Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Yet another SBI vs RBI thread

That was very informative, Prout. For me, that's a counter opinion to end all counter opinions.. an argument against what I thought most musicians wanted.

I have another question for you then, because ET can be stretched and compressed in different regions of the tuning. It's clear continuity is important to you.. progressive 3rds and 6ths. It's also clear that you prefer slower beating 10ths, 17ths and 24ths, especially when in the final paces of a piece, or in slow passages.

Chopin is a great example.. I relate to hearing 10ths and 17ths in integral passages, where if they beat too fast, they disturb the sonority way too much. Although, Owen Jorgensen mentioned his opinion for the reason Chopin avoided C major in most of his composing was because UT of the time was making the key of C too pure, and he was looking for more brilliance in the tone. Interpret that however you will.. pianos of that time had lower iH and softer, more subdued tone.

My question is if it is more important for you - on the modern piano - to have slower beating expanded intervals in a tuning, or slower beating smaller intervals, like 3rds and 6ths? And in what part of the compass? What about m3rds, which speed up with compression? In other words, what are the intervals of most importance to you (to be as pure, or slow beating as possible) and in what regions?

RXD.. thank you for another series of rich angles on these compromises.. very educational. I didn't see your post until I had written this one!

Well, as a musician, what I really want is on-the-fly just intonation. (I wrote a computer programme once in 1986 to reproduce Messiaen's 'O sacrum convivium' in just intonation. I had to decide when, at each modal shift, to start adjusting intervals to keep the new tonality just and yet still end the piece at the same pitch. Very challenging, but, O My!, what a glorious sound!)

However, as a service musician, I must accept the need for transposition, and therefore even UTs are out for most of my work. I do occasionally still tune and play in Young when doing earlier works with instrumentalists.

Regarding 3rds and 6ths - yes, reasonably progressive, not absolute - the iH may require otherwise. I can hear, but not count, beats up to about 12bps. By then it is more of a light buzz. I think the beat speeds in the 5-8bps range are the ones that bother me most; very obvious; like a soprano with a way-too-fast vibrato; you are left in doubt as to which pitch she was aiming for.

Interesting comment on Chopin. I hadn't heard that. His pieces have a lot of angst in them, so more brilliance may have helped. I have argued in the past that he may have used a Vallotti variant, which would have made the remote keys playable, but very active.

Within the limits of compromise, slower major thirds and faster minor thirds are OK. I like the dark tension of the minor third.

Even though the intervals become wildly distorted at the extremes of the compass, I find I still hear, or choose to hear might be a better expression, Major triads as being, well, Major triads, and so on. As a result, the stretch that produces the most calm, resonant sounding arpeggios from bottom to top of the compass, for me, is most important.

More great stuff.. thank you.



Very cool! This is what I wish could be achieved on a modern piano design for the 21st century! The difficulty you experienced is the same that I have thought about.. the algorithms on an auto-tuning piano would be extremely difficult to work out; to have passages end at the right intonation points while making internal shifts. A lot going on that is not easily quantifiable or predictable.



Yes; I know exactly what you are talking about.



I hadn't thought of this.. the faster m3rd being more acceptable than the fast M3rd, because of the dark tension preferable in the m3rd. Very good point.

So all of this is in argument against the pure 5th (even the pure 12th, in some cases)! From experience I know that stretching the 5th to where I want it on most scales, will disturb this balance too much. Good thing that on great scales, we don't have to choose one over the other, qualitatively.

Joining this together with what RXD said, it would seem that these M3rds and their extensions are most apparent to musicians in the tenor and bass. In the temperament and treble, it isn't as apparent (with the exception of extensions). Major intonation should be as calm and pure as possible, while minor intonation should take the tension. This would lead to the conclusion that it's best to contain stretch as much as the 5th will allow, especially leading into the bass.

Good discussions.. all of this indicates that an ideal ET falls into a very, very small window. With high iH, there is no window. So much is determined by the scale..

Oops! Sorry. I should have quoted:

Ha!! You're singing my song. However, just intonation on a fixed pitch instrument ain't in the cards.

What is in the cards is that 3rd wobbles progressive or not, are annoying, and need to be minimized. 2 note intervals including RBI's will always be heard with some degree of annoying wobble. However, as Stopper has shown, we mostly don't listen to 2 note intervals, but some version of a triad. When the 3 notes are sounding together, when beat masking is done correctly, the effect of the 3rd wobble is greatly reduced to an apparent still point. Take away the 3rd note of the triad, with only 2 notes sounding, and the wobble comes back.

This is why I find the pedagogical exercise of trying to reconcile annoying RBI's in 2 note intervals somewhat barking up the wrong tree.



