Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Do we hear 'in tune' intervals by size or beats?

Question: Do you, as musicians and/or tuners hear in a musical context, an interval, such as a third or fifth as being in tune or not by the width of the interval only and not the beat rate?

I ask this because in our discussions on tuning and temperament, we inevitably reach the extremes of the piano where the beat rates are too fast (high end) or too messed up by other interfering partials (low end) to use as a temperament check. C5E5 beats at ~21bps in ET. How do we sense that it is 'in tune' when heard in the context of music?

When fast beating intervals such as thirds and sixths are over wide-the musical sound is harsh. When they are too slow-the musical sound is muddy. Many musicians might use other descriptive terms There are no standards for qualitative terms regarding tone.

Definitely I hear for character of the sound resulting from the beat speed, or absence of beats, and relative progression of character resulting from beat rate change for adjacent intervals.

For me, the character of the beat speed is important for the initial cold estimates in a temperament sequence. This requires some experience and memory of the kind of sounds to expect. Relative beat rates then become important as the sequence progresses.

When tuning up through the 6th octave the RBIs become very fast, but it is still possible to look for a progression of character resulting from the rapid speeds. In that range, expanded perfect intervals can usually be identified as moderate beats if the note is already quite close.

For the low end, beat speeds often get confused depending on which partials predominate. Slow rolling for 10ths and 17ths is still audible however very low down but again looking for progression.

I think I may have worded my questions poorly.

If I am accompanying a trumpeter, for example, regardless of the temperament the piano is tuned to, how would the trumpeter and I know that his B5 was in tune with my G2D3G3B3 chord? Would we expect to hear harshness or beats if he was sharp or flat? You have to realize I've been accompanying for almost 60 years and I have never thought about how I perceive out-of-tuneness. I just know when it isn't in tune.

Prout,
There will be plenty of beats going on when accompanying trumpet while playing piano. The most obvious way to hear the ones that would indicate that the trumpet is out of tune relative to the piano is when the trumpet and piano are playing in unison or octaves.

I imagine his B5 would have to be in tune with your B3.
As a professional trumpet player, I do not, as a practice, listen to the piano unless I am forced to play a M3 in unison with the piano.

The other concepts of intonation used are one, an internal sense of intonation developed from the previous melody notes; trumpet and piano tones do not mix well to create beats anyway; trumpet is much louder and has a more consistent and solid sustain.

The other concept comes from the bass, electric bass or other bass instruments like tuba, if there is one in the ensemble. Generally we try to create a just intonation with minimal beats, on a chord by chord basis, built upon the bass pitch, if the music is slow enough to hear.

As far as C5E5 beating too fast, I tune E5 so that
C3E3 < C3E4 < C3E5 < or = C3A3, and E2C3 = C3E5, if E2 is in tune.
The RBI's are slow enough to hear and confirm the best compromise of E3E4, E3E5, A3E5, and E2E5.

Prout, your long experience as accompanist (collaborator) must go back to the days when the only pieces published for trumpet and piano reduction were the usual and the other one. Staff accompanists and those who otherwise specialise in collaborative piano playing have my greatest respect. Many are my personal friends.

As a studio trumpet player, I was often called on in specially composed music for film and television, to play stratospheric notes delicately and with no vibrato with other instruments in the mix, sometimes piano. In these cases, a musician is dependent on the piano being tuned by a tuner with no strange ideas of their own about tuning. All instruments have their own idiosyncrasies in tuning, particularly evident in the upper registers but we are all dependant on a fixed pitch instrument being tuned by a tuner sensitive to the requirements of collaborative music. Upper registers of most wind instruments have alternate fingerings available to those whose skill is sufficient to deal with the often compromised tone quality differences caused by their use.

There are so many ways to reference a piano for tuning for all instrumentalists who are put In the position of having to listen intently while playing. Unisons, of course, but the deceptive one was the middle and bass of the piano with no unisons as a reference. Judging larger distances, the melodic sense has a greater rôle. Much depends on the tone quality of the piano.

It is for this reason that I insist on nothing smaller than a seven foot piano for any examination accompaniment rôle..(lid fully raised, for balance and tone quality, but I have little control over this particular aspect).

Personally, I would far rather play with organ in the mix, for soul music or wedding music. (we're back to the usual or the other one again). The strangest sensation was playing the usual voluntaries with string quartet accompaniment, perhaps I didn't do enough of it).

Along with five adjudicators from the upoer reaches of the music professionI listened to several instrumentalists with piano at a soloist competition the other day, there was a trumpet player who played the usual with no evident tuning discrepancies. I found the clarinet to be one of the more sensitive to tuning when being played with piano as far as unison type measurement is concerned. It is on a similar tonal plane with usually no vibrato to cover discrepancies which become more evident. To string players, I found myself listening more horizontally than vertically (this is not either/or). Vibrato can cover what would otherwise be perceived as a discrepancy.

The subject is a large one. We cannot discount the skill of the musicians involved.

Very interesting, rxd!

I've seen you mention this 4th window technique a few times before; an interesting and original test, but I don't see how you derive the comparisons.

5:4 < 5:2 < 5:1 </= 5:3, and 8:5 = 5:1

I don't see that these comparisons are necessarily always true, but I'm curious to try and see if they work most of the time.

Prout:

First, a little bit of fun. If a brass instument is in Bb, a piano tuned to Reverse Well will be more in tune with the natural intonation of the instrument than if the piano is tuned in ET.

