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Re: Help with best octave sizes [Re: bellspiano] #2405712
04/02/15 10:54 AM
04/02/15 10:54 AM
Joined: Nov 2008
Posts: 5,919
Bradford County, PA
UnrightTooner Offline
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Originally Posted by bellspiano
I am sure I missed a memo somewhere. But why would one plan out a octave-based tuning class in great and rational detail, triple-check all the math, get the class accepted for the PTG national convention and then -- much later -- do a survey of what octaves sound good to interested techs? Isn't the ultimate purpose to have a pleasing piano? So why would one leave the aural test of the hypothesis (viz: pianos tuned by this mathematical method have a "better" sound) until way after the math chapters, so to speak, are published?

I guess one area of confusion for me is, in fact, the statement of the hypothesis. What is all this work trying to prove or disprove?


Dorrie: What is trying to be "proved" is not so much about tuning as it is about a tuning teacher. And therein lies the problem. Sigh...


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
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Re: Help with best octave sizes [Re: Mark Cerisano] #2405715
04/02/15 11:16 AM
04/02/15 11:16 AM
Joined: May 2010
Posts: 2,501
Vancouver, Canada
DoelKees Offline

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Originally Posted by Mark Cerisano, RPT
Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT

As for F3D4 not equal to G3B3, I've never heard that and in my spreadsheet with measured and calculated multiple B curves, F3D4 and G3B3 are within 2%.


Well, one of us must be wrong. I use IH curves measured from actual pianos and then compute a theoretically perfect temperament on F3A4, with all consonant intervals progressive.
Then I compute the beat rates, which I posted here long time ago, you can find this stuff in the old thread I referenced earlier.

For example for Steinway D the beat rates for the case under discussion are:
F3D4 = 8.0, G3B3 = 7.8, G#3C4 = 8.2.

For my Heintzman upright the result is:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For Pat's Hellas Helsinki:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For a Wurlitzer spinet:
F3D4 = 8.3, G3B3 = 7.7, G#3C4 = 8.2.

Kees



How did you arrive at a theoretically perfect temperament considering iH? What criteria?

I used theoretically calculated B values considering different octave spread. (Octave spread, my own term, is the cents deviation between the 6th and 3rd partials of a pure 4:2), and tried to produce as close to perfect ET using progressive M3, m3, M6, and P4 at 1bps +/- 0.2bps. I programmed my sequence into a spread sheet and could get very close to that using the appropriate sequence for the octave spread.

Also, I'm very curious, how did you measure inharmonicity? It's probably simple but I wouldn't know where to start. Could you help?

Regards,

Criterium for perfect: "with all consonant intervals progressive. "

Tunelab to measuring IH.

Kees

Re: Help with best octave sizes [Re: UnrightTooner] #2405720
04/02/15 11:34 AM
04/02/15 11:34 AM
Joined: May 2004
Posts: 864
Boston, MA
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bellspiano Offline
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Thank you! It is all becoming clear now --


Dorrie Bell
retired piano technician
Boston, MA
Re: Help with best octave sizes [Re: bellspiano] #2405821
04/02/15 05:50 PM
04/02/15 05:50 PM
Joined: Mar 2011
Posts: 585
Boston, MA
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Tunewerk Offline
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Boston, MA
Dorrie, I agree.

Concerning the application of math to this problem.. it can be very helpful and articulate, unless it is misapplied. Unfortunately using the type of math described here will do no more than what a tuning machine does.

The reason why this problem hasn't been solved to a greater depth yet is because you can't apply a model curve to anything on the piano with just a single measurement of 'B'. Even a few samples are still ineffective. Literally every string has to be sampled because every string on a piano is different. Models get us very close, but to transcend that last 10%, every string has to be taken into account to refine the model.

The result from that type of best fit analysis will never result in any kind of smooth, continuous curve. You could model the deviations with regressive polynomials.. but why? It's just an erratic engineering problem best solved with raw data.

