Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Partial strength - hammer voicing or soundboard ?

That is an interesting concept. Do you have any math that would predict the beat ratios, either of an organ pipe or a piano string?

I tried this with a simulator with no iH and with P1's only, ie with pure single sine waves per note. The only beating intervals are nearly coincident unisons. I find it impossible to recognise normal intervals with any degree of accuracy without hearing any beats, and therefore impossible to aurally tune with any accuracy.

BDB,
I don't see the significance of your wave model to pianos. It seems incomplete.

The partial tones are there as a result of simple harmonic motion in a somewhat less than perfectly elastic two dimensional medium with somewhat elastic boundary conditions.

In my mind I've named the guy on the right Joseph Fourier...

Doesn't seem to be a particularly rapid beat rate, but I'm sure he's getting his point across.

At any rate, it is an illustration of "ill-temperment".

Or Unjust intonation....

As I posted into another thread, just put graph sin(4.4*pi*x)+sin(4.41*pi*x) into google, select horizontal zoom and zoom out. The "beats" that you hear are an amplitude modulation effect. If you put graph sin(4.4*pi*x)+sin(6.61*pi*x)- essentially a major 12th that's off by 1Hz, you will still see an amplitude modulation (that you can also hear as beats). So you can tune any interval with pure sinewave. Of course sin(A) + sin(B) is "combinatronics". You don't need partials to tune, you just need to remove any amplitude modulation to zero. Also, organs do not produce pure sinewaves - even a B3's tonewheel generator does not produce a pure sine. Even if it did, you'd still be able to tune it.

There's no technical difference between "partials" and "harmonics" - they are both sinewaves at a certain frequency - just that the latter have an exact integer multiple ratio to the fundamental. Essentially our ears are spectrum analyzers that operate in near real time (there's about a 20ms processing delay in our brains) - so we hear the frequency relationships, but are unable to distinguish the phase relationships. If you don't believe the latter, synthesize a tone from sinewaves using whatever method you like and then offset the phase of the different oscillators - you will not hear any difference for any static setting of phase. Of course, if the phase is changing, this is perceptible as a frequency modulation.

Paul.

Using your logic, a single string, which contains partials, for example, due to iH, of 440, 881, and 1322.3 must beat like crazy all on its own. The only poster here who has heard that is Isaac. Maybe we learn to ignore the beating of a single string when tuning.

BDB,

Granted, organ pipes produce sine waves, yes. But they don't produce only one sine wave per pipe. Where do you think the different timbre of different stops comes from? Each pipe produces a multitude of sine waves. (To wit: its specific harmonic series.) The timbre of each stop comes from the relative strength of the fundamental and each overtone.

So, even in an organ, 174.6 does not beat against 220. Rather, the fifth partial (i.e. fourth overtone) of the first pipe beats against the fourth partial (i.e. third overtone) of the second pipe. Exactly as in a piano, except that the overtone series in an organ is harmonic (f, 2f, 3f, etc.)

And just like a piano string doesn't disintegrate because it moves as a sum of modes, neither does the air column inside an organ pipe disintegrate because it contains several simultaneous standing waves.

Still, no fairies.

Conversely: a pure, single-frequency sine wave of 174.6 and a pure, single-frequency sine wave of 220 Hz will not beat - most certainly not at 7 Hz! As Chris Leslie wrote, with pure, single-frequency sine waves, the only beating intervals are near-coincident unisons. [Edit: the 174.6 and 220 of an organ, or a piano for that matter, do beat, because their respective partial series contain near-coincident partials.]

Finally, a question:

If 880 is only a "fairy" inside an A220 string, why can I get an un-damped A880 to ring by playing A220? (Should we be "fairying" notes, rather than ghosting them?)

Actually in an organ, each stop is a fairy. Add them together and they make a different tone. It does not follow that just because you can add things together, you can take things apart from something that started out not put together. You could try this: Pick something up with your hand. Then chop your fingers off, put them back together, and see if it works as well as it did before.

Everything that you say is a result of partials can be explained through combinatorics. Just look at how waves may interact to see that.