Ditto. Really, for me its not about listening to smoothly changing beat speeds, musically, at all. Its about not being accosted with the sour wobble of RBI's in general. The 5-8 beat rates, which often result when a note in the 2nd octave is the bass of a chord and the 3rd up an octave or two, creates the most unpleasant beating. This beating is going to be present in any good tuning. So tunings will emphasize or de-emphasize different aspects of the beating, but the beating will be there and prominent musically...and, for me, highly annoying.

However!!!...

...This beating will only be in-your-face, if the 2nd octave notes are producing a nasal to slightly nasal mid partial heavy sound. This is very common in many instruments, especially small instruments. When the mid-partials predominate, it doesn't matter how you tune it, that triad, with the bass in the 2nd octave will be wobbling to beat the band. It ain't a tuning problem, its a board design problem. Free up the board to move down there, mess with the wire scaling and and the partial distribution will change towards the fundamental. This will not make the 5-8 bps go away, but it will become something a tuner learns to listen to rather than a musician being distracted by.

ji

Great points Jim.

Inharmonicity corrected ET does make the RBI's of the low M3rds beat faster than the book rates. If they beat at 3 to 4 bps the book says they should it would sound like mud. With a smoothly scaled and reasonably low inharmonicity bass scale-the fifths drop down to effective zero in the bass and the M3rds are fast enough to give a tremulant effect rather than a bow-wow-wow 3bps. Also the min3rds are slower.

If we didn't have inharmonicity-the the tempering sounds you described you dislike would be worse.

I find the wider M3rds and narrower min3rds of ET greatly improves the harmonic lexicon. I love how we can modulate by root movement of thirds and that the difference in quality between major and minor is dramatized. So much more interesting than always resolving by tonic/dominate root movement.

Very interesting to see how the board comes into this with your experience, Jim!



Do you know of a triad that conceals the beating of the 3rd? I'm trying to remember if I have heard a combination that tends to do this musically.

It doesn't happen in the protocols that are being discussed in this thread. It happens in the context of an entire compass that is tuned either via Stopper, Virgil Smith, David Andersen, and others, where the beat masking has been worked throughout the compass. The entire compass quiets down.

Check out the last chord, but also the entire texture...Keep in mind the word "quiet" is relative. There is beating, but its apparent prominence is reduced.

quiet triad

The tuning aspect of this, aurally, involves octave/fifth/octave triads, octave/fourth/octave triads, octave/fifth/ninth. In stoppers case 3rds are not part of the aural sequence, but rather the above "triads". The stretch is accomplished without any reference to 3rds. Appropriately progressing thirds come along for the ride. Same with Andersen, if I remember correctly. Out of the temperament, the thirds are a result, and are less in-your-face.

Very interesting stuff. Thanks for sharing this, Jim.

I've heard the beat cancelling effect involving the 8ve/4th/5th when the piano is tuned to the 12th at the right point, but was not aware of further implications of beat cancelling. This opens up new things to explore and listen for.

I get what you are saying about 'relative' quietness. I've wondered before if this wasn't a scaling/soundboard effect that led to favourable results in the tuning (when done very well). It certainly isn't phase cancellation.. but maybe some kind of phase smearing? I don't know. It's more interesting to me, coming from you, because you have soundboard and scale experience.

Thanks for explaining more..

As a musician, I abhor just intonation and I think that on-the-fly intonation is a cliché.

I agree, Tunewerk, "..ET falls into a very, very small window..", and IMO the ideal ET was hidden by a huge mountain of prejudices and hallucinations, the most harmful being the idea that beats needed to be zeroed.



So, if I understand correctly, you say that octaves can only be 'beating octave', (please correct me). I would agree, and perhaps that is why they were using the word "apparently"...

As for my description above, of how octaves develop their beating, I was referring to strip mute tuning, so only middle strings. What I describe above is something I could demonstrate at any time.

Regards, a.c.
.

Alfredo,

Do you know what Just Intonation is?

I find it hard to believe that any person, musician or non musician, who knows and has heard Just Intonation, could abhor it.

Sorry, but from my perspective, you have just lost any credibility.

Well, prout, I can't say I abhor Just Intonation. I do find it disturbing, like sickening sweet. I am sure that is only because I tune pianos. There are real dangers in it when vocal groups are singing bitonal parts and then try to get back together.

Many interesting comments.

My search for smoothly progressing RBI are a means to an end.

The end being what many have alluded to.

Identifying octave spread which identified the 6:3 size and accompanying m3/M3 equality creates the aforementioned beat masking chords. Read above about the Dom 7th chord in 2nd inversion for a small octave scale. Also the m7b5 chord for a medium octave scale. And the mM7 chord for the large octave scale. (Large octave scale is a much wider spectrum so doesn't fit as well. You can see the RBI in the graph are a little less smooth because if this but thankfully they are rare.

