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I've been following these tuning discussions with great interest - technical interest only.

Alfredo writes:
Chas 4ths are progressive. The 4ths beat rate progression invert on C3.
Chas 5ths are progressive. The 5ths beat rate progression invert on E4 (tuning centre strings).

Two questions:

If beats (4ths) are supposed to invert from wide to narrow, (5ths) narrow to wide at some point in the register (it should depend on the piano, I think), then how can that be if the octaves are continuously stretched ever so slightly sharp from the tempered section and ever so slightly stretched flat below the tempered section?

How can one slightly stretch each octave note and expect those widened octaves to pave the way for an already widened 4th to become narrower? ...and narrow 5ths to be wider?

That means if the beats invert, then at some point, there are no beats, meaning that a particular 4th or 5th will be tuned pure (just)? Is this to provide a piano with the "color" as in not equal? Or do they invert in that their slow beat rates become faster/slower depending (4th or 5th) and not become pure intervals? I understand these things are better off seen/heard in-person, rather than described on a forum thread.

Sorry if I am missing something and you are repeating yourself.

I know, Issac, I will stop stretching so much the bass notes!

Glen

Sample tuning - please excuse playing errors

http://www.box.net/shared/rryoo393l4

http://www.box.net/shared/062bz3yefx

http://www.box.net/shared/27hq5la89d

Hello Glen,

I'm happy to answer your questions for anything you may find unclear or illogical.

you ask:..."Or do they invert in that their slow beat rates become faster/slower depending (4th or 5th) and not become pure intervals?"...

Take this as a practical aid, nothing numerical but it can work as general reference and as a way to represent how intervals go.

Pre-form (centre strings from C3 to C6): 4ths never become pure. From bass up to C3-F3 they faintly slow down, from C3-F3 going up they get wider. Usually I go from C3-F3 down the bass, so in this direction 4ths get wider.

C3-F3 and C3-G3 have the same beat rate, between 1/2.5 and 1/3 bps.

5ths, from bass, go faintly narrower up to A3-E4 where they invert. Usually I go first up to C6, then from A3-E4 down the bass, so in this direction 5ths get less and less narrow (centre strings).

G#3-D#4 and A#3-F4 will be equal beating (as a reference).

From A3-E4 up, 5ths (on centre strings) get less and less narrow, while 4ths keep on getting wider. After G4-C5 4ths collaps. I use 5ths and octaves to go on, both very faintly progressive, octaves-beat rising in a shorter time, 5ths getting closer and closer to pure.

It takes a while for 5ths to get wide (Pre-form on centre strings). I check 10ths progression, starting from A3-C#5.
When I get to E5, I check my first 12ths A3-E5, it has to be pure (Pre-form on centre string).

I go up on centre strings with 5ths, octaves, 10ths and pure 12ths (on centre strings), up to the first 15th A3-A5. Then I have plenty of checks intervals, and I use all of them for what I need to do/hear.

When I get to C6 I go down, from A3 to C3 (or strings crossing). Then I check the whole three octaves Pre-form temperament (C3-C6 on centre strings), and start unisoning from C3 up. You may find this Pre-form sequence (not a must) in this thread.

Regards, a.c.
.

Thanks, Alfredo,

Okay, thanks. Your fifths go from narrow-to-pure-to-wide up the register, and narrower down the register.

I strip mute as much as possible, so the center string is left unmuted - a non-issue - That is how I was taught, tune center strings first before unmuting to tune unisons. I suppose you call that pre-form.

I follow the paradigm (similar to Kent's article) to temper 4ths slightly wider than the tempered 5ths are narrow, proportional and progressive, not equal as you have it.

It seems that when I do this, then apply a slight stretch to the octaves moving in each direction from the tempered section, there is no inversion of 5ths, they only beat slower as I move up the register - it simply does not invert any 4ths or 5ths above or below the tempered section.

In order for me to start to do what you suggest, I would have to make, for example, C3-F3 and C3-G3 have the same beat rate, between 1/2.5 and 1/3 bps - that is contrary to my novice training, and certainly not out of the realm of possibility to eventually add that method to my developing tool-box.