I think a little hunting on youtube will yield some nice strobe pictures of vibrating strings that have multiple harmonics on them. Violinist all know how to play harmonics, so strings can support multiple pitches that are in harmonic relationships with each other.

By the way, the inner ear is the ultimate Fast Fourier Transform device.

If you want to hear partials, just strike a bass not with the damper up on a note an octave and a fifth above. You will hear the latter string vibrate in sympathy with the third harmonic of the bass string.

BDB: An organ pipe produces a unique tone as a result of its length/width ratio, taper, pipe material (wood, tin), and whether or not it has a reed. These variations give rise to various standing waves of various harmonics in the pipe.

gynnis: BDB has a different way of thinking about sound wave structures from many of us. The fact that we produce pictures of vibrational modes on a string, and that a violinist can create harmonics by touching the string at a node point, does not mean that they actually exist as independent entities. It simply means that we create a paradigm for observation, and we see what we expected to see. From that observation we can model and predict certain string behaviours to a reasonable, but not exact, level of accuracy.

I did similar experiments in 90s and had the same observations: sine waves don't beat audibly like coincident partials do. There is a HUGE range that still sounds in-tune, even when it's not. It's not impossible to tune aurally but, you'd have to listen using a completely different skill set--and accuracy is not very consistent.

A single pipe on a pipe organ does not produce a pure sine wave. The "flute" pipes produce close to a sine wave, so it has very weak harmonics. But even these weak harmonics are enough to be heard when tuning a pipe organ, so even the flute stops can be tuned by beats using intervals like octaves, 4ths, 5ths, and 3rds. Pipes in other stops have even richer harmonics as they deviate more from sine waves.

As for experiments with pure sine waves, here is a trick you can add: Take the sound of two sine waves that have a nice frequency ratio, like 3:4. As was mentioned already, you will not hear any beats because there are no harmonics to beat. But, take that same sound and add a little distortion. Turn up the volume until the speaker cones are buzzing a little, or place a paper clip on the speaker cone - anything to slightly distort the sound. Then you will be creating harmonic distortion, and beats will suddenly appear.

@BDB: Combinatorics is the study of things like latin squares, projective planes of finite order, balanced incomplete block designs and Hadamard matrices. I don't think this field describes how beats are produced.

@BDB



Can't you really see the diferent modes of vibration?

These are partials. If they can be heard, if they can be seen, then they exist and are not an abstraction.

One must be careful to understand the experiment and the method of recording the observations. Remember wagon wheels turning backwards in a movie on a wagon clearly moving forward? What you see is an artifact of the recording process.

One can clearly see the fan blades stopped when strobed at the correct rpm, yet we think that the fan is still moving because we can feel the airflow. A movie made of that fan would clearly show that is stopped.

Our hand cannot easily pass through a solid wood tabletop. It is clearly solid because we can't see through it. Yet there are theories and observations that show the space occupied by atoms is mostly empty, and, it is possible for our hand to pass through the tabletop, just not very probable.

All I am saying is that BDB provides a different view and food for thought.

Prout,

The video was addressed to BDB.

Don't tell me you also believe partials do not exist!

Do you?

Strobos hide us part of what is happening, so what we see is an incomplete succession that can be missinterpreted.

What I've posted is a ultra high speed video, exactly the opposite.

It hides nothing to our view as strobos do.

Your analogy is invalid here.

It i seen how the bad center (that one woobble a lot) is sending some twisdting wave on the small piece of wire there.

I cannot believe it is the end of a long bass wire. not it is tense enough

This could be a totally different topic. I don't believe in anything. I never have.

I do partial analysis using accepted techniques. It allows me to visualize, in my mind, a way of thinking about sound waves. I don't know and I don't care if there is some sort of absolute "truth" about things. BDB's thoughts are as valid as anyone's posting here on this thread.

Some people (mostly fundamentalist types, not necessarily religious) spend their lives espousing an absolute faith in some idea or phenomenon. I spend my life asking questions, positing ideas, in the hope of being shown a different way of thinking about something. I gain much in the process.

I welcome BDB and his ideas.