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

We programmed this piece in contrast to another setting of the text in a college chamber choir. Our director, who is also professor of organ, hosted Mr. Messiaen when he came to do a recital. When she told him we were doing his 'O Sacrum' he winced and said, "Why you do this one? It's too hard!"
And it was- very satisfying, but very hard.

To the topic then, singers have to adjust to make the intervals work.

jw

Originally Posted By: Tunewerk
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.


I wasn't talking about the tritone. I was talking about the minor 3rd between the 5th and 7th.

Let's use 100hz as tonic. The major 3rd would be 125hz and the 5th would be 150hz. The interval and ratio between the major 3rd and the 5th is a minor 3rd and 6:5, respectively. But where do you put the 7th? As a minor 7th (7:4) at 175hz above the tonic or as a minor 3rd (6:5) above the 5th at 180hz?

If i remember correctly,Leonard Bernstein in his book"the unanswered question", refers to what we call a minor seventh as an augmented sixth. I can see his reasoning.
He presents a different slant on all this, apart from getting the numbering of the partials wrong, it is a worthwhile read. I used to see a copy or two in used book stores stateside from time to time.

Old acoustics books differentiate between a large minor third such as, to use your numbers, that between 125hz.and 150. A small minor third, that between 150 and 175. A large major second between 175 & 200 a small major second, a large then small minor second, etc., as the intervals become smaller.

Jeff. I like your parallel between the natural intonation of a Bb brass instrument and RW when transposed to piano pitch. Most all of the tendencies are indeed the same.

BDB appears to be getting us to think outside of the box and to double-think the way we perceive various concepts. All areas of thought needs somebody to stand up to convention and popular thought or else we face the possibilities of always driving down the wrong path. The famous last words in science is that so and so's thoughts are preposterous and can't be the case because we know we are correct.
Whether BDB is right or wrong, he is to be commended for provoking thought into the discussions.

I agree that dissident views are necessary to further our knowledge, though, in this case, it was not germane to the discussion.

I do take issue with your statement "The famous last words in science is that so and so's thoughts are preposterous and can't be the case because we know we are correct. " No real scientist would make the above statement. Science attempts to describe and predict what we observe. A scientist can only state that a falsifiable theory predicts what we observe to a given level of precision, nothing more. Only some religions, advertising agencies, naïve humans and, perhaps 'scienticians', to use a term from "The Simpsons", believe in 'absolute truth'. But this too is not germane to the discussion. Back to beats, or no beats - that is the question.

By size or beats?

I say by size, and my reasoning is simple.

When tuning unisons, for some reason, when close, I can hear and tell wether the string is sharp or flat.

Same goes with intervals. A wide or narrow fifth by the same amount will not sound the same.

You kinda know with time what side of flat or sharp the unison or interval is beating.

I cannot explain it, but size is more important and relevant to me, beats are there all the time, and I prefer ignoring them. As soon as you zone in on a beat, another comes up. Too many partials.

When you ignore them, you can look for the ideal place for the note, where there are the LEAST beats.

Sure, if you focus, there will ALWAYS be beats. Very frustrating to always compromise.

Such is the life of a piano tuner.

And thank god for ETDs.

Both are prerequisite to fine tuning. We can hear both, as supported by historical tuning practice.

Beats have simply become more prevalent as an accurate measuring device for tuning. Nothing in equal temperament is actually in tune, so beats help quantify (measure) the quality (location) of interval overlap.

If you tune by beats alone, the tuning will be dead, or 'off'. If you tune by interval quality alone, the tuning will be inaccurate.

Many times I navigate by beats alone when the spectrum is full of partial noise, or if a given partial is too weak to accurately tune to. Given a strong spectrum, I will always tune to the whole tone, interspersed with beat checks to measure where I am.

Harmonic intervals (2 notes at the same time) is one thing, melodic intervals (2 notes after each other) is another thing.