I'll give it a try sometime and see what happens.

Thanks for the feedback.

Glen

Hello Glen,

You write:... "Your fifths go from narrow-to-pure-to-wide up the register, and narrower down the register."...

Yes, narrow-to-pure-to-wide up the register, on center strings.

..."I strip mute as much as possible,"...

I do not. I mute from midbass strings-crossing up to C6. I do not find larger muting and "one go" unisoning convenient, for stability, though it may be time saving.

..."so the center string is left unmuted - a non-issue - That is how I was taught, tune center strings first before unmuting to tune unisons. I suppose you call that pre-form."...

Does Chas Pre-form mean “muting the strings”? No.

Chas Pre-form (Preparatory Tuning) is referred to a form where all wide intervals, 3rds, 4ths, 6ths, octaves, 10ths, 15ths and so on, beat a little faster, then narrow intervals are little less narrow. This Pre-form is drawn on center strings. Actually, 12ths are pure, 5ths get progressively pure and wide (on center strings).So:

- “a more accentuated tuning curve” answers “what” Pre-form is

- “muting” or “center strings tuning” answer “how” I draw Chas Pre-form

Is it like in pitch-raising? No

Chas Pre-form is (beat wise) the tuning form I must draw for gaining Chas ET.

Posted 12/16/2009: From mid-section to the highest tones, I need to tune mid-strings at higher pitches, so that all check intervals, in those sections, will have a "preparatory" faster (wide intervals) beat rate progression.

...“I follow the paradigm (similar to Kent's article) to temper 4ths slightly wider than the tempered 5ths are narrow, proportional and progressive, not equal as you have it.”...

Careful. In my experience, only C3-F3 (4th) and C3-G3 (5th) have the same bps. I strongly suggest you to spend time for careful reading, before you need correcting yourself (takes longer).

...“It seems that when I do this, then apply a slight stretch to the octaves moving in each direction from the tempered section, there is no inversion of 5ths, they only beat slower as I move up the register - it simply does not invert any 4ths or 5ths above or below the tempered section.”...

Have you looked at the sequence? I set 5ths inversion together with A3-A4 and A3-D4 and E4-A4, right at the beginning. A3-E4 beats narrower than D4-A4.

...“In order for me to start to do what you suggest, I would have to make, for example, C3-F3 and C3-G3 have the same beat rate, between 1/2.5 and 1/3 bps - that is contrary to my novice training, and certainly not out of the realm of possibility to eventually add that method to my developing tool-box.”...

I get the same beat rate on C3-F3 and C3-G3 as a result, so only a reference point, not a starting point, at least in my personal way. I’ve never tried starting from there…but who knows?

...“I'll give it a try sometime and see what happens.”...

Let me know, a.c.
.

Thanks for sharing your own personal way when it comes to setting your intervals.

I am at the stage now in my tuning journey where developing a consistent tuning model (sequence of interval setting, sequence of checks, ensuring pin stability, with the intention of the piano producing a musical sound that satisfies my ear and enhances the customer's playing experience), is key...

...consequently, I've been paying close attention to setting the temperament using Bill's contiguous thirds and ET via Marpurg as the basis, and sticking pretty close to what Kent describes in his Every-Which-Way Temperament Sequence article - Thank you Kent and Bill!

At this early stage, the path I am on seems to be working pretty well, so at some point I will experiment with your method. I am just not that adroit to add a third method yet, but it is good to know there are many good sequences available such as yours.

Thank you for sharing your perspective and for sharing your time, Alfredo.

Glen

Glen,

I'm sure you are doing well, tuning wise. I've heard your recordings, very good indeed.

If you like a more severe comment, add recording of chromatic intervals (the main ones, including 12ths and 15ths), played slowly (3 secs each), up to the 8th octave.