Octave sizes for ideal tuning must vary because of partial density and bandwidth availability at the octave as opposed to other partials - if we are to use the definition that Kees supplied above, which I believe is accurate. Cent width for each semitone will always be slightly unequal to reflect the ideal balance from irregularity in the scale itself.

This is highly variable and will change to reflect the differences in instruments, nevermind subjective taste..


www.tunewerk.com

Unity of tone through applied research.
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Re: Help with best octave sizes [Re: Mark Cerisano] #2406001
04/03/15 08:09 AM
04/03/15 08:09 AM
Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
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Mark Cerisano Offline OP
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Posts: 3,087
Montreal, Quebec, Canada
Dorrie,

I have been tuning by measuring octave spread and choosing an appropriate sequence to help me tune accurate ET with little or no refining for some time. It works for me and it is fun. When I submitted the class to the PTG, they accepted it.

I could give the class now, based on my own opinions but I would like it to be a bit more concrete than that.

Octave sizes for instance. Specifically, the first octaves tuned, need to be tuned as they will be in the final temperament, without any references other than, "Does it sound good?", if my goal is "accurate ET with least refinement". Octave spread helps me do that. I think the octaves I tune using octave spread are very good, but I need to find out if others have the same conclusion or the method would not be interesting to them. That's the reason for the thread. Also, the topic still fascinates me.

This thread is part "gather more research to back up what I use" and part "just for the fun of it".

You did not miss anything if you find the posts interesting. You needn't read them in the context of "this sounds like someone who is unsure of themselves, yet giving a PTG class".

You can never be too unsure when you are trying to prove something. There will always be someone who will try to make you look like a fool. Thanks to some people here on PW, I have come to realize that. They may sound mean and spiteful, but they do provide a service.

Last edited by Mark Cerisano, RPT; 04/03/15 08:22 AM.

Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2406030
04/03/15 09:40 AM
04/03/15 09:40 AM
Joined: May 2004
Posts: 864
Boston, MA
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bellspiano Offline
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Thank you, Mark. I appreciate your clarification, as well as your willingness to teach and learn.


Dorrie Bell
retired piano technician
Boston, MA
Re: Help with best octave sizes [Re: Chris Leslie] #2406039
04/03/15 10:03 AM
04/03/15 10:03 AM
Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
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Mark Cerisano Offline OP
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Montreal, Quebec, Canada
Originally Posted by Chris Leslie
Mark, in the end do have any results on your survey? What kind of octaves corresponded with peoples preferences?


There was no obvious preference for any one octave.

Here are my thoughts as to why:
1. The octaves were open. Rolling unisons could have made choosing difficult.
2. The octaves themselves were not tuned well enough for this test. Some were too close to each other.
3. The design of the test was not ideal. Having to choose between only two octaves resulted in the subject's preference for the best size possibly not being available.

Recommendations:
1. Use only single strings
2. Use a better test
3. Use a better test

I am working on a web app that allows the user to listen to an A3A4 octave and tweak A3 until they consider the sound the best possible.

I am using actual recorded piano strings and altering the a3's using Audacity.

I will have multiple pairs of strings that have different iH.

One problem I find is that Audacity can only change the pitch by 0.058% which corresponds to about 1 cent.

I am going to code it anyway since I can't find a way to get anything more precise. Hopefully I will be able to measure a difference using checks that will provide some insight.

My hypothesis is that best octave sizes tuned with no other criteria other than best sound, may have a quite large window.

My sequences still produce more accurate interval sizes than I could any other way, mainly because I am using RBI all the time so my ear gets better over the tuning and as I use the method through the years.

A question I have for those who seem to criticize the RBI approach is:
How do you check your temperament when you are finished? Don't you check the RBI progression? If so, then using an RBI sequence will improve your ability to hear the progressions. Do not misread this. SBI are necessary and required as a check to make sure the RBI are as you hear them - the ear can be fooled.

