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Re: Better Equal Temperament Sequence? [Re: DoelKees] #2488631 12/07/15 09:35 PM
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Tunewerk Offline
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Sorry about that Kees, didn't intend to come across that way. Some stuff doesn't translate very well over the internet.

It's not that important.. what I'm saying is simple. Writing on this forum teaches me that I better be laboriously exhaustive in explaining, or 10 people will flip out.

Easy to go overboard and come across as overbearing.


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Re: Better Equal Temperament Sequence? [Re: Tunewerk] #2488653 12/07/15 11:32 PM
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Originally Posted by Tunewerk
Sorry about that Kees, didn't intend to come across that way. Some stuff doesn't translate very well over the internet.

It's not that important.. what I'm saying is simple. Writing on this forum teaches me that I better be laboriously exhaustive in explaining, or 10 people will flip out.

Easy to go overboard and come across as overbearing.

No problem.

You state what you are saying is simple which sounds promising. So what is it that you are saying? I think (please correct me if I misunderstand) you are saying the partials in pianos are so irregular that it is misguided to try to aim for progressive RBI's and ETD tunings are therefore of relatively poor quality.

Before refuting this, can you confirm this is your opinion?

Kees

Re: Better Equal Temperament Sequence? [Re: DoelKees] #2488656 12/08/15 12:10 AM
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Originally Posted by DoelKees
You state what you are saying is simple which sounds promising. So what is it that you are saying? I think (please correct me if I misunderstand) you are saying the partials in pianos are so irregular that it is misguided to try to aim for progressive RBI's and ETD tunings are therefore of relatively poor quality.


That's not how I see it. If it came across to you as that extreme, then I did a disservice in communication.


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Re: Better Equal Temperament Sequence? [Re: Tunewerk] #2488660 12/08/15 12:18 AM
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Originally Posted by Tunewerk
Originally Posted by DoelKees
You state what you are saying is simple which sounds promising. So what is it that you are saying? I think (please correct me if I misunderstand) you are saying the partials in pianos are so irregular that it is misguided to try to aim for progressive RBI's and ETD tunings are therefore of relatively poor quality.


That's not how I see it. If it came across to you as that extreme, then I did a disservice in communication.


OK, thanks for the clarity. So what is the simple thing you are saying then?

Kees

Re: Better Equal Temperament Sequence? [Re: DoelKees] #2488669 12/08/15 01:25 AM
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The Entropy tuner employs what I'm talking about as a general principle. This is the idea I am describing and closest to what I employ in my work.. reduction to an entropy minimum.

The point I was making earlier with tuning machine code is probably the simplest logical proof. If one partial is chosen to align the temperament region (such as the 4th) because of its regularity, then the others will suffer misalignment by definition, on scales that exhibit irregularity.


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Re: Better Equal Temperament Sequence? [Re: UnrightTooner] #2489269 12/09/15 10:04 PM
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Originally Posted by UnrightTooner

So I listened carefully to your excellent recording. I take it that it is the A#3-D#4 P4 that you think stands out. Well that means there should be something out of sorts with the F#3-A#3 M3 and/or the F#3-D#3 M6. It sounds to me like the A#3 is a bit flat causing the F#3-A#3 to beat slower than the F3-A3 M3. but I may be wrong, and I doubt I could do better!

I downloaded the recording and tried to measure the F3A3 versus F#3A#3 beatrates. Result is I can't hear nor see on the spectrograms the F3A3 beats at all. Looks like some partial (either F3:5 or A3:4) is very weak.

Can you actually hear the F3A3 beats?

Kees

Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2489333 12/10/15 06:00 AM
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Kees,

I would pin-point it to a weak F3:5, because I can't hear the beat of the M3, M6, M10 or M17 on F3. Ryan plays all of these during the recording, and try as I may, I don't hear them beating. (At least not with laptop speakers or ear buds - perhaps proper headphones reveal a weak beat.)


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Re: Better Equal Temperament Sequence? [Re: DoelKees] #2489348 12/10/15 07:43 AM
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Originally Posted by DoelKees
Originally Posted by UnrightTooner

So I listened carefully to your excellent recording. I take it that it is the A#3-D#4 P4 that you think stands out. Well that means there should be something out of sorts with the F#3-A#3 M3 and/or the F#3-D#3 M6. It sounds to me like the A#3 is a bit flat causing the F#3-A#3 to beat slower than the F3-A3 M3. but I may be wrong, and I doubt I could do better!