For me, the talk of RBI preference is moot. If you want the best sounding SBI, you have no choice. Consider pure 12ths. They are produced by mirroring the M17 above the temperament with the M6 within the temperament. Similarity, pure 4:2 are produced by copying the speed of the M3 in the temperament to the M10 above. And my position is that, based on octave spread, you have no choice what the best M3 and M6 speeds are for the temperament if you are going for beatless ( best sounding octaves with least movement) and progressive RBI. No choice. Certainly if you start messing with sizes not dictated by these rules, precision will suffer, and this may be just as important as musical quality; consistency.

We all get used to a type of intonation, so it is understandable that one is disturbed by hearing a different intonation. Your description of Just Intonation as sweet is interesting, and I have heard vocal groups that strive for JI end up so far away from the starting pitch that the basses couldn't sing the bottom notes.

On the other hand, to listen to a truly fine string quartet, or vocal quartet or sextet, performing in JI, is eerily stunning to me.

Dr. White, in his book you have mentioned many times before, suggests always starting the tuning of an interval from a pure (just) interval in order to hear the stillness, then tempering it to the correct number of beats for ET.

Your mention of pitch drifting when singing in JI reminds me of something disturbing that happened during a choral festival I was in in HS. I wondered then what happened, I wonder now what was the point of the director.

He had us sing a major chord, like Bass C, Tenor E, Alto G soprano E. The Bass and alto parts then went up a half step to make it a minor chord, then the tenor and Soprano up a half step to make it a major chord again, and back and forth. After going up, maybe a P4, he played the chord we were supposed to be on, on the piano. Ugh!!! We were chided for not keeping on pitch. I was sure it was everyone else, as I could hear very clearly where our pitch should be, in JI of course, which I realise now would not end up at the "correct" pitch. I wonder now what was happening to the singers with AP during this drill.

I can't stand it either. It sounds dead and artificial to my ears. There's a reason why singers tend to use vibrato of around 7Hz and it's related to how our brains work (our eyes also have some involuntary motion at around that frequency).

Paul.

Well, I guess I am in the minority, at least here on PW!

I have a friend who has 'absolute pitch' (I know, I know, let's not get into an argument about really good pitch memory). She spent a year with Tafelmusik Chamber Choir, trying to sing in Just Intonation at 415Hz (and other pitch references) , which is what they do. She had to quit because her absolute pitch was essentially an extremely accurate memory of the ETs, as a professional pianist, she had been exposed to as a child. For her, pure M3s, low 7ths, variable size M2s, was too difficult.

Jeff, chromatic scales (what your director was doing with your choir) are very, very difficult for singers. Hard to sing perfectly logarithmic semitones, and equally difficult to sing variable size semitones, unless you have AP and use it to adjust the sizes of the intervals to reach the reference pitch at the end of the exercise.

I would like to hear a piano with the key of C tuned to Just Intonation. It would be interesting to hear how the iH would affect the stretch requirements.

I like the ET on my piano, even as imperfectly tuned by me as it is. The iH gives such a nice undulation to the overall sound. The M3 beating partials, as bad as they are, at least decay eventually to a more relaxed sound.

Not so with a pipe organ - plus you have true harmonics now beating against the distorted ET intervals. Werckmeister or a close variant works much better for the majority of the organ literature.

pyropaul - Artificial is not a term I would use to describe an essentially natural harmonic sequence such as produced by a blown pipe or a bowed string or a human voice.

ET is, in fact, a completely artificial construct with regard to naturally occurring pitch relationships. Well, the only natural thing about it is the 2:1 octave ratio, and even the existence of that ratio is abhorred, I think, by Alfredo.

You could use PianoTeq to model a piano in JI.

Its funny, but vibrato was a construct used for a period of time in recent past history. It wasn't in use before, and is much less used, (or not used at all) except for ornamentation value, by most contemporary orchestras and singers. I'm not denying the value of vibrato, only its overuse.

It is so refreshing to go to an orchestra concert and actually hear the pitches being played. It requires better players and much more accurate intonation coordination between the woodwinds and strings, in particular.

For me. JI on a piano just sounds...I don't want to say wrong, but it does sound awful to my ears. Having said that, as a trumpet player and singer, I wouldn't dream of producing beats on purpose. That would just sound wrong.

I believe this has to do with conditioning. We have all heard beating M3's on a piano since the beginning of time. Even UT's have beating M3. We now associate those beating RBI with the tone of the instrument. Remove the beats and you remove the tone.

There are keyboards and software that tune "on-the-fly" to eliminate any beating RBI. Google it. It is an eerie sound.