In the end, the RBI approach for me is just a workout to improve my filtering ability and sensitivity to beat speed differences.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2406065
04/03/15 11:33 AM
04/03/15 11:33 AM
Joined: Dec 2006
Posts: 2,758
Mexico City
Gadzar Offline
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Mexico City
Originally Posted by Mark Cerisano, RPT
My hypothesis is that best octave sizes tuned with no other criteria other than best sound, may have a quite large window.

My sequences still produce more accurate interval sizes than I could any other way


I ask me why then you have not yet "discovered" that in spinets and some consoles the best sounding octave is a narrow 4:2 / wide 2:1

I still remember when you used to say that a 6:3/4:2 balanced octave was the unique option.

That kind of octave allowed you to use what you called the P4 window. Which is severely altered with any other octave size.

Now you have accepted the possibilty of a narrow 6:3 with a pure 4:2. And you have modified your P4 window concept accordingly.

But you still ignore the case of a narrow 4:2/wide 2:1, which reverses your "P4 window"

This would force you to accept the P4 window is not valid in all pianos!

I agree with you that a good sounding octave is a too wide range but IMO if you tune a pure 4:2 in a spinet you are definitely out of this large window. How is it that you have not noticed that?

You do not have to believe me! You can ask other tuners. Ask Ron Koval which kind of octaves he uses for tuning the smallest pianos. Or better: use your own ears! Tune a good sounding octave in a spinet, put it right in the middle of the "good sounding" large window and measure its size with the m3M6, M3M10 and M10M17 tests. You will find, as me and many others, that it is a narrow 4:2 / wide 2:1

If you open your mind an accept this fact, then the way to tune accurate octaves of the same size is to tune A3A4 as the best sounding octave, leaned to the wide side, and then measure it. You can then tune the same size of octave for F3F4.

And for your P4 window, I think it is of a limited use as it is not universal. It is valid only in some regions of the scale of some selected pianos with specific octaves's sizes.


Last edited by Gadzar; 04/03/15 11:41 AM.

Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx
Re: Help with best octave sizes [Re: Mark Cerisano] #2406079
04/03/15 12:19 PM
04/03/15 12:19 PM
Joined: Dec 2006
Posts: 2,758
Mexico City
Gadzar Offline
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Gadzar  Offline
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Mexico City
It is a commonly accepted fact that, when tuning the temperament, fourths must beat at approx 1bps and fifths must beat slower, at approx 1/2 bps.

That's how I was taught. But I used to have a little console. It was my practice piano. It was on this piano that I learned to set the temperament. I soon realised that in this piano if I tuned a narrow fifth D4A4 beating at around 0.5 bps and then a wide fourth A3D4 beating at 1 bps, the resulting A3A4 was not clean. For it to be clean I should have the P4 A3D4 purer than the P5 D4A4.

This was against all I were been taught!

At that time I supposed I was wrong as I was a beginner. But now I know I was right. In this piano, complementary fourths must be tuned purer than fifths in order to have clean octaves. In other words this piano requires narrow 4:2 octaves in the temperament region.

I know almost all aural tuners will say no! But I am comfident I'm right. I've seen numerous tuners who use this kind of setting in their Verituners, but I have never seen an aural tuner tuning A3D4 purer than D4A4, except Alfredo Capurso if memory doesn't fail.




Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx
Re: Help with best octave sizes [Re: Mark Cerisano] #2406086
04/03/15 01:16 PM
04/03/15 01:16 PM
Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
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Mark Cerisano Offline OP
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Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
When I look back, I am truly amazed at how much I have changed my approach to tuning.

Yes, I used to advocate 4:2+/6:3- as the best size.
Yes, I now recognize a variety of sizes between pure 4:2 and wide 4:2.
Yes, I have found a piano recently that its F or A octave tuned well as a pure 2:1, narrow 4:2.

