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Tooner,

I have an ETD, which I believe is the best available nowadays.

It measures 12 partials of each string while you are tuning. So it collects iH data of more than 400 partials for each tuning.

It brings you the ability to design the tuning the way you want. You can set which type of intervals you tune at 8 different points of the scale, and for each set point you can specify the type of interval and the desired tempering in bps. You can specify, for each set point more than one interval type. And the program will accomodate the tuning to satisfy your specifications.

This is called: Style.



For example:

Built in Average Style

A0 6:3 0.33 100%
A2 6:3 0.24 100%
A3-4 4:2 0.32 100%
F5 2:1 0.30 100%
A6 4:1 0.5 100%
C8 4:1 0.00 100%


Custom made Style for studio (upright) Pianos

A0 10:5 0.00 20% 6:3 0.00 40% 4:1 0.00 40%
A1 8:4 0.00 60% 6:3 0.00 20% 4:1 0.00 20%
A3-4 6:3 0.00 20% 4:2 0.00 80%
A6 4:1 0.00 50% 3:1 0.00 50%
C8 4:1 0.00 67% 8:1 0.0 33%


You can see in the Studio style that at A6 I ask for mindless octaves by balancing 4:1 and 3:1 at 50% each.

Or in the built in Average Style the temperament octave A3-4 will be tuned as a wide 4:2 type octave beating at 0.32 bps

Or in the Studio style the low bass will be tuned as a medley of 10:5, 6:3 and 4:1 with the percentages specified.

So, you can decide how to tune the piano at the desired locations in the scale. It gives you an enormous power over the tuning you want.


It is by far much more powerfull than your simulator!

And guess what...

It has not ears! It only measures frequencies and tranlsate them to numbers and it calculs a tuning following the style you have designed.

I doesn't know if it sounds good or not! You have to hear the resulting tuning and adjust the programming if it doesn't sound good!

My ETD has very usefull features. It is great for pitch raises, for repeating a tuning you liked, it is very flexible, you can design the tunings exactly the way you want, etc...

But it has limitations.

It is extremely difficult to interpret numbers, one have to tune them and hear them to know if they are really what we thought.

That is why I prefer to do my fine tunings by ear.

So when I write here in this forum I prefer to talk about tuning and not about numbers.

Gadzar:

"I see your Schwartz is as big as mine." Dark Helmut from Spaceballs.

Now are you going to talk about what you hear or not???

I was writing at the same time than you.

For the tuning of stacked octaves, try this:

Tune A4 to the fork
Tune A3 to A4 as clean as possible
Tune A2 to A3 as clean as possible

Now listen to A2-A4, chances are that this double octave won't be as pure as it can be. Maybe you won't hear a noticeable beat but try and you will find a better tuning for A2 while sounding A4. So we better find a compromise in the tuning of the three intervals A3-A4, A2-A3 and A2-A4.

For the flatness of a high note compared to a lower chord this is a well documented physical phenomenom that has much to do with the way our brain deals with pitch perception. If you tune a beatless interval the high note will sound flat to our ears.

I have several singer clients who always complaint that the treble notes are flat. My tactic then is to tune one note to their taste.

"Tell me when to stop" I play the note one octave lower and then the note I am tuning while raising the pitch.

When they ask me to stop I play the two notes together and evidently the octave sounds horrible.

"Is that what you want?"

"No, never mind" is the answer.

The point here is to tune the middle as wide as possible by tempering the A3-A4 octave and tune the treble as high as possible without having too busy single octaves at the top of the scale. There are no objective limits, it is question of personal taste.

If you are tuning octaves only by tuning octaves, that is not good enough. I do comparisons with thirds, fourths, and fifths and their octave cognates to make sure that the octave works for all intervals, not just the octave.

BDB:

I do so also, now, but my point is whether beats are heard in multiple octaves when tuning single octaves aurally pure.

Gadzar:

You still have not said what you hear.

Still reading/learning/assimilating with interest...

Glen

Hopefully it's a little entertaining, too.

As far as I am concerned, they are. The area in which octaves and their multiples sound aurally pure is rather wide. Checking the other intervals narrows it down. Everything ends up in that narrow range.

Yes,

The sweet spot in tuning octaves is very large, one have to listen to other intervals to correctly tune them, always aiming to the wide side.

Tooner,

I don't follow you. I have said the way I tune. And I do it by hearing. What are you asking me?

BDB:

I have to agree that there is a wide area of where an octave sounds pure. But if I tune an octave directly, the area is very small where it sounds most harmonious. When these octaves are stacked I do not hear beats in multiple octaves. But I rarely tune octaves directly anymore. That very small area is not where I want the octaves tuned.

Gadzar:

If you stack octaves that are tuned as harmonious as possible, do you hear beats in the multiple octaves?