One colleague of ours asked for a "short description, summarizing the CHAS method to focus the attention on the important principle, to understand the system more quickly." I post my reply here too, in case it may be of some help:

About the method, i.e. the tuning sequence, the principles are:

- the use of all intervals for an ET where all intervals are progressive
- the use of low partials beats for reducing iH's influence
- not counting but comparing beats (progressive and even beating ones)
- guessing only the first octave for eventually perfect it
- drawing a more accentuated stretch curve for compensating the piano's adjustements (let the piano get the form)
- inverting the beat rate progression of 5ths for eventually gaining even beating 12ths (narrow) and 15ths (wide) all along the keyboard.

About the system:

- the static zero-beating approach is replaced with "stable dynamism"
- zero-beating "pure" intervals do not equal "more consonant"
- beats return the strings partials qualities (energy), so giving character and tension (read colour) to each single interval
- no interval needs to be beat-less
- all intervals (all partials) can compromise for an optimum, resonant and stable beating whole
- flows of beats determine infinite sound atmospheres.

Using few words, Chas theory's approach is based on beats synchronism of only beating intervals, and synergy.

Soon I'll be writing about the string/pin/lever relation, as I think this may help controlling the effects of our tuning onto the piano's structure.

Regards, a.c.

Alfredo:

Several questions. The fourth one is really the point of this post.

1. When you speak of a preparatory tuning, do you mean what most American and Northern European tuners would call setting the bearing or setting the temperament, along with getting other notes close to the final form?

2. I'm starting to wonder if there is a separate tradition of Italian tuning and temperaments. Most of the temperaments I've examined come from Germany, France, England, and the U.S. Your terminology, and your love of metaphor, makes me wonder if Italy, or at least Sicily, has developed a parallel tradition. Who taught you to tune?

3. Was he or she in turn taught in a specific school or by a specific method that may have a name--something we could learn more about? Are there books by Italian tuners or theorists that you could point us to?

4. More specifically, I wonder about something that may seem cliched, and that I hope you will not find insulting: Is there is a tuning tradition in Italy that derives in part from accompanying singers, from bel canto? I ask this question because your playing, and tuning, have a vocal, singing quality. And your metaphor of the bow reminds me of a similar metaphor I've heard singers use when teaching about vocal projection.

Please understand that I am not not trying to flatter you by saying that your tuning sings. (But it does.) I'm instead trying to learn if there is a slightly separate Italian tradition, perhaps tied to opera and accompanying solo singers, that we can learn more about. (And I appreciate metaphors, but as Kent says, a written tuning sequence provides more precise information...)

I suspect that, behind all of this math and theory, there is
a love of singing, and a piano adapted to vocal performance. (I'm not trying to undermine your mathematical ideas--I'm praising the results, and curious to learn if the desired tone arises from a tradition.)

Thank you for your comments, Alfredo!

This past weekend, I had some extra time during one of my tunings in order experiment and learn better using some of your methods. Certainly, a wider octave stretch up the scale did contribute to the narrowed 5ths becoming more pure and the already wide 4ths becoming a bit wider. That was already happening somewhat. I found myself not wanting to have those 12ths go beyond pure above C6 or so. Perhaps it will require more practice or more stretch! Clearly, a console spinet will require a different (heavier) stretch than does a well-scaled grand piano.

Perhaps this weekend, time permitting, I will record those wider intervals (12ths) on another tuning on a grand and send them to you.

Pin and string setting are key components for me, as the stability of the tuning is accomplished there. I am wondering how the technique of pin/string setting in the unisons contributes to the string's (piano's) overall tone.

I am interested in learning more your experience(s)/method(s) in tuning unisons up and down the scale as a method of providing better tuning stability and maintaining interval widths as strings are brought up to pitch.

Single bass notes come last in the tuning for me, even after all the tri-chord unions are complete up to C8. Not sure why I do that, but it seems that the bass notes on a well-scaled piano contribute a great deal to the overall sound of the instrument. It might be that I do this to prevent stretching too much the bass, as I have had a tendency to hear a slight "roll" - (all that drama!)

