, or other?
As Yuri said, it probably has something to do with the harmonic overtone content of the instruments. Since steel strings tend to sound brighter, I’ll speculate that the dissonant quality arises from the higher frequencies. However the quality of build and setup and where along the neck the instrument is played can have a significant bearing on the outcome of such a comparison.
I tried the samples and chose just tuning by a hair. I had often thought my fretted instruments always sounded very slightly wonky as well, but my sense of tuning has become more acute since playing fiddle where I was sounding wonky ALL the time!
If you’re a fiddle player, the question is very easily answered. If you don’t play fiddle, get a violinist to demonstrate the examples below to you.
First, when you tune the instrument, you will take an A from a tuning fork or another instrument, and then tune the other strings in perfect fifths by ear. It’s easy to hear when the strings come into tune with each other - the “beats” disappear and there is no clash. This is a perfect fifth, a natural and very sweet interval. Any minute movement of either string away from this interval will produce a “clash” - beats. In equal temperament, perfect fifths have to be sacrificed in order to preserve perfect octaves.
The “error” in ET fifths is small, however. It is much more noticeable in thirds. On the fiddle, you can play two-note chords - for example G on the D string and B on the A string. Tune your fiddle to a piano’s A. Then play this chord, tuning your G to the G string an octave below. Tune your B to the piano’s B. The resulting chord sounds pretty harsh. Flatten your B very slightly by sliding the finger back gradually and hear the chord really become sweet as you hit the natural third.
Try these two experiments and your doubts will be banished. The sweetness and “rightness” of the untempered third explains why Irish and old-timey fiddle players of previous generations invariably play, for example, slightly flat F#s. It’s not that their ears are defective!
Sure, it’s an interesting academic question. But since this is a whistle forum, I wonder if it makes much sense to answer except in the practical context of whistle performance.
My impression is that most whistles are tuned by default to equal temperment for a “nominal” breath pressure of each note. Good players can then adjust pitch up or down depending on the context.
Playing alone, I probably favor 12TET, since the whistle more or less encourages that, and since I’ve long been brainwashed by playing other instruments and music in an equal tempered world. Playing with other fixed pitch ET instruments such as accordion, concertina, keyboards, and most fretted strings, I’ll also play in ET. Playing with just tuned pipes, I’ll tend to adjust accordingly. Playing with a fiddle, I’ll tend to follow the fiddler’s preferred approach to their intervals.
But, honestly, it’s something I hardly think about at all, and I’ll bet most whistlers are like me. In sessions or mixed groups, you just play what sounds good, and any considerations of temperment are mostly unconscious. With a melody instrument, the purity of intervals is not an issue that hits you as strongly anyway, especially on fast tunes, though moreso on slow tunes and airs. My subjective impression is that it’s mostly keyboard players who fret (!) about academic questions of intonation.
In typical trad group performance, you might get everything from ET to JI to everything in between happening all at the same time, and the resulting “dissonance” just becomes a characteristic (and not necessarily unwelcome) part of the overall tonal texture.
I have a just-tempered Reyburn Low-D. It is my only Low-D whistle. I accompany my wife on her fiddle and my daughters on voice. They won’t ever let me play anything else with them.
I would say there is absolutely a noticible difference. Buy a Just-Tuned whistle and viloinists and vocalists will love you. The only disadvantage of the just tuning is the C nat 0xx000 is weak. But other fingerings are better.
I thought this was interesting, from the “Triad test” on the web site:
each with a slight vibrato (5.2 cents either way). This is mainly because without this tiny (sinusoidal) vibrato, the Just intervals (5/4 and 6/5) would sound too ‘plain’ thanks to lack of timbre ‘phasing’.
But that “plain” sound is what is nice about just intonation, at least with real instruments, as opposed to synthesized ones used in your test. The synthesized ones are simple and “artificial” enough to sound plain when the harmonies are too pure. So your vibrato with differing frequencies is essentially making up for a plainness in tone, like the way accordions are often tuned, with two “unison” reeds slightly detuned from each other to give a thicker, warbly sound. This is of course less “pure,” but might sound more pleasing to many as opposed to the “plainer” sound. It also masks the “beating” from the equal-tempered scale.
A test with triads using the natural sound of a richly-toned acoustic instrument with no vibrato would give very different results, I think.
I think the mind/ear wants each interval to be as pure as possible, but Dan doesn’t necessarily agree with this. I think one thing we can learn from all this is that in the 12 note chromatic scale on fixed instruments you can’t have everything pure. If the 4ths and 5ths are pure, the 3rds and octaves can’t be. If the 3rds are pure, the 4ths, 5ths and octaves can’t be.
I don’t know how to explain why, but I think maybe Dan can if we can get him away from his computer games!
I’ve been wondering how well electronic instruments are now able to produce a satisfyingly rich selection of voices.