Through the PTG I was taught to tune 4:2+/6:3-. This approach worked on many pianos, but not those that sounded best as pure 4:2/very narrow 6:3. Now I have found a system that refines that approach to include more pianos.

Yes, I see narrow 4:2 in the field, specifically with reversed octaves where the 6:3 is wide. But, IMHO, they are anomalies created by scaling errors. I have not found on these pianos that many of the octaves in the temperament have this same relationship. This is confirmed by the one or two wild B numbers seen around the break/coil change section in an iH graph.

When teaching my method, I will just mention to be aware of these possibilities, check neighbouring octaves to make sure it is an anomaly, and try to compromise if somethings don't fit.

Thanks for your comments.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2406109
04/03/15 02:24 PM
04/03/15 02:24 PM
Joined: Jul 2007
Posts: 1,404
Sicily - Italy
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alfredo capurso Offline
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..."A question I have for those who seem to criticize the RBI approach is:
How do you check your temperament when you are finished? Don't you check the RBI progression? If so, then using an RBI sequence will improve your ability to hear the progressions. Do not misread this. SBI are necessary and required as a check to make sure the RBI are as you hear them - the ear can be fooled."...

Hi Mark,

I use a precise sequence because it enables me to shape the same (tuning) form, no matter the size of the piano. I do not wait until I am "finished", I check intervals while I am tuning, trying to map small approximations in my mind and creating the right relation/progression between SBIs and RBIs, as their number increases.

The RBI progression F3-A3-C#4-F4-A4 allows you to check thirds that imo are too distant (two tones), so anything can happen with the three thirds (F#, G, G# and so on) that are in between those thirds. Yes, on the one hand you get the feeling that you can discern their progression, as their bps difference is large, but it does not seem to help when it comes to controlling and refining small bps differences, i.e. when you need fine ears and hammer technique.

After 7 steps I can compare two M6 (A3-F#4 and B3-G#4) which are one tone distant, two more steps and you can compare three chromatic thirds, which is imo easier than comparing distant thirds and help me make their chromatic progression correct and very compact.

As for the form I tune, 4ths and 5ths are strictly related, especially from C3 to C5; they regularly invert their beat rate progression, always in the same place. That should tell you something more about M6s, and explain why 4ths (and SBIs) cannot be second-order nor ignored.

In general, the ear needs to be trained so that it cannot be fooled. After all, it is only around F4 that thirds get pretty fast. In any case, that is perhaps one more good reason for trusting and relying on 4ths and 5ths, in fact the latter are easy to evaluate quickly, all the way up the scale.

Also, I seem to remember that tuning SBIs wasn't that difficult, considering the hammer technique of a beginner, thirds would variate too much at the slightest movement of the hammer, or perhaps it was more the general "mood" I preferred, small variations for slow beats and check... I am not sure.

Regards, a.c.
.







alfredo
Re: Help with best octave sizes [Re: Gadzar] #2406117
04/03/15 02:52 PM
04/03/15 02:52 PM
Joined: Jul 2007
Posts: 1,404
Sicily - Italy
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alfredo capurso Offline
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Sicily - Italy
Originally Posted by Gadzar
It is a commonly accepted fact that, when tuning the temperament, fourths must beat at approx 1bps and fifths must beat slower, at approx 1/2 bps.

That's how I was taught. But I used to have a little console. It was my practice piano. It was on this piano that I learned to set the temperament. I soon realised that in this piano if I tuned a narrow fifth D4A4 beating at around 0.5 bps and then a wide fourth A3D4 beating at 1 bps, the resulting A3A4 was not clean. For it to be clean I should have the P4 A3D4 purer than the P5 D4A4.

This was against all I were been taught!

At that time I supposed I was wrong as I was a beginner. But now I know I was right. In this piano, complementary fourths must be tuned purer than fifths in order to have clean octaves. In other words this piano requires narrow 4:2 octaves in the temperament region.