BTW, I am a big fan of Kent's tuning sequences - a huge help for my speed and accuracy. Bill's ET via Marpug and progressive 3ds has been helpful as well.

Thank you, Alfredo. More tools for the toolbox for this novice!

Glen

Hi all, because, I did not get the point immediately, when Afredo says the 5ths invert, he talk of the 5 ths beats of course (not of intervals that enlarge above just).

Glen , the 12 th stay on the tempered side, the 5ths may get wider in the high treble but not in an audible way.

Yes above pure at C6 the 12ths are substracting something to the tuning. But it happens depending of the way we tune.

In ALfredo's method they are tuned pure above C5 (C6 ? it depends of the initial pitch I guess) on the middle string so to settle afterthat when unisons are done.

When enlarging the medium it allow to stay with tempered twelves more easily, it is done often .. managing the enlarging is what is difficult.

It took me some time to read that correctly.

Till next ..

P.S Jack , I don't believe there is a really different method from Italian tuners, what makes Alfredo is almost very classical in fact (nothing really out of comprehension, nor far from usual way to tune, I may say more sticking to the rules , in fact (with coherent progressiveness of all intervals).

When listening to it or seeing it done, nothing stick out as unusual (but each action is weighted).

Yes, I should have read his sequence more closely.(I was carried away by my own metaphor of a singing piano?)

If I understand correctly, the 12ths can't used as checks below A3, since checking on 3:1 would give wider M5's than are desired in the tenor and bass. Are there any other checks for the ranges below that point, using 12ths or other intervals?

Hi Glen,

you write:..."Certainly, a wider octave stretch up the scale did contribute to the narrowed 5ths becoming more pure and the already wide 4ths becoming a bit wider."...

I'd better underline that I talk about centre strings tuning. 5ths transit pure in between C5 and C6, but very faintly. Once I tune unisons, I keep 12ths (delta-narrow) and 15ths (delta-wide) as the correct form's reference. Those intervals will conferm whether my stretch evaluation on centre strings was right or not.

..."That was already happening somewhat. I found myself not wanting to have those 12ths go beyond pure above C6 or so."...

After unisons, if 12ths have gone behond pure (wide), the high register sounds sour (tart? acrid?), 10ths and 17ths are like too salty, too nervous, almost shouting.

..."Clearly, a console spinet will require a different (heavier) stretch than does a well-scaled grand piano."...

I know it is hard to believe but, maybe by referring to always the same low partials, I do not need different stretchings on small pianos, nor a different beat-net, except for mid-bass if the scaling is very poor.

..."Pin and string setting are key components for me, as the stability of the tuning is accomplished there. I am wondering how the technique of pin/string setting in the unisons contributes to the string's (piano's) overall tone."...

A great deal, that contribute is vaste. Like voicing, unisons build up the sound body, unisons determine the sound's consistency and duration, together with the sound colour. Pin setting too is foundamental, tuning's stability and pin block singing go with pin Vs string balanced opposition. Make sure that the string's tension is coherently distributed along the three sections of the string.

..."I am interested in learning more your experience(s)/method(s) in tuning unisons up and down the scale as a method of providing better tuning stability and maintaining interval widths as strings are brought up to pitch."...

You mean the order of tuning. Indeed I think that the bridge and sound-board can better adjust in that way, the changes in loading/tension are better spread out.

..."Single bass notes come last in the tuning for me, even after all the tri-chord unions are complete up to C8."...

For me too. But at that end, after the bass, I check all unisons and refine the 8th octave.

..."BTW, I am a big fan of Kent's tuning sequences - a huge help for my speed and accuracy. Bill's ET via Marpug and progressive 3ds has been helpful as well."...

Very good and thanks, I like your enthusiasm.

a.c.

.

Jake, all available intervals are checked, but in their primary beat, not by comparing beats of other intervals (hence not checking at different partial levels). for instance 5ths are listened for their 3:2 beat, not with a M6 M10 test (I know some will say it is the same !)