There are now electronic keyboard instruments that can provide “automatic just intonation,” which adjusts pitches in real time to create accoustically perfect chords according to whatever base note is used. That’s rather similar to what a highly trained chorus does.
Yes, I’ve read about them. Just one more button to push–hopefully with the foot–and knowing when to push it! (assuming the keyboard realizes you can’t always signal base note changes)
Thanks for all for your replies! I would still be interested to hear from any JI die-hards if you prefer anything whatsoever about the ET versions. Try the ones on this page to make sure: http://www.skytopia.com/project/scale/third
I would be grateful if you could listen to the tests shown in the link above to explore different aspects of why you found/find equal temperament to be out of tune.
If you find that the Saw wave tests sound out of tune in ET, then do you find the tests with octave partials also sound out of tune?
Glad to hear! Yes, you’re right - with vibrato, and/or with simpler timbres such as sine waves and octave partials, and at least for me, it’s easy to confuse them.
Haha, no I composed the music, but even though I play the piano, it’s the computer that’s playing the music.
Yep I’m a student currently in my last at university, and just about to study tuning and temperament even further for my dissertation. Although I took a keen interest in tuning and temperament years before I went.
Again, I count the perception of beats to be a different type of consonance to the 12 basic interval types. The first is relating to how harmonic two pitches will sound to form a single timbre. The second type I call ‘chromatic consonance’, and is related to how ‘sweet’ intervals will sound. How “chromatically consonant” an interval will sound varies from person to person, from what I’ve gathered.
I’d be grateful if you could also try the Sample A/Sample B test that Lorenzon gave above and then maybe visit my third comparison page. If you find that the Saw wave tests sound out of tune in ET, then do you find the tests with octave partials also sound out of tune?
Being a pianist myself, you could well be right! However, the subject is interesting anyway, because it forms an important root of music, at least its harmony (no pun intended!).
I agree, and I also love the droning sound that just intonation provides. However, I am not looking for that kind of consonance (what I call ‘harmonic consonance’), but instead for what I call ‘chromatic consonance’ which is related to how sweet an interval sounds (and this type varies from person to person). I had to make the JI interval sound timbrally/‘harmonically’ the same as the equal tempered version, so as to make it fair comparison. It’s just unlucky that we have separate the phenomena like this.
With real instruments, intonational errors and other complicated phenomena start to creep in, so ‘synthesized’ sounds are necessary to keep the tests as objective as possible. However, I do agree that the just intonational, droning, timbral effects can be even nicer with real instruments, but I’m pretty sure this is mostly thanks to their almost-but-not-quite-spot-on JI intervals, creating phase-like effects. See my new M.third comparison page, and listen to the “Almost Just Intonation” examples.
The other important thing to say is that even with vibrato, the JI sound is still very much in the JI pitch interval range, and far away from ET.
That could well be due to the tiny vibrato. Listen to the appropriate tests on this page, and you’ll hear the characteristic droning sound of JI: http://www.skytopia.com/project/scale/third/
Lol! Funny you should say that as I have been playing a few more as of late Anyway, yeah it’s down to mathematics in the end. Obviously, JI intervals can be represented by close, but different ratios. At a basic level, with JI, you need two slightly different whole tones (10:9 and 9:8 ) so that you can obtain the different intervals of the octave properly.
I think one of the simplest examples is this: Take the JI major third which is 1.25. Now modulate to E major, and take the major third again. In equal temperament, this is G# or 800 cents. In JI, it falls significantly short of this at 772 cents, and 42 less than the usual JI minor sixth. Then if we ever want to play a minor sixth with C as the bass note, we have a problem houston, as we need two different notes. See this pic, and you can see some of the differently sized gaps between each interval: http://www.skytopia.com/project/scale/eq-ji.png
Even then, you’ll find interval contradictions popping up, as the music will often find it itself slightly transposed up or down a little compared to when it started (at least when changing keys). Also, according to this site, mixing harmony with melody, you can’t make all intervals Just with dynamic JI: http://www.music-cog.ohio-state.edu/Music829B/tuning.html
When you’re singing in a choir, you try to “lock in” with the other singers as closely as possible, which provides that resonance or “richness” that Jerry describes (and which you seem to call a “droning” quality). True, some of the harmonics won’t be as precisely matched up, and that may add to a pleasing sound or timbre, but the chord itself I think is mainly defined by the fundamentals (again, especially in the real world with acoustic instruments). I’ve never heard of singers trying to “almost match” to creating beating or phase effects.
It appears you like phase effects, which is a matter of taste. That’s why accordions are available with differing amounts of “tremolo” for different sounds. And it’s not only personal taste, different genres of music stongly favor distinctly different amounts of tremolo in accordions as part of their “signature sound.”