I downloaded the recording and tried to measure the F3A3 versus F#3A#3 beatrates. Result is I can't hear nor see on the spectrograms the F3A3 beats at all. Looks like some partial (either F3:5 or A3:4) is very weak.

Can you actually hear the F3A3 beats?

Kees


Just listened again. I hear them, I guess they are a little weak. There is always the possibility that they are not there, but I hear them anyway. You know, like if a tree falls on the person cutting it down, do you hear him scream?


Jeff Deutschle
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Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2489431 12/10/15 11:47 AM
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They are pretty clear to me - so yes I can hear the F3-A3 beats.


Ryan Sowers,
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Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2489546 12/10/15 06:10 PM
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I just measured Ryan's F3A3. I clearly hear beating on my laptop, but the actual amplitude difference between F3 and A3 is almost 20db, F3 being weaker, which makes me think I am hearing something else.

A more interesting sound is F#3A#3. It has an unusual movement to it. I measured it and found a single fifth partial on F#3 (about 6db down from A#3) but two clear partials on A#3, both within 2.5db. They are split by 1.6bps, so it is both slower and faster than F3A3 and G3B3.

Edit: Nice temperament by the way.

Last edited by prout; 12/10/15 06:17 PM.
Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2489795 12/11/15 04:06 PM
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To my ears the beats on F3 are just as clear as all the others.


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Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2494675 12/29/15 03:02 AM
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Hi,

Sorry for the delay, I couldn't post for a while.

I've tried to do the challenge proposed by Jeff: tune two independent ladders of CM3s. I couldn't do it. The M3s I get are not progressive.

Starting from previously tuned notes A4 and G4 I tuned progressive CM3s F3A3, A3C#4, C#4F4 and F4A4 without listening to other M3s, as I could also tune progressive CM3s D#3G3, G3B3, B3D#4 and D#4G4 without listening to the previous tuned M3s, but then when checking D#3G3, F3A3, G3B3, A3C#4, B3D#4, C#4F4, D#4G4, F4A4 they were not progressive.

That means that I'm not able to tune a ladder of CM3s accurate enough to tune a good ET without any other reference than the CM3s themselves.

I need to tune some other notes which I can then use to check and correct my initial ladder of CM3s.

For example:

1.- In the ET Via Marpurg sequence we first tune the ladder of CM3s F3A3, A3C#4, C#4F4 and F4A4, we then tune A#3, C4, D4, E4, F#3 and G#3 as pure P4s and P5s from the previous tuned notes.

This gives us some M3s that can be used as references to check the tuning of the initial ladder of CM3s. For example we can check if F3A3 is slower than F#3A#3. We can check if A3C#4 is faster than G#3C4 and slower than A#3D4 and we can also check if C#4F4 is faster than C4E4. If some of the previous checks prove wrong the corrections are obvious and we can get a very accurate ladder of CM3s.

2.- Another example is the Sanderson/Baldassin sequence. First we tune the initial ladder of CM3s F3A3C#4F4A4 then we tune A#3 as a P4 from F3 and F#3 as a M3 from A#3 comparing F#3A#3 to F3A3, it must beat slightly faster. Now we can hear to P5 F#3C#4 which becomes a test interval. If it sounds too tempered that means F3 is too sharp or C#4 is too flat or both. If it sounds too pure that means F3 is too flat or C#4 is too sharp or both. In either case this gives us enough information to correct F3 (and F4) and C#4 to have good P8s, M3s, P4 and P5.

3.- In the Coleman A-A sequence, after tuning A4, A3, F3, F4 and C#4 as a ladder of progressive CM3s, he (Jim Coleman) tunes then D4 as a tempered P4 1 bps wide aprox. from A3 and A#3 as a tempered P5 0.6 bps narrow aprox. from F4. And he checks the resulting M3 A#3D4. It must beat slightly faster than A3C#4. If it's too tempered that means FA is too tempered compared to AC#, if it's too pure then FA is undertempered compared to AC#. Corrections are obvious.

And I guess every CM3s based sequence has the same kind of checks available that allow us to correct the setting of the initial ladder of CM3s.