That is way quieter for the ear.
The idea also to check only intervals that follow each other and are not contiguous or in ladder, is easier, and install the tuner in close contact with the beat acceleration curves within the piano.

I have seen the method as being really closely in the "heart" of the subject at all times (assuming the final result wanted is understood)

I'll let Alfredo explain , so to avoid mistakes.


Because the process involves a good sence for beats speed (on one string) it may be used by beginners, they will probably learn more how to listen efficiently and understand what they have there

And when you finally have obtained a progressiveness of all beats while you did not use the usual test, you feel more confident (in the method and in your ability to realize it), that also is a good thing.


Isaac

My Bro's Raphaël Oleg (violonist) said that he liked your tuning, find it very smooth and gentle, while enlighted. (he asked if I had a grasp on the method, too..)

Jake, you ask:

...1. When you speak of a preparatory tuning, do you mean what most American and Northern European tuners would call setting the bearing or setting the temperament, along with getting other notes close to the final form?

The Pre-tuning sets the Pre-temperament, and I do not distinguish the traditional one-or-two octaves temperament from the whole keyboard's. In other words, the Pre-tuning is my (attempted) final tuning, but the piano gets the final form, i.e. the final 88 keys temperament, only when I unison. The piano's final form (where the piano will adjust) is what I have in mind when tuning centre strings, and the Pre-tuning stretch (on centre strings) needs to be a little sharper from C4 up.

...2. I'm starting to wonder if there is a separate tradition of Italian tuning and temperaments. Most of the temperaments I've examined come from Germany, France, England, and the U.S. Your terminology, and your love of metaphor, makes me wonder if Italy, or at least Sicily, has developed a parallel tradition. Who taught you to tune?

I do not think we have a separate tradition. I use metaphores in the hope to explain myself, but also because pianos issues like tension, stretch, energy and accuracy, are part of my (our?) dayly life. I was helped by two Italians and three Japanese top tuners, Otani sun, Saida sun, Osato sun.

...3. Was he or she in turn taught in a specific school or by a specific method that may have a name--something we could learn more about? Are there books by Italian tuners or theorists that you could point us to?

I think the Japanese ones may have got some hints from Germany. About Italian books, I can certainly point them to you if you wish, in the three I read I found the same mistakes about octaves and fifths, and no concern of what I'm describing.

...4. More specifically, I wonder about something that may seem cliched, and that I hope you will not find insulting: Is there is a tuning tradition in Italy that derives in part from accompanying singers, from bel canto? I ask this question because your playing, and tuning, have a vocal, singing quality. And your metaphor of the bow reminds me of a similar metaphor I've heard singers use when teaching about vocal projection.

For sure, in Italy there is a strong singing tradition. Opera singers from all over the world come to Italy for refining their technique. I like singing too but my in tune urge derives from my ear. So, I can only tell you about my family tradition, one orchestra director, one singer and many amatorial musicians.

Vocal projection has similar sounds issues: control and balancing of body tensions (piano structure), tone building (unisons), resonance of the head cavities (pin-block singing).

..."I suspect that, behind all of this math and theory, there is a love of singing, and a piano adapted to vocal performance."...

My case is a bit more extreme. I do like singing and I've got a bad desease: music in all its forms, and rhythms. When I compare beats I am on a rhythm-level, I'm there with all my intention while my ear is the supervisor.

..."(I'm not trying to undermine your mathematical ideas--I'm praising the results, and curious to learn if the desired tone arises from a tradition.)"...

Do not worry, I find you very polite. Thank you, a.c.

.

I have always used 12ths as a limit for stretch. As I am actually getting the use of the method and sequence Alfredo use, I am changing the way I consider that.
SO my answers can only be temporary !

The first octave enlarge very little, the beat begin very late. In my usual way, I let the piano and room acoustic decide of the width of that first octave (F3-F4) and check it with 6:3 4:2 with approx 1/3 bps at 4:2 level. But I have seenn and used more than that, up to 1/2 bps, and some concert tunings I've seen (a little extreme but very sonorous) had more than 1Bps. The beats are hiding in the spectra, they only push the resonance of the ocatve. If they are slow enough they couple after a little time, and the octave is heard as pure.

