Just intonation intervals really sweeter than 12et?

[Yuri]

Yeah, pipe organs tend to be tuned in non-ET. (not just Temp, though,, but some sort of shop temp these days, there are heaps of them.In the past , Bach's time for example, the 1/4 comma meantone, usually. The point is, a lot, if not most organ music of the Renaissance and Baroque eras, and still quite a lot of later times doesn't use many keys/modes. You seldom find more than a couple of flats or three sharps in it. Which is why non-ET temperaments are practicable. With romantic and later music's love of all sorts of outlandish keys and also frequent key changes, ET is the best suited one. But the least well in tune one, too. You can't even contemplate playing jazz without ET. but playing Bach in ET is a crime, should be banned by the Geneva Convention. (just kidding there, but not entirely)

[Lorenzo]

Nothing is as unforgiving as a reed. They bring out the worst in ET intervals because, unlike strings, they have no rich overtones or false harmonics to cover and confuse the note. Everything is bared. Maybe that's why they (accordian and pump organ makers) created the "wetness" effect to add richness.

Bach had a lot of compositions in certain keys, like Fugue in Dmin, Fugue in F, Emaj, Cmin, Bmin, etc., it make one wonder if he retuned his instrument for each key he played in. He didn't modulate that much on the keyboard did he?

[Yuri]

In those times there were quite a lot of keyboards with more than 12 keys per octave. A split D#/Eb and Bb/A# on one keyboard was not uncommon. There are some harpsichords, a couple of clavichords and even a couple of organs surviving like that. But in normal use retuning a few strings was considered quite acceptable. After all, they didn't have to hurry back to the comfy armchair after the commercial break, so they had quite a bit more time than we do.
And in any case, these pieces that use remote keys are rather uncommon. I'd say tey don't make up more than perhaps 1 % of all keyboard music of the time.

[dwhite]

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

When I say phase-like effects, I only mean the type that normal instrumentalists and singers should be unable to avoid. We're talking in the range of a couple of cents here, and still very much Just intonation. Those samples on my site demonstrated the synthesized 'static-ness' of the Just intonation intervals compared to the "Almost just intonation" intervals. Give them a listen, and you'll see what I mean.

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.

Yeah, I would associate 'pleasing'='sweet'='12ET', and 'pure'='droning'='JI', but obviously these terms aren't universal. The only way I can unambiguously describe what I mean is if I say:
"the type of consonance that isn't associated with timbral effects (Ji/pure intervals)", i.e. the other type. Of course, that can be confusing if someone finds this type exactly coincides with the pure intervals as so many people seem to find. In other words, to me, the equal tempered third and the JI third sound good in different ways, but to many, only the JI third is valid, and the equal tempered third always sounds wrong.

his 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.

It may be easier for the singer, but not necessarily sound better. I don't know if you've heard of the general octave tuning issue (not to be confused with the piano octave tuning issue) where every octave sounds a little too flat yo human ears, so needs to be detuned by some cents for each octave to sound 'in tune'.

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 was wondering a bit too, but from what I can gather, I think one example may be the augmented triad. In JI, if you have both major 3rd intervals in tune, then the augmented 5th won't be, and vice versa.

Either:
* 1.25, 1.25 and 1.5625 or...
* 1.264911, 1.264911, 1.6.

(Can't have 1.25, 1.25 and 1.6.... for C-E, E-G# and C-G#)

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.

I think you must be right. However, the article didn't state whether the mistuning was in a harmonic (chord) context (against another note), or melodic (linear) context. I find it hard to believe that when aiming for chords, 25 cents of misaccuracy is so common...

[Jerry Freeman]

FWIW ...

As I said, I'm not an established musician by any means (I'm just a humble whistle tweaker and house trailer repairman). However, there are definitely things that sound well in tune to me and things that don't.

The other day, I found myself singing "Feed the Birds, Tuppence a Bag," from Mary Poppins, and I noticed the first two notes are a major third. There was a way to sing that interval that sounded right to me, and it seemed pretty specific, so I wondered what a tuner would show.

Unmistakeably, it's a just third. So I went to the piano to see what an equal tempered third sounds like. Even in sequence, not note against note, an equal tempered third sounds harshly out of tune to my ear. I'm certain that's not from listening to any particular tuning and having acclamated to it. It's "just" what sounds right.

Best wishes,
Jerry

[Lorenzo]

So I went to the piano to see what an equal tempered third sounds like. Even in sequence, not note against note, an equal tempered third sounds harshly out of tune to my ear.

Right. In ET, the 4ths and 5ths sound pretty good at the expense of the 3rds/6ths. Since they can't all fit in pure form, something has to give somewhere, so the 3rds take the beating (so to speak). My uncle, who spent countless hours teaching me to set the temperament octave, would test his progress by hitting the minor and major 3rds. They'd waver pretty good and he'd shake his head, with tears in eyes, and say, "isn't that beautiful?"