I know almost all aural tuners will say no! But I am comfident I'm right. I've seen numerous tuners who use this kind of setting in their Verituners, but I have never seen an aural tuner tuning A3D4 purer than D4A4, except Alfredo Capurso if memory doesn't fail.




Hi Rafael,

I am sorry, perhaps it was someone else. As it is, also I tune A3-D4 very very close to one bps, and D4-A4 has to sound almost pure. As you know, I use a strip mute, so that is referred to middle strings. What is relevant is that from A3-E4 to D4-A4 fifths get closer and closer to pure. Fourths get a pretty evident/progressive acceleration from C4-F4 to E4-A4, in fact E4-A4 is about 2.5 bps.

Regards, a.c.
.


alfredo
Re: Help with best octave sizes [Re: alfredo capurso] #2406141
04/03/15 04:15 PM
04/03/15 04:15 PM
Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
M
Mark Cerisano Offline OP
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Mark Cerisano  Offline OP
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Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
Originally Posted by alfredo capurso


I use a precise sequence because it enables me to shape the same (tuning) form, no matter the size of the piano. I do not wait until I am "finished", I check intervals while I am tuning, trying to map small approximations in my mind and creating the right relation/progression between SBIs and RBIs, as their number increases.

The RBI progression F3-A3-C#4-F4-A4 allows you to check thirds that imo are too distant (two tones), so anything can happen with the three thirds (F#, G, G# and so on) that are in between those thirds. Yes, on the one hand you get the feeling that you can discern their progression, as their bps difference is large, but it does not seem to help when it comes to controlling and refining small bps differences, i.e. when you need fine ears and hammer technique.

After 7 steps I can compare two M6 (A3-F#4 and B3-G#4) which are one tone distant, two more steps and you can compare three chromatic thirds, which is imo easier than comparing distant thirds and help me make their chromatic progression correct and very compact.



This is exactly how I am tuning. I try to set intervals as they must sound in relation to each other, as I tune them. I have also previously noted the large window for the CM3 ladder.

I am now calling it "Tuning ET for Least Refinement". Like you, using appropriate checks to tune intervals so they will all fit with each other after the last step. Errors are discovered along the way. I am using finer and finer beat speed windows, the CM3 ladder containing the largest of these windows.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: UnrightTooner] #2406195
04/03/15 08:38 PM
04/03/15 08:38 PM
Joined: May 2010
Posts: 2,501
Vancouver, Canada
DoelKees Offline

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Originally Posted by UnrightTooner

But, you know, I might not be paying enough attention to how the M6s beat about 1/2 bps faster due to iH. Perhaps that is why I only get so close to progressive RBIs, and perhaps why trying to tune with RBIs alone failed. To make the outside M6/inside M3 test beat equally, with typical iH, requires an error of 1 cent, which could be in one or more notes. I've got a P22 tomorrow morning that I can take my time with...

Sounds interesting.

One thing worth mentioning is that the M6/M3 and M6/+M3 tests (the latter my name for where you move up the M3 one step) are very sentivive to octave stretch. If you stretch the octave the M6 will get stretched more than twice as much as the M3 as it spans a bigger range.

According to my data/calculations the M6/+M3 test is always spot on, for all dozen or so pianos I've checked if 4:2/6:3 octaves are tuned. If you have 4:2 octaves it's a different story: the M6 beats now halfway between the M3 beat and the +M3 beat. (E.g., F3D4 is in between G3B3 and G#3C4.)

I suspect if you have even smaller octaves the standard test becomes the most accurate one, but have not calculated that.

Kees

Re: Help with best octave sizes [Re: Gadzar] #2406207
04/03/15 09:20 PM
04/03/15 09:20 PM
Joined: Nov 2008
Posts: 5,919
Bradford County, PA
UnrightTooner Offline
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Joined: Nov 2008
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Bradford County, PA
Originally Posted by Gadzar
It is a commonly accepted fact that, when tuning the temperament, fourths must beat at approx 1bps and fifths must beat slower, at approx 1/2 bps.