Yes, if I stack clean octaves I do hear beats in the multiple octaves. But eventually I can stretch these single octaves to elliminate those beats.

For me harmony involves several, minimum 3, different notes. From a musical point of vue an octave involves only one note!

So I don't understand what you mean by tuning octaves as "harmonious" as possible.

Jeff, I did not say that it is the higher partials that tell the ear what pitch a note is at - to me it is much simpler than that. if the majority of the prominent partials are flat or sharp, the octave will be heard as too flat or too sharp.
This, and I stand by it, has to do with inharmonicity. The logical 2:1 octave leaves , because of the partial stretch in inharmonicity, all other intervals flat or sharp from the same side of pure, and as a result, the tone will be considered flat/sharp.

So what we aural tuners do is that we find the best clean-sounding spot for our octaves, where the 2:1 is a bit wide, the 4:2/6:3:s close to pure, and matches above that maybe slightly narrow. This is our clean-sounding octave, because it has taken the full piano tone into account.

Thanks, Gadzar:

I would say that your use of “clean” and my use of “harmonious” are the same.

Pat:

Then it seems like a self-fulfilling prophecy that has no real meaning or reason to mention. Something like: When an octave is tuned to its best, clean sounding spot this utilizes all audible partials according to the strength of each one. And when the human ear is determining pitch, it utilizes all audible partials according to the strength of each one. So the best, clean sounding octave is also correct pitch-wise.

Now we could say that this particular octave is stretched from theoretical pitches because of the effects of inharmonicity. But we cannot say that this particular octave is stretched from what sounds best either harmonically or melodically.

Perhaps one of the confusing things is the adjective octave in the term “octave stretch”. It raises the question as to what octave is being stretched: the theoretical, the 2:1, the harmonic, or the melodic octave? If the adjective octave is not used, I think it is easier to define stretch in general.

What I am finding interesting in this discussion is what is perceived when harmonic octaves are stacked. To me the result is harmonic multiple octaves, but not melodic multiple octaves. To Gadzar the multiple octaves are not harmonic, beats are heard. I am not sure about BDB.

I think this is the best way to consider Mark's question about whether stretch beyond what occurs when tuning harmonic octaves is needed to create harmonic multiple octaves. In other words, is stretch necessary to satisfy iH or just the ear?

So what do you hear, Pat? When the best, clean sounding octaves (what I call harmonic octaves) are stacked, do you hear beats? And do they sound acceptable pitch-wise?

All:

I am sorry I was so antagonistic yesterday. I apologize. I was having a bad day, as is usual for me. Yesterday was a bit worse than others. I will try to do better.

FWIW, I just compared the beatrates of double and triple octaves for some different tunings. Out of 4:2 octaves, mindless octaves, and twelfths, pure twelfths were definitely the best for keeping the beating of both the double and triple octaves slow. That is not to say that some other hybrid would not be better. It is just a comparison of these tuning schemes.

(Sorry Gadzar, I know you are not interested in the numbers from my simulation, but others may be.)

I'd say that beats are not particularely nonharmonic, (musically speaking, not theoretically) and that we may play with them, not fight them !

exemple :

http://www.ambassade-du-piano.eu/videos,concert-akihiro-sakiya-part-3-26759.html

Jeff,

I think it comes down to this issue:

What do you, Gadzar and each one of us call a "clean", "pure" etc. octave? If each one of us were to tune an octave as cleanly as we could, would all of us achieve the same width? My money is on the answer "no". How else do you explain that your stacked clean octaves give beatless multiple octaves, but Gadzar's don't?



Well I think we can rule out the theoretical octave, because even a 2:1 octave is wider than a theoretical octave because of inharmonicity. So, even the "most basic" of octaves on a piano is already wider than theoretical.

As a layman, my understanding of a "clean", "pure" octave is exactly this "basic" 2:1 octave, because the only note that is compared to the lower note is the (fundamental of the) upper note. Hence, again in my understanding as a layman, any octave that is wider than 2:1 is stretched, but a 2:1 octave is not stretched (because anything narrower than 2:1 would be narrower than beatless, and surely you can't call a "narrower than beatless" octave "stretched"?).

And yes, inharmonicity can be unhappy - especially if the Tooner is having a bad day.

Mark:

You have a point. The only usable octave that can be accurately defined when talking about stretch is the 2:1 partial match octave.

But I think different tuners could tune exactly the same stacked aurally pure octaves and not agree whether the resulting multiple octaves have a beat or not.

For example, I often will listen to a double octave and it sounds beatless to me, but when I check with the M3-M17 test I find it does have a beat that I do not perceive. But I suppose if I had hands like Magilla Gorilla and could tune a double octave directly, I would tune it as a pure, beatless 4:1 double octave because my ear would lock onto the beat of that particular partial. This is definitely the case with twelfths. (I have a tool that spans the twelfth.)