Just intonation intervals really sweeter than 12et?

[dwhite]

Hi all,

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.

Dan
----
http://www.skytopia.com

[Yuri]

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.

[azw]

Yuri, do steel and nylon stringed guitars use different temperments? (I'm wondering why the classical nylon string guitar sounded better to you.)

[Cayden]

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.

[Romulo]

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?

[Lorenzo]

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?

I finally found the section of your web site that deals with intonation and intervals...
http://www.skytopia.com/project/scale.html#poll

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.

Sample A

Sample B

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?

EDIT: Ah, found it http://www.skytopia.com/profile/profile.html

[m31]

Yuri, do steel and nylon stringed guitars use different temperments? (I'm wondering why the classical nylon string guitar sounded better to you.)

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!

[StevieJ]

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!

[MTGuru]

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.

My 2 cents (no pun intended!) ...

[Doc Jones]

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.

Doc

[BoneQuint]

I finally found the section of your web site that deals with intonation and intervals...
http://www.skytopia.com/project/scale.html#poll

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.

[Jerry Freeman]

I finally found the section of your web site that deals with intonation and intervals...
http://www.skytopia.com/project/scale.html#poll

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.

That's interesting.

I listened to those and thought, "Neither sample sounds like just intonation." I could hear the beats, and I didn't hear the characteristic richness.

Best wishes,
Jerry

[Lorenzo]

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!

[Jerry Freeman]

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.

Best wishes,
Jerry

[Lorenzo]

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)