That's how I was taught. But I used to have a little console. It was my practice piano. It was on this piano that I learned to set the temperament. I soon realised that in this piano if I tuned a narrow fifth D4A4 beating at around 0.5 bps and then a wide fourth A3D4 beating at 1 bps, the resulting A3A4 was not clean. For it to be clean I should have the P4 A3D4 purer than the P5 D4A4.

This was against all I were been taught!

At that time I supposed I was wrong as I was a beginner. But now I know I was right. In this piano, complementary fourths must be tuned purer than fifths in order to have clean octaves. In other words this piano requires narrow 4:2 octaves in the temperament region.

I know almost all aural tuners will say no! But I am comfident I'm right. I've seen numerous tuners who use this kind of setting in their Verituners, but I have never seen an aural tuner tuning A3D4 purer than D4A4, except Alfredo Capurso if memory doesn't fail.




Rafael:

The temperament octave is understood to be F3-F4. The D4-A4 5th that you mention is not in this octave and should beat faster than 1/2 bps.


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Help with best octave sizes [Re: DoelKees] #2406209
04/03/15 09:35 PM
04/03/15 09:35 PM
Joined: Nov 2008
Posts: 5,919
Bradford County, PA
UnrightTooner Offline
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Bradford County, PA
Originally Posted by DoelKees
Originally Posted by UnrightTooner

But, you know, I might not be paying enough attention to how the M6s beat about 1/2 bps faster due to iH. Perhaps that is why I only get so close to progressive RBIs, and perhaps why trying to tune with RBIs alone failed. To make the outside M6/inside M3 test beat equally, with typical iH, requires an error of 1 cent, which could be in one or more notes. I've got a P22 tomorrow morning that I can take my time with...

Sounds interesting.

One thing worth mentioning is that the M6/M3 and M6/+M3 tests (the latter my name for where you move up the M3 one step) are very sentivive to octave stretch. If you stretch the octave the M6 will get stretched more than twice as much as the M3 as it spans a bigger range.

According to my data/calculations the M6/+M3 test is always spot on, for all dozen or so pianos I've checked if 4:2/6:3 octaves are tuned. If you have 4:2 octaves it's a different story: the M6 beats now halfway between the M3 beat and the +M3 beat. (E.g., F3D4 is in between G3B3 and G#3C4.)

I suspect if you have even smaller octaves the standard test becomes the most accurate one, but have not calculated that.

Kees


The P22 turned out very well. There were some interesting things I noticed about how the BW sequence is affected whether you use the M6/M3 or M6/+M3. I will continue to take note.

Of course when you stretch an octave, the M6s will increase speed more than the M3s all else being equal. But typically you would only stretch the octaves in a low iH piano where you can expect the M6/M3 to be more equal than the M6/+M3 with 4:2 octaves.

But here we are again starting with the octave. Approximately 1 bps 4ths and 1/2 bps 5ths seem to always work out to a good octave, and I am now thinking, also an M6/+M3 equality, or as close as the piano and my ears will allow. Splitting the difference between M6/M3 and M6/+M3 is not very practical in actual tuning.


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Help with best octave sizes [Re: Mark Cerisano] #2406210
04/03/15 09:48 PM
04/03/15 09:48 PM
Joined: Dec 2006
Posts: 2,758
Mexico City
Gadzar Offline
2000 Post Club Member
Gadzar  Offline
2000 Post Club Member

Joined: Dec 2006
Posts: 2,758
Mexico City
Jeff,

Franz Mohr tunes his temperament from A3 to A4.

And what I said about narrow 4:2 octaves also includes F3F4.

Do you tune F3C4 P4 purer (slower) than C4F4? I guess no. I know no aural tuner who does that. But I know several ETD tuners (Verituner users) who set their ETD to tune narrow 4:2 octaves at F3F4 and A3A4 for small pianos.