There's a couple pages at the Piano World Forum where tuner Bill Bremmer describes getting in trouble with the Piano Technician's Guild for stretching the octaves--in order to get his pianos more towards JI. This link starts on page 2 but read page 1 after seeing Bill's post.

It has always been considered unthinkable to stretch the octaves on fixed chromatic instruments...at least in the mid-range. Every tuner stretches the octaves on the high and low ends. I knew one old timer that would stretch the last and upper octave (all 12 notes) way up and out of hearing range. Most people didn't even know. Way up there, an A and a G sounds the same to most people with a fallible human ear anyway.

[Jerry Freeman]

his 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.

It may be easier for the singer, but not necessarily sound better. I don't know if you've heard of the general octave tuning issue (not to be confused with the piano octave tuning issue) where every octave sounds a little too flat yo human ears, so needs to be detuned by some cents for each octave to sound 'in tune'.

I think this is a different issue. Although good ensemble players and singers may not produce intonations that are mathematically exactly "just" because of adjusting octaves to accomodate the human hearing apparatus' tendency to hear perfect octaves as slightly flat, there's still a profound difference between chords that use just intervals vs. chords that use equal intervals.

Rather than considering the need to stretch octaves as somehow negating the validity of just intonation, I think it's more like a subtle adjustment that leaves the underlying scheme fundamentally intact. After all, the difference between a just third and an equal third (about 14 cents, I think) is far beyond the subtle adjustment needed to stretch the octaves so they sound in tune.

Here's an article on the octave stretch phenemenon:
http://www.mmk.ei.tum.de/persons/ter/to ... retch.html

The fine intonation produced on violins, flutes, oboes, clarinets, trumpets, etc. is controlled by ear, i.e. in terms of pitches and pitch intervals in comparison to memorised templates. So it must be concluded that it is the internal standard pitch scale of a musician and listener that on the average is stretched. This has been documented by Ward (1954a) in a most direct manner, namely, by having absolute-pitch possessors adjust (on an electronic oscillator) each and every tone of the scale without any reference. The result indeed was a stretched tone scale. For the octave interval it is particularly easy and safe to verify that the corresponding internal pitch template indeed is stretched, and this does not require the faculty of absolute pitch. As the phenomenon of octave stretch practically is sufficient to enforce stretch of the entire tone scale, one may say that scale stretch is explained by octave stretch. And the psychophysical explanation of octave stretch in turn is included in the theory of virtual pitch [16] , [17], [18] , [22] , [38], [55], [56].

You can listen to a chorus or ensemble and hear clearly that the chords are "pure" compared to how the same chords sound on an equal tempered instrument (you can listen to the soundclips I linked to above for examples).

The article on octave stretch mentions that the entire scale is stretched. That would mean that the just intervals would remain just and the equal intervals would remain equal, only slightly stretched to accomodate the human hearing apparatus. Again, as I said, I don't see how this conflicts with just intonation.

You stated:

It may be easier on the singer but not necessarily sound better.

I don't think it's safe to assume that singers and ensemble players don't make the stretch adjustment. The whole process is done by ear, so it would seem reasonable that they do make the adjustment. I rather doubt that it's something they would need to think about. Singing what sounds right will likely create music that is just intoned with a stretch adjustment to accomodate the perceived flatness of a "perfect" octave.

Best wishes,
Jerry

[Jerry Freeman]

There's a couple pages at the Piano World Forum where tuner Bill Bremmer describes getting in trouble with the Piano Technician's Guild for stretching the octaves--in order to get his pianos more towards JI.

Based on some quick Googling, I think this is a separate issue from just intonation. But like just intonation, it's another way that scales and intervals need to be adjusted from an arbitrary scheme to get them to sound right to the ear.

In the case of octave stretching, it would be an adjustment away from mathematically arbitrary just intonation, but not an adjustment towards equal temperament. And it would be a more subtle adjustment than the difference between just and equal.

Best wishes,
Jerry

[Lorenzo]

In the case of octave stretching, it would be an adjustment away from mathematically arbitrary just intonation, but not an adjustment towards equal temperament. And it would be a more subtle adjustment than the difference between just and equal.

The octaves for Just and Equal (F4 and F5 for example) would both be the same, flawless, no beats, pure as the driven snow. It's what happens inbetween where problems arise. Stretching the ocatves a little allows for more of a just tuning within the temperament octave. It allows for some of the thirds to be closer together. It's also a tradeoff since this would affect both the 5ths and the octave. So, it's a related issue anytime Just Intonation is being sought.

