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Hi Isaac,

I appreciate your comments and I think we may be able to see eye to eye.


You say you are not focusing on it but you mention it in your last post. The fact that you can easily determine the speeds as M3<M10, that is what you say clearly, means they are 4:2+. There is no question. Not same or approximate, clearly you say faster.



Since I like to use checks, I do not have the same problem; I can easily hear very small differences in speeds; I listen for tone, not actual beat speeds. I use the attack of the note, where the beats are most prominent, as you have often suggested, and I make my assessment in a fraction of a second; no time to accel or decell.


Most heartily agree. One must make assessment quickly, and not compare beat speeds, but tonal difference. E.g. faster beating intervals have a brighter tone for me, so I compare tone.


Again agree. That is why I use multiple checks including open interval tuning, whole interval tuning. I often catch my own mistakes. But in the end I always must use 4:2+ or I cannot tune all intervals clean. I am currently discussing with Mark Davis and hope to prove this point theoretically, and then I will post recordings on different pianos. Wish me luck. I suggest those who use 2:1+ (on large grands) may be tuning 4:2+ as well.

"Most heartily agree. One must make assessment quickly, and not compare beat speeds, but tonal difference. E.g. faster beating intervals have a brighter tone for me, so I compare tone."


Yes that's how it happens, I agree.

WHat IO state is that I dont allow my ears to focus on the 4:2 relation if this is not what the piano want as a final result. That said, we may remind that once the unison is tuned the final pitch is changing, most often for the lower, so sticking on the 4:2+ is certainly more secure than trying to attain an open 2:1 octave immediately.

In the end of the tuning, or when in small corrections, it is often unnecessary to change the pitch of the 3 strings to correct a 10th that is a little slow (hence an octave a tad compacted)

As I tune by strip muting on a large medium portion of the scale, I am obliged to enlarge a bit, despite that I keep the 23:1 resonance as my goal, may be if I follow the 4:2 this will tend to enlarge my octaves more when I'll be in the 5 th octave..

Possibly using the 2:1 is not so different in the end, simply it allow to work on the resonance level immediately in the tuning, while when tuning by FBI, the tuning is clean of course but we pay less attention to the octaves than we could.

Learning to tune with octaves beating slowly (as 1 for 5 sec) is an excellent exercise. the beat is primarily at 2:1, it helps to master all the beats at slow level.

I really agree that the beats of FBI are recognized in a pinch, that is what was unnerving me with the ETD, giving the impression I was waiting for the machine (as you dont move the pitch if you want a clear display)

Of course beats are not "counted" we learn to count ta stack of M3 when learning to tune, or to recognize the "movment" sensation provided by a correctly set M3 . Then, depending of the scale and the voicing, the speed sensation can differ a lot so hopefully slow beating intervals are also used.

I have seen also pianos tuned with some perfect FBI speed and progression, but without particular attention to the octaves nor 5ths. The evenness of progression of the FBI provided a very playable scheme, the piano did sound absolutely just and tuned, simply little of the own personality of the instrument is used then, it sound like those transparent papers that can be used to see thru... if you see what I mean.

I tune with open double unisons, no mute strip, for this reason. The unisons have already settled by the time I am listening to them. But this topic may require a new thread. I am not ready for that yet.

The theoretical discussion is also with Jeff Deutschle, not just Mark Davis.

I usually pass gas instead of mustard, but here's the page from Reblitz. As you can see, the lowest P4 and highest P5 both beat at 0.79 according to Reblitz.

Kees

Busted. I realized I had made that mistake when I saw the Wikipedia link but I never got around to correcting it. Thanks for bringing it up. However, the logic still applies because the Reblitz and Wikipedia both are listing theoretical data for a piano with 0 iH, no stretch. I have stated that I believe the stretch is taken up mostly by the fourth in reality. I stand by my claim that 4:2+ octaves in the mid and high range are superior but I am open to criticism. This is my experience with every piano I tune, no matter what the size. I am still trying to prove the theory.

I follow the same logic/principle ( 2 strings unison minimally necessary to know/hear the final pitch of a note) , but I am more at ease with the strip, as I said final corrections can be done most often without changing the center wire.