Mark,

The vast majority of pianos I tune are spinets (Wurlitzer) and consoles. Exceptionaly I tune grands. I have only two concert grands in my list of serviced pianos

So for me, spinets are the rule and large grands are the exception.



Last edited by Gadzar; 04/03/15 09:56 PM.

Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx
Re: Help with best octave sizes [Re: UnrightTooner] #2406224
04/03/15 10:45 PM
04/03/15 10:45 PM
Joined: May 2010
Posts: 2,501
Vancouver, Canada
DoelKees Offline

2000 Post Club Member
DoelKees  Offline

2000 Post Club Member

Joined: May 2010
Posts: 2,501
Vancouver, Canada
Originally Posted by UnrightTooner
Originally Posted by DoelKees
Originally Posted by UnrightTooner

But, you know, I might not be paying enough attention to how the M6s beat about 1/2 bps faster due to iH. Perhaps that is why I only get so close to progressive RBIs, and perhaps why trying to tune with RBIs alone failed. To make the outside M6/inside M3 test beat equally, with typical iH, requires an error of 1 cent, which could be in one or more notes. I've got a P22 tomorrow morning that I can take my time with...

Sounds interesting.

One thing worth mentioning is that the M6/M3 and M6/+M3 tests (the latter my name for where you move up the M3 one step) are very sentivive to octave stretch. If you stretch the octave the M6 will get stretched more than twice as much as the M3 as it spans a bigger range.

According to my data/calculations the M6/+M3 test is always spot on, for all dozen or so pianos I've checked if 4:2/6:3 octaves are tuned. If you have 4:2 octaves it's a different story: the M6 beats now halfway between the M3 beat and the +M3 beat. (E.g., F3D4 is in between G3B3 and G#3C4.)

I suspect if you have even smaller octaves the standard test becomes the most accurate one, but have not calculated that.

Kees


The P22 turned out very well. There were some interesting things I noticed about how the BW sequence is affected whether you use the M6/M3 or M6/+M3. I will continue to take note.

Of course when you stretch an octave, the M6s will increase speed more than the M3s all else being equal. But typically you would only stretch the octaves in a low iH piano where you can expect the M6/M3 to be more equal than the M6/+M3 with 4:2 octaves.

But here we are again starting with the octave. Approximately 1 bps 4ths and 1/2 bps 5ths seem to always work out to a good octave, and I am now thinking, also an M6/+M3 equality, or as close as the piano and my ears will allow. Splitting the difference between M6/M3 and M6/+M3 is not very practical in actual tuning.

By "very well" you mean you got progressive M3's and M6's? An elusive goal, practically speaking probably overkill, but a worthy goal to aim for.

Regarding splitting the difference being unpractical: to pull that off you should be able to detect progressive M3's on a 24 notes per octave quartertone piano tuned in ET. Yet as I think Mark has pointed out, if you are lousy at darts you should still aim for the bull's eye.

I appreciate your comments about the octave. So if you aim for the M6/+M3 equal beating test you should get 4:2/6:3 octaves on large grands, and 4:2 or less on smaller pianos.

So maybe that should be Mark's magic bullet to determine best octave size a-priori: if you pass the M6/+M3 test, you automatically will have optimal octave sizes.

Maybe.

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2406228
04/03/15 11:03 PM
04/03/15 11:03 PM
Joined: Dec 2006
Posts: 2,758
Mexico City
Gadzar Offline
2000 Post Club Member
Gadzar  Offline
2000 Post Club Member

Joined: Dec 2006
Posts: 2,758
Mexico City
Originally Posted by Alfredo Capurso
Hi Rafael,

I am sorry, perhaps it was someone else. As it is, also I tune A3-D4 very very close to one bps, and D4-A4 has to sound almost pure. As you know, I use a strip mute, so that is referred to middle strings. What is relevant is that from A3-E4 to D4-A4 fifths get closer and closer to pure. Fourths get a pretty evident/progressive acceleration from C4-F4 to E4-A4, in fact E4-A4 is about 2.5 bps.