For what I know on a moderately stretched temperament octave all octaves toward up are highly stretched in the "standard" German Steinway concert tuning ("stretch to the max, but coherent") As much as the spectra of the piano can accept.

Hence those too vivid major harmonies in the 5th octave that can be heard in slow moves sometime.

Stretching on a well open medium lower the speed the RBI raises, and provide more global coherence.

The unison quality is more than part of the stretch in fact. their projection "push the spectra" more or less high depending of the way they are build. I wonder if we can call "opening of the unison" the fact that center string is related to the wanted justness, while the outer strings are dealing with the iH and are more or less in the high end of the spectra.

Coupling the partials, is not always allowing the fundamental to couple as soon, hence the opening of the tone.

In may usual way, I use a strong fundamental coupling that projects the whole spectra (attack tuning), then only I body the tone. (the sensation may be felt under the fingers)

That makes for 2 actions (and once coming from under) while coming from above at any time seemm more stable and keep the charging of the pinblock optimum.
At some moment the attack is also tuned, (taking the question from the opposite) it is because of the time needed for the coupling of the partials, it enlarge the attack time.

What I dont get is that I was believing that I acted on the first millisecond of tone, while there they are a consequence of the remaining, the tone is bodied from too open, if I get well the point. I may say that getting use to recognize the flow of energy within the string is a real shortcut to unisons, but the tone may be "wedged" afterthat, the other end of the spectra open. (as when correcting unisons on a concert piano).
I hope I'll get by with something more analytic after more tunings.

Hello Isaac,

I thank your Brother and you for reporting his comment. It will be meaningfull for me to also know whether he finds Chas Theory's approach (sections 2.0, 3.0) shareable or somehow obscure.

..."I have always used 12ths as a limit for stretch...I am changing the way I consider that."...

For stretch, I was used to evaluating RBIs and follow my ear for judging how much "salt" (stretch) wanting to add. Today I'm used to evaluating RBIs, add a little bit more salt in consideration of piano's dynamics, up untill I get the first 12th, A3-E5. There I get the Pre-tuning stretch's measure.

..."SO my answers can only be temporary !"...

This is grasping! Indeed a challenge, how can it be possible to grasp Time? Going along its version-in-version (O).

..."The first octave enlarge very little, the beat begin very late."...

Yes, the slow beat-rolling raises after almost 2 secs.

..."The beats are hiding in the spectra, they only push the resonance of the octave."...

Yes, nice way of describing it. All partials, in the octave intervals, want to sing. Or, the octave can sing and deliver all partial sounds in the natural order and the most lyrical way.

..."If they are slow enough they couple after a little time, and the octave is heard as pure."...

Yes, partials only need to be sung/displayed by the octave.

..."The unison quality is more than part of the stretch in fact. Their projection "push the spectra" more or less high depending of the way they are build."...

Yes, unisons can change the whole outcome.

..."I wonder if we can call "opening of the unison" the fact that center string is related to the wanted justness, while the outer strings are dealing with the iH and are more or less in the high end of the spectra."...

Open or close is in fact what we can do with the sound's body, by unisonsing.

..."Coupling the partials, is not always allowing the fundamental to couple as soon, hence the opening of the tone."...

Yes, like if partials were drained away.

..."In my usual way, I use a strong fundamental coupling that projects the whole spectra (attack tuning), then only I body the tone. (the sensation may be felt under the fingers)"...

I bear in mind two targets: sound duration and colour univocity all along the keyboard, wich I check using the "diabolus in musica": http://en.wikipedia.org/wiki/Tritone

..."That makes for 2 actions (and once coming from under) while coming from above at any time seemm more stable and keep the charging of the pinblock optimum.
At some moment the attack is also tuned, (taking the question from the opposite) it is because of the time needed for the coupling of the partials, it enlarge the attack time."...