In meantone the semitones are drastically unequal, giving a particular poignancy to chromatic scales. Example:

https://www.youtube.com/watch?v=EHExcd6PYxQ

In most Persian scales one m3 is 20 cent narrow relative to ET, which is a purely melodic effect as the music is monophonic. The equivalent of our leading tone is usually 10-15 cent sharp, also a purely melodic effect.

Bradley Lehman on his website also talks about tuning the M3's by "quality" rather than beat rate.

If I am not mistaken I think Bill Bremmer also mentioned that if you can't hear the beats when tuning the skeleton M3 F#A3C#4F4 you should try to make them have the same "quality".

Kees

Tuning a piano to itself is full of compromises that should be child's play to an experienced tuner who is not afraid to make the odd decision.

Since I broached the subject of the Railsback curve and it's impact on tuning of instruments to be used in consort with other disparate instruments, it has become evident that this aspect is little understood.

Jeff has recently mentioned but one of parameters that have to be managed. Multiply this by the numbers of instruments or classes of instruments and all their various intonational tendencies, we get an idea of what is involved when all this is put under the microscopic examination of microphones.

Since it was brought home to me rather crudely and patronisingly the abysmal level of understanding by at least one tuner (alfonz) about the Railsback curve and it's impact on fine tuning, I was spurred on to do more research. The Railsback curve is simply a measurement of a very real phenomenon in pianos.

Before going further, anybody not familiar with the Railsback curve would do well to consult the Wikipedia entry. It is an adequate basic explanation for our current needs. ETD users will not be impacted by it because they don't need to listen. Aural tuners will not be aware of it unless they look for it or have been in a position where it applies. I will point out that the seemingly erratic peaks and valleys in that graph in wikipedia are not necessarily tuner error but are consistent with my general findings on the sudden vagaries that can occur in even the most careful piano scaling. I had electronic verification to keep my aural tunings 'honest'. I stretched Only as far as the double octave dictated but found that the triple octave often fell in line but when it didn't, it really didn't.

Only when the piano is used with other instruments does it become an issue.

To this end, since the last show of ignorance of this factor, I have carried three ETD's with me and examined the departure from theoretical pitch of every piano I've tuned lately.

While I have only made an empirical overview of what is actually happening because all this was measured during actual refinements of tunings I have only measured where the tuning departs from the theoretical values by more than a couple of cents. Because of time constraints.

I have been surprised at the variance in piano makes and models concerning where the significant variance begins in the treble. Mostly it's only the last two octaves, becoming increasingly significant towards the last octave where there is a difference of 30-40 cents.
When the significant variance starts earlier, involving the last three octaves, it is even more progressive towards the top. Many pianos behave this particular way with the extended sharpness in the treble. Perhaps that may be a contributing factor to that kind of piano not being used much where microscopic intonation is important. By sIgnificant, I mean three cents or more.

This morning I did an impromptu experiment, I tuned the bass of a 6'4 grand with particularly good depth of tone in a resonant room to theoretical values (no Railsback curve) and had passing students evaluate it by downward melodic octaves between F1 and F3 one perceived them all as sharp, ( I did note the major instrument posted by each but that is of no consequence here). Of the rest, some heard a few notes as flat but many heard the majority as in tune but the same few as sharp. I had them tune only the one they perceived as most sharp down to where it sounded most in tune. Of those, nobody went below half way to the next note. (only a few Hz. In that register). Most were within 25-35 Hz. Low. I must add that I only asked them to tune one string of a pair, wedging off the other string. This reduces depth of tone by more than half and produces an attack that musicians are not used to so is not entirely a fair test. ( nobody perceived the single strings as sharp). I intend to do something more formal sometime.

None of this proves anything, the finger pointing at the moon is not the moon. I would appreciate constructive feedback how to more properly conduct tests.

Thanks Kees for the Sweelinck. A well chosen example of semitones. (Michael really shouldn't be playing, and why in A=440, but, in this case, it gives us time to hear every little thing.)

I think we are getting closer to the thought behind my original question. In the example Kees gave, I hear subtle qualitative (colour?) differences among the semitones, but could not tell you if one was wider or more narrow than another.

Interesting results rxd.