Using the word “sweet” as you do is misleading to me – I think of “sweet” as something that’s as pure and smooth as possible, even if that might not be my favorite sound. I think a word like “pleasing” would better match what you’re talking about and avoid confusion.
As far as melodies go, I’d say I have very little preference whether it’s equal tempered or just or whatever – and I could rarely even tell. It’s only when chords come in that it’s much of an issue.
A third approach is to continuously adapt the tuning as the music unfolds. This can be done with a computer, where the tuning of each successive note in a sequence is adjusted so that just intervals are always used. Unfortunately, this adaptive approach causes the “tonic” pitch to vary over the course of a melody: the “doh” you end with will not necessarily match the “doh” you begin with. For many melodies, most listeners find such adaptive tuning to be unpleasant. Another problem with this approach is that it only works for single-note melodies. Once you add harmony, it is impossible to ensure that both the harmonic and melodic intervals are just. A final disadvantage is that adaptive tuning is really only practical using a computer. It would be a significant challenge for human performers to adopt adaptive tuning.
To begin with, I don’t believe it’s a significant challenge for human performers to adopt adaptive tuning. As we’ve discussed elsewhere, it’s what highly trained musicians do all the time.
From that thread:
From Wikipedia:
In practice it is very difficult to produce true equal temperament. There are instruments such as the piano where tuning is not dependent on the performer, but these instruments are a minority. The main problem with equal temperament is that its intervals must sound somewhat unstable, and thus the performer has to learn to suppress the more stable just intervals in favour of equal tempered ones. This is counterintuitive, and in small groups, notably string quartets, just intonation is often approached either by accident or design because it is much easier to find (and hear) a point of stability than a point of arbitrary instability.
Based on what little I’ve read about automatic just intonation, I’m not convinced that the statement you’ve referenced about its drawbacks (aside from requiring a computer) is correct.
I think good musicians get to be good at figuring out by instinct which notes most need to be “tweaked” to a just interval, and in relationship to what other notes. Computers are trying to adjust ALL the intervals, and you can’t do that in most music. Maybe programmers haven’t yet hit on an algorithm that prioritizes as well as a well-trained human.
Jerry, I think the “adaptive tuning” mentioned in the article is a very specific method, not the sort of tweaking a musician does. It seems to be to try to adjust as many intervals as possible, even at the expense of changing the pitch of the whole scale – it appears you could start out at A440, for example, and wander around until you reached A460 or something. That would be tough for humans. That the article doesn’t even mention what people actually do when adjusting is quite an oversight (common to the academic, theoretical point of view).
The article seems to miss the point in a few other ways. It mentions even professional musicians aren’t good at hitting exact pitches, which is true – in isolation. But the issue isn’t about singing a melody in exact just intonation or whatever. It’s mostly important when singing against another note, especially in a simple relationship such as an octave or a fifth, and then their accuracy will be MUCH higher than mentioned in the article, because they can hear the resonance, the blending of the pitches. That’s when temperament is a real issue anyway, so arguing about pitch inaccuracy in a vacuum is almost meaningless.
Well, it is a can of worms, isn’t it?
First, a quick reply to steel v nylon: yes, it is the very different overtone content. Believe me, it really requires a library’s worth of stuff to really understand the whole process. What complicates the problem even more with strings that the overtone that in theory should be produced are not actually sounding at their theoretical value, because we live in a very untheoretical world, and such things as material resistance, material impurities, and other factors all knock the theoretical values off to a larger or smaller degree.
But in a nutshell. If two waves are an exact fraction of each other, they merge into one very clearly defined wave. That’s when we hear them as pure. When there is distuning, they set up complex patterns, that are heard increasingly out of tune, the larger the mistuning is. In all 12-note systems there is plenty of distuning. Just temperament, by the way is not used for keyboards, as it is a diatonic system, as soon as you add semitones, you leave it. Equal temp. is the only system where all intervals are mistuned, by the way, except for the octave.
But I seriously suggest that anyone taking it really seriously should go to the local university library and start from there. It’s a huge subject, unfortunately a hell of a lot of musicians are not even aware of it’s existance.
That fugue played with JI is a fine example of dissonance as the tune steps up from G# to Eb about ¾ of the way through the clip. To my ear, that chord progression sounds far better in ET, otherwise I’d probably like the Just version.
Playing with other fixed pitch ET instruments such as accordion, concertina, keyboards, and most fretted strings, I’ll also play in ET. Playing with just tuned pipes, I’ll tend to adjust accordingly. Playing with a fiddle, I’ll tend to follow the fiddler’s preferred approach to their intervals.
Anyway, yeah it’s down to mathematics in the end. Obviously, JI intervals can be represented by close, but different ratios. At a basic level, with JI, you need two slightly different whole tones (10:9 and 9:8 ) so that you can obtain the different intervals of the octave properly.