Mark:

No big deal as far as I am concerned. It was just an error, a "brain-fart". It is all part of exploring a subject.

OK, you are trying to prove a theory: 4:2+ octaves in the mid and high range are superior. Starting with a clean slate, how do you intend to prove it?

Please do not try to put answers into my mouth. Your comparison is like apples and oranges.

I am gong to be brutally honest. I have noticed that you will hop from one side of a discussion to another just to try to get an argument started or to keep it going. For that reason I will not give you an answer. I am not interested in playing games.

It is sad, because I have much to say on the subject, and much to ask. It is not something I understand completely. If someone else starts a serious inquiry, preferable by starting a new Topic about the effect of iH and stretch on the relationship of different beatrates, I will enthusiastically join in.

Thank you, Mark.

I suspect Isaac is right. The difference between aa A3-A4 2:1 octave and a 4:2 octave on a concert grand is only about one cent, or 1/4 bps. Delibrately tuning a wide 2:1 could easily result in a wide 4:2.

Jeff

We are at cross purposes again.

I asked because I was interested.

The logarithmic nature of iH, its doubling every octave or thereabouts, is what you need to know to show that the stretch of the 12th tends to be the same as the inharmonicity of a note's third partial.

You assumed I was playing games, loading the dice, on a previous occasion. I was not, and am not, but I let it rest.

I very much doubt that I hop from one side of a discussion to another for the sake of it. People take me to task for being too single minded in pursuit of an argument.

It's true I have kept the odd discussion going. Have you ever done such a thing? What is wrong with that in a forum anyway, interesting things often emerge.

No doubt I have sometimes misunderstood where you were coming from, as they say, but I am not so sure I'm alone in that.

I will leave beat rates to you and Mark but perhaps I'll ask a question about the effect of the relative strength of partials on tuning one day.

Well, we have agreed that a 4:2+ octave produces:

2:1 wider (instead of very wide)
4:2 wide
6:3 narrow
8:4 narrower

and that the 2:1 and the 8:4 beat at a similar speed,
and the 4:2 and the 6:3 beat at a similar speed.

Right?

Also, you have agreed that the higher partial frequencies are increasing in difference from the theoretical, the higher up we go on any one string (from the formula) and that iH increases uniformly for the mid and high treble (from Tremane's graph).

Are we good so far?

Are we good so far? Partly yes. The part that is no you should find useful in your proof, although in the end I think it is a matter of priority and preference.

According to Young's paper: http://www.afn.org/~afn49304/youngnew.htm the amount that any given partial is higher in cents than the theoretical frequency equals the string's iH in cents times the square of the partial number. Now according to emperical measurement, this is only approximate. But rather than resort to tabular values, as Mr. Scott's Tunelab program does (the tabular values can be found in the online manual), let's just use Young's equations for discussion.

When including the effects of iH when calculating beatrates of an interval we must remember that the first partial is also affected. This is discussed in the paper. Also remember that iH is different for each note and in a well scaled piano will be mostly logarithmic.

All that said, if you "crunch the numbers" for an octave where the 4:2 partial match beats wide at the same speed as the 6:3 partial match beats narrow, the 2:1 partial match will also beat at this exact same speed. The 8:4 partial match beats much faster, however.

So I disagree "... that the 2:1 and the 8:4 beat at a similar speed, and the 4:2 and the 6:3 beat at a similar speed." Actually the 2:1, 4:2 and 6:3 beat at a similar speed. The 8:4 beats much faster. But let's remember that the cents that an interval is wide or narrow is another thing altogether. (I have mentioned this before.)

So, Mark, you haven't mentioned how you might decide to try to "prove" that 4:2+ octaves are superior. If you were to say that your proof would be that there is a "masking effect" you would have a good point. But you should "crunch the numbers yourself."

Mark, unfortunenately you seem to make a lot of contradicting statements as you go along, choosing to pretend and forget what you have said. I have found this throughout your writings.

I am not really sure what your whole argument is about and what you are trying to prove?

You have been threatening to post a video on many occasion and for sometime now. I think you should either just stop saying you are going to do it or just get on and post it/do it.

I tried your test m6=M17 and found it to be invalid in the middle and treble of the piano. What part of the scale are you using this check? BTW, I do use the M6/M17 check and clearly hear it.