Re: Better Equal Temperament Sequence? [Re: Gadzar] #2494719 12/29/15 08:46 AM
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Glad you are posting again, Rafael, and thanks for giving the challenge a try and telling us how it turned out. It will be nice to have someone to talk to about sequences again.

Originally Posted by Gadzar
...

And I guess every CM3s based sequence has the same kind of checks available that allow us to correct the setting of the initial ladder of CM3s.



I would expand on your thought: ANY sequence has "checks available that allow us to correct the setting of the initial" intervals. But how and when the checks come into play makes the difference between sequences.

As you know, I give serious study to the mechanics of sequences. We also have to keep in mind human tendencies. I am thinking that these human tendencies affect our selection of sequences and probably, usually create a positive feedback loop in our minds emphasizing some intervals over others. This is apparent for no other reason that everyone thinks the sequence they use ought to produce progressive RBIs, but it seems to be an extremely rare occurrence. We fool ourselves.

I will mention problems with 4th and 5th based temperaments first, using Dr. White's sequence as an example. Despite what 4th and 5th tuners may believe, it would take an immortal to tune progressive SBIs, but SBIs need not be progressive for RBIs to be progressive. So they make the 4ths and 5ths sound good and the M3s sound progressive, maybe, and the M6s fit in, too. To get these RBIs to work the temptation exists to make them more progressive than they should be by having F3-A3 beat a bit slow and C#4-F4 beat a bit fast. Since there are only 4 M6s, all of which must also sound progressive if the 4ths are reasonable because of the M3-M6 test, there are no checks for this over-progressiveness until the temperament is expanded, unless ..... unless the m3s are listened to, but who wants to mess up a good thing by doing that! Besides, this type of error can't be discerned until very late in the sequence. And humans, being who they are, will tend to hear and believe what they have already decided they want to hear.

So consider CM3 based sequences. When it comes down to it, they are fitting M3s within M3s, even with additional checks, or perhaps even because of them! This allows what I call Marpurg errors to creep in. For instance with up a 3rd, up a 3rd, down a 5th, such an error will not be obvious until very late in the sequence. But if the tendency of the tuner is to perceive progressive M3s as being the definition of ET, then like the 4th and 5th tuner, their "baby" will be the prettiest one of all.

If you will forgive me, the checks you mentioned for ET via Marpurg and Coleman A-A sequences point this out. Take a ladder of CM3s, tune some SBIs, listen for new M3s that should be progressive with the old ones. Of course, will the corrections really get all the errors out of the right places, or will some tendency for over-progressiveness come into play. But notice the REAL tendency to use new M3s to check old M3s! If you take a look, each of these sequences can use new chromatically progressive m3s or M6s as checks... but that is not how CM3 tuners think.

Have you taken a look at the 8-note temperament, Rafael?






Jeff Deutschle
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Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2494789 12/29/15 12:15 PM
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Take for example the ET Via Marpurg sequence with little modifications in the order you tune the notes:

1. Tune A4 from your pitch source.

2. Tune D4 from A3 as a pure P4. Use the M3=M6 test.

3. Tune A3 from A4 as a "pure octave". I know there is no such a thing but anyway tune the best sounding octave you can achieve. By hearing at P5 D4A4 you can know the kind of octave you've tuned. If it sounds pure you have a pure 4:2 octave, if it is a slightly wide P5 then you've tuned a 4:2+ octave and if it is a slightly narrow P5 then you've tuned a 4:2- octave. Do not worry if this P5 is wide or narrow, the tuning of D4 at this point is temporary and it will be retuned later, what matters here is to tune the best sounding octave A3A4.

4. Tune F3 from A3 as a tempered M3 aprox. 7 bps wide.

5. Tune A#3 from F3 as a pure P4. Use the M3=M6 test.

6. Tune F4 from F3 as a "pure octave" (the best sounding octave you can achieve).


Up to this point you have three M3s tuned: F3A3, F4A4 and A#3D4.

Normally M3 F4A4 should be the same size than F3A3 as F4 and A4 are "pure octaves" from F3 and A3.

Normally also A#3D4 should be the same size than F3A3 because A#3 and D4 were tuned as pure P4s from F3 and A3.

So the three M3s F3A3, A#3D4 and F4A4 are supposed to be the same size. They should have the same tempering.

Unless you have big jumps in the iH of these notes they must be equally tempered M3s. We note this as F3A3 = A#3D4 = F4A4.