When I played trombone professionally (not studio, but in circuses and military bands) the biggest intonation problems I noticed where with the F and, even more so, the Eb horns, but also some with the woodwinds. It's one of those things where you figure everyone else is out of tune... Yeah, sometimes the piano, with stage bands, didn't seem to quite fit in with what the horns were doing. I hear such things much more now and really don't care to hear the piano with any other instruments at all. I guess it is essential with much choral music, though.

In general, I think it is a shame that much music for piano in an ensemble is written without regard for what the piano really is - a percussion istrument...

Thank you all for your fascinating stories and knowledge.

My bass friends always complain about the bassoons being sharp in the higher registers when playing in unison with the basses.

I must admit I love the natural horn, especially when it is allowed to be natural. Britten's work for tenor and natural being an example. That flat seventh sends chills up my spine every time.

I asked my wife, who sang with Tafelmusik for 25 years, how they knew they were in tune. Without prompting, she said, it's all about beats. When approaching cadential material, or singing slowly in homophony, they tune pure, beatless thirds and sevenths against the tonic. No high leading tones in that ensemble. She said it is easy, in the midst of a group, to hear the beats.

So Jeff, maybe there is a place for RW after all!

Conjecture - If we could hear a pure sine wave (not likely possible as all reproducers introduce harmonic distortion, possibly including our own ears) we could not aurally tune a beatless interval to it, as there would be no beats.

Ask your wife what they do when they have a dominant 7th chord or a diminished chord or an augmented chord.

Back when Nixon was President, I was part of a festival where the director had us do a strange exercise. We sang a major chord, then turned it to minor by having the tonic and 5th go up a semitone then back to major by having the 3rd go up a semitone and so on. After doing this a half dozen times, he had us stop and played the chord we were supposed to be on. Of course, we were no where near right, and I have wondered if he really knew why. We did it again and did better, but I think it was because those with abosolute pitch kind of took over. At the time I didn't know about tempered intervals and couldn't understand why others didn't just hear the, well, "justness" of when an interval is right and thought that was why we didn't end up where we should, which actually will cause the error. The director never explained, and I now suspect didn't know.

Singing untempered intervals can get you in deep trouble with complicated harmonies.

Interesting exercise Jeff. There is no easy way to maintain a pitch reference when singing in just intonation without tempering some intervals. That is why, for example, the Bach Six Motets were written with instrumental parts, and are performed not a cappella , but with instrumental doubling, which keeps the reference pitches, but still allows for many just intervals.

Tafelmusik uses mostly a Vallotti variant temperament for German baroque music (and a variety of other temperaments for French works), so the continuo instruments tune their fifths to the keyboard and everyone plays/sings as in tune and just with each other as is possible. Dominant sevenths are always tuned just. It took a while for me to get used to hearing a 'flat' seventh.

Prout:

I do not think a dominant 7th can be tuned just. Consider the minor 3rds.

I don't think that's true. Decent hi-fi systems can produce harmonic distortion figures post-speaker of sub 1% - even our ears are not too bad if they're not overloaded. It is certainly possible to hear beats between sine waves at almost-integer ratios (eg octaves). Just try it out with an electronic/computer tone generator and some headphones. I can certainly hear the beat between a 440Hz and an 879Hz tone generated using Audacity. Same thing with 440Hz and 659Hz (though my ears also introduce the sound of 220Hz due to the difference frequency produced). Even with pure sine waves, the amplitudes superpose (going back to the discussion about multiple partials in the same string at the same time) so there will be peaks and troughs that we perceive as beats.

Paul.

Sorry Jeff, poor choice of terminology on my part. I think I meant ( not sure now) that the seventh of the dominant seventh chord is tuned as the just P4 of the tonic key, so CM7 Bb is the P4 of F major, at least according to my wife.

When she spoke of beatless sevenths, for example B natural in C major is tuned as a beatless M3 with G, which gives a low appoggiatura to the C tonic.

I agree with the your statement regarding empirical evidence. I too can easily hear the beats using a sine wave generator. But my conjecture was a truly pure 440 Hz sine wave beating with 879 Hz should produce a 439 Hz resultant. OK. Maybe I've answered my own question with your help. The 439 Hz resultant will beat with 440 Hz to produce a 1 Hz beat.

Thanks.

Beats are a combinatorial phenomenon caused by the coincidence of maxima and minima of two waves. They do not require any particular waveform, but different waveforms will sound different. Something similar to a sine wave will give the characteristic "wah-wah" sound, while square waves will click.

You don't really get a clicking sound with square waves. Try it in Audacity and see. I just did 440 + 440.2Hz and you hear a "phasing" sort of sound as the harmonics cancel out in sequence.

Arguably, it can, since the tritone is an unstable interval, artificial to the 12-TET scale, with many definitions.

(1) 5:4
(2) 6:5
(3) 6:5
(4) 5:4 * 6:5 = 3/2
(5) 6/5 * 6/5 = 36/25
(6) 5:4 * 6/5 * 6/5 = 9/5

Everything being held together by the pure internal intervals and a pure 9/5 D7th produces a pure 36/25 tritone, listed by Haluska as the classic diminshed 5th.

Definitions for the tritone include:

Classic augmented 4th, 25:18 (569c)
Lesser septimal tritone, 7:5 (583c)
Just augmented 4th, 45:32 (590c)
12-TET artificial tritone, (600c)
Greater septimal tritone, 10:7 (617c)
Classic diminished 5th, 36:25 (631c)

The lesser and greater septimal tritone are the most consonant (lowest prime number combination) versions of the tritone, but the closest ratios to ET are the 17:12 (603c) tritone and the 24:17 (597c) tritone.