If the temperament octave (F4 to F5 for example) were tuned to pure thirds all the way, the last interval (C#5 - F5) would be about 42 cents sharp. That would be unacceptable by anyone's standards...in a choir, an orchestra, or on a keyboard.

Just third intervals, or triads, can always be achieved in a choir, in any key, with any progression or chord. But, it can never be achieved on a piano except in a very limited way as noted before, because suddenly other intervals become unacceptable. Just thirds are also possible between three violins, but never on a mandolin even though they are tuned the same. Frets vs. no frets. Micro-adjusting vs. non-adjustable.

But coming full circle, do pure intervals really sound better? Pure Just Intonation can also be described as colorless, dull, sterile, dry, and boring. Tempered intervals can be described as colorful, exciting, rich, wet, and sensational...unless they're too far off!

[Jerry Freeman]

But coming full circle, do pure intervals really sound better? Pure Just Intonation can also be described as colorless, dull, sterile, dry, and boring. Tempered intervals can be described as colorful, exciting, rich, wet, and sensational...unless they're too far off!

Perhaps if you sample an artificial chord in isolation. But in an actual performance, I certainly wouldn't use those words to describe just intonation. Exactly the opposite, to my ear. Much more resonant, rich, colorful. Powerful. Tempered intervals sound harsh to my ear, not colorful or rich. Chaotic, and not in any artistic way.

Best wishes,
Jerry

[Jerry Freeman]

Really, this seems like a very strange idea, that equal temperament might sound better.

I've never read anything indicating that equal temperament was developed so the music would sound better. Only that it would work at all to be able to modulate across various chords and keys on a single, fixed tuning instrument.

Isn't the whole idea of equal temperament that performers and audiences were willing to accept some compromise in the quality of the tonality for the benefit of greater flexibility?

I suspect the reason some people nowadays think it sounds better is because it's so pervasive and so entrenched, habituation has taught people to think it sounds "right."

Best wishes,
Jerry

[StevieJ]

Really, this seems like a very strange idea, that equal temperament might sound better.

I agree, but it seems unlikely that dWhite is going to agree with us. And that's fine - I prefer to sleep in soft cotton sheets, but I totally understand people like Lorenzo who like things to be more exciting and probably spread fresh sand in their beds every night.

Seriously I haven't even listened to the samples on the pages that dwhite pointed us to - evidence of a closed mind, perhaps, but then time is tight and I prefer to take examples from the real world of real instruments, where I find the results to be incontrovertible evidence that equal temperament = sand in the sheets. (This is not to deny its convenience or the various problems that exist with all other temperaments.)

Talking of which, Lorenzo I don't understand your apparent problem with moving your finger to obtain a slightly different tuning on a note on the fiddle deliberately. (Unless I missed the fact that you have perfect pitch, in which case one has to ask, can having your brain hardwired to ET really be called perfect pitch?). I'd suggest experimenting with tunes like Paddy Fahy's jig and playing the Bs as Paddy Fahy himself does - slightly flat of ET. Open up a new world!

Another real instrument that I amuse myself with (well not everyone might call it a real instrument) is the button accordion, and this morning testing the major thirds with only voice (reedbank) sounding revealed a real case of not only sand but also road salt in the sheets.

Which got me thinking about the fact that multiple voices do seem to soften this very harsh interval to some extent, which led to some further thoughts about the tuning of boxes and concertinas that I might post in the squeezebox forum later in an attempt to snap it out of a coma.

Have a good day everyone and remember that even temperament in every field except music is surely a blessing.

Steve

[Bloomfield]

Another real instrument that I amuse myself with (well not everyone might call it a real instrument) is the button accordion, and this morning testing the major thirds with only voice (reedbank) sounding revealed a real case of not only sand but also road salt in the sheets.

Ouch! Not to complicate things further, but I've spent sometime with Roghaire Dubh (The Black Rogue) and I find that neither an "in tune" C-sharp nor an "in tune" c-natural oxxxox on a Generation or Feadog sound right. On the flute, the c-sharp oooooo tends to be a bit flat anyway and the c-natural played oxxooo is often a bit sharp (and somewhat dull). It sounded best to my ears when played oxoooo (feed that into your electronic tuner), which shows you how very far I have traveled down this dark road.

[StevieJ]

Alasdair Fraser I believe coined the term "C-supernatural" to describe Cape Breton fiddlers' use of exactly the note you are seeking.

[Jerry Freeman]

Well, ya know ...

There isn't just one just intonation scale.

Each note is based on a whole number ratio of the tonic frequency. There are several alternate whole number ratio/just intonation notes that might be used in various places. One would guess that the Csupernatural that sounds right in those settings is a different whole number ratio/just intonation pitch than the one that's used more often, but it's nonetheless a just intonation pitch.

Best wishes,
Jerry