This leads me to an amateur's ignorant question - Is it better to stretch the high treble to the already stretched low bass, or stretch the low bass to the already stretched treble? If the high treble is generally tuned using 2:1 or slightly larger octaves, it would seem that puts a restriction on the amount of stretch in the low bass. On the other hand, if one stretches the low bass to match some partials in the midrange, it leaves you to stretch the high treble to find a compromise between the low bass and midrange.

Following rxd's comments on the Railsback curve and Prout's questions, I'd like to take the opportunity to point out that smooth curve shown in the Wikipedia article is not necessarily an idealised tuning curve.



If you put your thumbs over the last few notes in the bass and treble, you'll see the remaining notes can be approximated by a straight line. That is not always so in the treble where there is often a more pronounced curve, as rxd says.

My question is whether there can be a tendency to put too much stretch into the lower bass and upper treble to accommodate the lowest and highest notes.

Perhaps with other tuners, but never with me!

Hi Prout,

I tend to believe that, when it comes to musical ear and intonation, there are different levels of "accuracy" that we, as individual, can experience. If our level is similar, we can share our "intonation", if it is not, we can only talk about it.

Personally, when listening to or playing music, I have always referred to my sense of "in tune", and it would be the intervals that - in case - sound flat or sharp.

Tuning lots of notes and strings it is a different question, I do not think a piano can be tuned without considering beats, but again, I can only refer to what I need.

Brass instruments like a sax may need some sort of correction that, up to a certain point, can be made with the larynx, of course you need to hear that and be used to singing.

An example,

http://www.youtube.com/watch?v=NEDixv-Bed4

The phrase starts at 0:15 and it is played again at 4:58

Perhaps you notice a difference?



Oh, careful with statements that sound like 'absolute truth' :-)

Prout,

In a different thread, at one point I posted the link below:

http://www.youtube.com/watch?v=Gl64LXryFS8

You would like to know if I listen to beats? No, I simply hear that that harp is all over the place.

The same piece is played here:

http://www.youtube.com/watch?v=-ip64cG7gK4

And by a different artist (with a different tuning), here:

http://www.youtube.com/watch?v=evI-sCxYM3Y

Before I tell you about my impressions, would you let me know about yours?

For me there is no tendency. I am creating a specific curve depending on which intervałs I choose to be pure/tempered. The greatest stretch occurs if I tune pure 19ths which sound nice on a concert grand, but all the other large SBI's are wide. (I think. I haven't done the analysis in a while) But wide by a very small amount due to it being a large piano and low iH. The octaves are the widest but not heard as offensive due to short sustain.

Yes, Alfredo,

I will tell you my impressions. The second harp sounded beautifully in tune but the first sounded out of tune. The piano did not sound particularly good. I think the loud "bang" must have been someone trying to shoot the pianist but missed.

Here is Clair de Lune on a piano the way I usually tune it: https://app.box.com/s/q7vosp2amts8b83kuy8t

Thanks for posting the graph, Ian.
Do you know who O.L. Railsback was (is)?

In answer to your question and that of Prout, which are similar, is that the Railsback curve describes to us what is actually happening in the piano. That is; when tuned even with the narrowest tolerable octaves, the acoustic piano is already stretched more, much more than any other modern musical instrument used in the western tradition.
Is that enough on a fine toned instrument?

There is a multicoloured graph from what appears to be a Japanese source in the google images section that gives some examples of extreme extra stretching to where only the middle octave and a half is in tune (on pitch).

Some instruments exhibit more stretch than others and it is audible when they are both tuned the same way by the same tuner. There was a blind selection of pianos for the BBC in the 1930's where a comparative flatness (and weakness) in the treble was commented on and those manufacturers tried to compensate by extra stretching. Other manufacturers didn't find it necessary. This is anecdotal to me but the transcripts must exist somewhere.

Well, perhaps the piano is stretched more than any fixed pitched instrument. But most instruments are not fixed pitched. My ears tell me that stretched octaves are the norm in musical performance, not the exception.

For once, I totally agree with Jeff! The higher violins play, the higher their pitch. Opera sopranos too.