Hi Mark,

Sorry for your frustration. Hopefully I can clarify for you.

Yes I said



and



But I didn't say I don't use checks. I said I can tune octaves "without the need to use checks". I just am more consistent with the checks.



I think I have shown that you are making assumptions about my writings and that I am not contradicting or choosing to pretend and forget. What I do know is that it is easy to become quite frustrated when someone is trying to tell you something that you don't agree with.

As I see it, you have three choices when someone is trying to convince you of something you do not agree with:

1) Ignore them and consider them to be clueless and off track with their theories. (I'm not opposed to that)

2) Consider the topic beyond your comprehension at the moment and choose to revisit it later.

3) Make a serious effort to figure out what they are talking about. (And in the process you will find holes in their argument and that will help them patch those holes and understand their own principles better. That's the thesis process.)

I hope you choose 3)



Simple, that the 4:2+ octave is superior for a fine tuning in the mid to high treble. (4:2+ being between a 4:2 and a 6:3)



Sorry. I have some recordings but it takes time. I do have another life. I want to wait for the recordings until Jeff and I have finished our conversation.



Are you using the m6 BELOW the check note, for the triple octave test?
Also, I didn't say it was easy. It is difficult to compare these fast beating intervals. You must listen for tone, and match that. You can also play all three notes together and listen for beating of the beats (wah-Wah-WAh-WAH-WAh-Wah-wah-Wah...) If you hear that, they are NOT equal.

The range is starting at F3F6, and then I use it as I am going down from F3. E.g. E3E6, D#3D#6, etc, until the break. But lately I have been able to get it to work past the break.

I use the M6M17 test too and started using it about 5 years ago. Then, as I stretched out my hearing and tried to get better double octaves, etc, I was drawn to temper the 12ths by an amount that produced better double octaves and pure triple octaves. (They are probably not pure; who can really tell at those speeds? But I can hear when they are not close enough and a re-listening of the other related intervals usually smokes out a drifter/error.)

Mark, here you go again. Where do you get that I am frustrated?
I may dislike certain traits of yours but I am certainly not frustrated.



I do not consider you clueless at all. Though I do not agree with you on everything you have said and do not like your manner in most, if not all your posts.



What topic are you speaking about here? Your superior 4:2+ octave size?



Where to from here Mark? I know the 4:2 narrow, just and wide octave and tests. I tune 4:2 just and 4:2+ octaves for my temperament and treble. So what would you like me to say? That you are right that the 4:2+ octave in the middle of the piano is superior because you say so?

I would have you to re-read Ryan Sowers fine post!

Could you please demonstrate this surprising (and not well-known) fact?

If not I will, but I learned this from you...

Kees

Mark, I do not like the tone of your posts. They are verging on an attack of my personality and I believe that is against the forum rules.

My reason for continuing these posts is to prove "my superior 4:2+ octaves" But, they are not just mine. Read what you posted by Bill Bremmer:



That's the 4:2+.

So, if you want to know why it is superior, keep reading the posts. Otherwise, stop attacking me please.

People get upset when you mention 13 y experience and having a degree in Mechanical Engineering to support your arguments, that's all. I've got similar reactions when mentioning my PhD.

I think Jeff hit the nail on the theoretical mustard with the observation about the 2:1, 4:2, and 6:3 beatrates being equal when tuning equal beating 6:3/4:2 octaves in the mid-upper range. Something like killing 3 birds with one stone. This may be the reason for the 4:2+ being the best.

Of course, the proof is in the mustard.


Kees

Ok, so I finally managed to upload a video of a piano I tuned with pure triple octaves using the P4 window and the pure triple octave test.

Please be kind. It took me over an hour to upload and add subtitles. The piano was not a good one and it was a pitch raise, so there is a mis-matched bichord and some unison drifting. But before the drift, I thought it sounded pretty good.

I just put my phone face down on the piano, so you don't see anything, and I didn't talk because I was tuning at a customer's home. I think the subtitles make it easier to listen and appreciate.

Note: You have to turn on the subtitles to read what's going on.

http://www.youtube.com/watch?v=9Eci3cwlVEM