From above is how I get unisons. Turn the pin clock-wise the right amount, charge the pin anticlock-wise just a little over, i.e. little little flat, release and accompany the pin on the desired point, the correct energy relation between the string's pulling and the pin's charge. As for centre strings, also the unisons must be the correct outcome of energy balance. BTW Isaac, do you play billiards?

..."I may say that getting use to recognize the flow of energy within the string is a real shortcut to unisons, but the tone may be "wedged" afterthat, the other end of the spectra open. (as when correcting unisons on a concert piano)."...

Oh, this last one, for once, I do not get what you mean!

Best regards, Alfredo.

.

Jake, you wrote:

..."If I understand correctly, the 12ths can't used as checks below A3, since checking on 3:1 would give wider M5's than are desired in the tenor and bass. Are there any other checks for the ranges below that point, using 12ths or other intervals?"...

Below A3, i.e. tuning G#3 and down, I use 4ths (wide, pro-slackening), 5ths (narrow, pro-slackening), 6ths (pro-slackening), octaves (pro-widening), and check 10ths (pro-slackening) and so on. From C3 down, Chas 4ths invert and get wider and wider.

Isaac, you write:

..."Because the process involves a good sence for beats speed (on one string) it may be used by beginners, they will probably learn more how to listen efficiently and understand what they have there."...

Too often I've seen tuners very much concerned with beats, fearing they would not hear them, fearing to turn their lever and depart from a point, where they had causally got, wich they may never find again. In my opinion, the whole approach needs to be different.

..."And when you finally have obtained a progressiveness of all beats while you did not use the usual test, you feel more confident (in the method and in your ability to realize it), that also is a good thing."...

You are right (O). Using normal tests, we try to check some sort of equal beating, true?

Now, what is more difficult, guessing equal beating or progressiveness of chromatic intervals? Are we better in detecting equality or diversity?

About equality, we may swear two beats are equal, while not perceiving the infinitesimal long-time difference. About diversity, if we hear two different beats, say one little faster than the second one, how many chances that we are wrong are there? And that we confuse slower with faster?

Even leaving tests and exposure to iH aside, in my opinion, guessing equal beating is a hard task, it opens to errors and the banal approximations + settlings are going to sum up.

So I'd say that comparative progressiveness may be the truest and most vivid confirmation that I'm gaining my favorite tuning, ops, Pre-tuning form.

Regards, a.c.

.

Isaac,

you were wondering about energy.

On this subject, I found of interest this reading:

http://en.wikipedia.org/wiki/Potential_energy

and the book example too: "When the book hits the floor this kinetic energy is converted into heat and sound by the impact."

Regards, a.c.

P.S.: http://fr.wikipedia.org/wiki/%C3%89nergie_potentielle

.

You may agree on one (O) foundamental factor : Relating Time or Timing.

I was a child when I was taught that every action demands its own time (do you know of any home-saying?). Only later on I could relate this principle to myself and to my actions result, depending on the object.

As for many situations now, also when I turn and charge a pin, I know I have to look for the best Time relation between what I do and how, and the effects of what I’m doing.

Many pins have their own reaction-time, each pin may demand its own time for me to charge it.

The time I spend for tightening the string, turning the pin clock-wise, from flat up to the spot and wide, it is also the time I need for "reading" the single pin’s behaviour and it may as well be the time the pin itself needs for re-adjusting its structure.


.

Alfredo:

I'm having some problems working with the Scala file for CHas in PianoTeq, partly because I'm still trying to understand CHas, and partly because I'm still trying to understand some of the intricacies of Scala:

1. I know that you don't set a separate bearing or temperament before tuning, but Scala requires that one start the tuning on one pitch. By default, that pitch is middle C. I'm not sure that's the best place to start. Would A3, the A below A=440, be a better place?

2. Does the s1 offset occur at each octave, or does it come at the start of each unit of 24 notes?

Thanks. (The Scala file that was posted on the PianoTeq site may be fine. I'm just having trouble believing that it was so easy for someone to create and get right the first time.)