7. Tune C#4 from A3 as a wide M3 beating slightly slower than A#3D4. In theory it must beat aprox. 0.5 bps slower than A#3D4. So make sure A3C#4 beats not faster than A#3D4. These chromatic M3s should be progressive not inverted.

You have now four equally tempered M3s: A3C#4 = A#3D4 = F4A4 = F3A3

8. Tune C4 from F3 as a pure P5. Use the M6=M10 test (pure 3:2 fifth).

9. Tune E4 from A3 as a pure P5. Use the M6=M10 test.

You have now five M3s with the same tempering:

F3A3 = A3C#4 = A#3D4 = C4E4 = F4A4

10. Check M3 C#4F4. This M3 is our test interval. It will tell us if our initial estimation of 7 bps for the beat rate of F3A3 was right or not. C#4F4 should beat aprox. 0.5 bps faster than C4E4. If it beats slower then F3 is flat, F4 is flat and C#4 is sharp.

If C#4F4 is overtempered compared to C4E4 then F3 is sharp, F4 is sharp and C#4 is flat.

11. Re-tune F3 accordingly and go to step 5. Repeat until C#4F4 beats aprox. 0.5 bps faster than C4E4.

Now you have a very accurate ladder of CM3 which can be used to tune a nice ET with the ET Via Marpurg sequence or any other CM3s based sequence of your preference.

Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2494792 12/29/15 12:20 PM
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Jeff,

Please give a try to the sequence I've posted above before discarding it and saying: "CM3s tuners think and act this or that way..."

Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2494796 12/29/15 12:38 PM
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O.T.

Jeff,

I've followed the 8 note mini-temperament with interest. I was going to point you out that you mistuned some P4 in the video but then you corrected the error later in your procedure which makes a point thumb

It is very intersting from a theoreticall point of view but for practical purposes I don't like the idea of taking a P5 as the base to tune the temperament and having to accept the size of the resulting octave. I prefer to start with an octave and find the appropiate size for the fifths, fourths and thirds.

And also I find a little difficult to figure out which notes and in what direction to retune when adjusting the size of intervals, I guess it comes with practice.

The video is too dark!

Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2494799 12/29/15 12:44 PM
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Rafael, to save us both time and frustration, let's just pretend we start with an absolutely perfect set of CM3s from A0 to A7.

Now, please, you choose a sequence and let's see where it goes. smile


Jeff Deutschle
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Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2494831 12/29/15 02:01 PM
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The biggest issue I have with the "best sequence" type of discussion, is it seems to assume that there is a "right" way to tune the intervals. In my reality, every interval that is tuned is only approximate. The theoretical beat rates are just that: theoretical. They don't hold up in the real world, although they can be very close.

This is the reason why I say a temperament needs to be "discovered" and not imposed. You have to get things close to know where you stand and to get a feel for the quality of temperament that will work on a given piano. Once you get a "sketch" or "rough draft" of the temperament, you can use that as a starting point for tuning a more refined version.

The temperament can usually be further refined by expanding to a 2 or 3 octave range, because you have more intervals giving you more information.

As the result of some of these discussions, I find that I am leaning on SBIs more than I used to. I used to depend a lot more on RBIs. Now days I really try to pay attention to both and find the best compromise.


Ryan Sowers,
Pianova Piano Service
Olympia, WA
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Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2494858 12/29/15 03:18 PM
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I agree with Ryan. There is no better sequence. But there are good tuners and not so good tuners a bad tuners and tooners.

Originally Posted by UnrightTooner
Rafael, to save us both time and frustration, let's just pretend we start with an absolutely perfect set of CM3s from A0 to A7.

Now, please, you choose a sequence and let's see where it goes. smile


Oh I guess I would choose a sequence à la meantone, where you divide a given M3 into four equally tempered fifths less two octaves. Or divide the M3 into 2 fifths plus two fourths.

For example:from F3 tune up a fifth to C4 down a fourth to G3 up a fifth to D4 down a fourth to A3. Checking the progression of RBIs as they become available.

Re: Better Equal Temperament Sequence? [Re: bobrunyan] #2495154 12/30/15 11:38 AM
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Thanks, Rafael! I am trying some different scenarios and noticed something I wasn't expecting... More later.


Jeff Deutschle
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Who taught the first chicken how to peck?
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