Hi Alfredo,

No. It was indeed you. But you said that you tune A3E4 sensibly faster than D4A4.

My fault, I confused the notes, the intervals and their relative beat rates! Haha...

Sorry.

P.s. That was surprising to me because usually in ET "all" intervals increase their beat rates when going up the scale. So the fact that you tune A3E4 sensibly faster than D4A4 caught my attention as this seems to be reversed.

Last edited by Gadzar; 04/03/15 11:14 PM.

Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx
Re: Help with best octave sizes [Re: Mark Cerisano] #2406244
04/03/15 11:58 PM
04/03/15 11:58 PM
Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
M
Mark Cerisano Offline OP
3000 Post Club Member
Mark Cerisano  Offline OP
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M

Joined: Jan 2010
Posts: 3,087
Montreal, Quebec, Canada
I propose that the difference between actual M3/M6 beat speeds is not that much, and in the end, if we assume F3D4 = G3B3, we will not create that much error, especially if we consider octave spread.

What I've done is to force the equality and see what happens to the interval sizes.
I force the equality by tuning F3D4 = G3B3, etc. Also, I use the following test to determine the appropriate m3/M3 equality:

Small Octave Spread. Difference between 4:2 and 6:2 < 0.5 cents.
Aural test: Tests for the 4:2 and 6:3 are so close that they both test out as pure, as pure as the ear can tell, anyway.
m3/M3 equality: F3G#3 = A#3D4

Medium Octave Spread. Difference between the 4:2 and the 6:3 is between 0.5 and 1.1 cents.
Aural test: The 4:2 is wide and the 6:3 is narrow and the octave sounds better than tuning a pure 4:2.
m3/M3 equality: F3G#3 = B3D#4

Large Octave Spread. Difference between the 4:2 and the 6:3 is greater than 1.1 cents.
Aural test: The octave sounds best as a pure 4:2 even though the 6:3 is very narrow.
m3/M3 equality: F3G#3 = C4E4 or higher.

It is important to use the m3/M3 equalities because that is the only way, as far as I know, to create bisecting beat speed windows that allow us to transition to the other CM3's. If we use a m3/M3 equality that belongs to a different octave spread, other than the octave spread we have determined fits the piano we are tuning, the progressions suffer. (I have created RBI/SBI curves and this conclusion is supported. I have posted some of those curves previously but I will again if anyone wants to see them.)

So, the question is, what happens to the RBI and SBI progressions when we force the M3/M6 equality?

I already posted some of these but here they are again:

These are the B curves I used for the calculations. The B values for F3, A3, F4, and A4 are those that produced the small, medium, and large octave spreads. Many other combinations could produce the same octave spread, but I choose those that were within the upper and lower limits found on Tremaine Parsons' iH graphs. The other B values were interpolated.

[Linked Image]

Here are the theoretical beat speeds produced when using my bisecting beat speed sequence appropriate for each octave spread:

[Linked Image]

[Linked Image]

[Linked Image]

My premise is, these are close enough ideals to aspire to, especially since it seems so difficult to get progressive RBI by ear anyway, and here is an aural method that produces this accuracy depending on how good you are at hearing and setting RBI (using SBI as confirmations of course).

The actual sequence will be published in the Journal in June (at least that's what I was told). After that, I would be happy to post it here and even upload a video of me doing my best using it.

(The octave size survey seems to conclude that the actual ideal octave sizes are not that critical since there doesn't seem to be a preference for one size or another, but I will still create my web app that will allow users to tune their own octaves to within 1 cent. However, this method does zero in on one acceptable octave size depending on iH, and then uses a method that allows all the other octaves within the temperament to be tuned as the same size. These can always be confirmed for best size after the temperament is tuned, of course.)


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
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