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Alfredo:

In another Topic you posted ”I'd better precise: 4ths beat very much in the bass, progressive slowering up to C3 and progressive fastening, going up. At C5 4ths collaps. 5ths go the way you say, "fastest in the middle of the piano and slower to the ends". Actually, at the ends 5ths sound pure, this gives you an idea of how slow they beat, of how little they can be narrow. But in Pre-tuning (centre string), high 5ths get wide.

OK, I seem to have misunderstood the beat rate progression of the 4ths and 5ths when you tune. This makes much more sense. When 4ths get slower, 5ths must get faster and visa versa. And the faster the 4ths are in relation to the 5ths, the wider the octave type. So the progression of 4ths and 5ths indicate the widest octave type at the ends and the narrowest in the middle.

This type of tuning is inconsistent with equal beating 12ths and 15ths which call for a general narrowing of the octave type while going up in the treble. But then, if I understand you correctly, this is the “Chas Preparatory Tuning” which when after the unisons are tuned, produces equal beating 12ths and 15ths. I did make a post a while ago about a possible explanation for how the tuning could change when tuning unison, but since I have never experienced this I am going to continue to consider this to be an “Indulgent Mystery.”

Ohi Jeff, good news.

..."When 4ths get slower, 5ths must get faster and visa versa."...

Yes, From the bass up to C3. Here, 4ths get faster and 5ths too continue to get faster up to A3-E4. I'm glad if you get this and I apologize if my English was not correct.

you write:..."This type of tuning is inconsistent with equal beating 12ths and 15ths which call for a general narrowing of the octave type while going up in the treble."...

Actually, Prepare-Chas octaves are S shaped, so 5ths from the bass can go narrower up to mid-range, then invert and go less and less narrow.

..."But then, if I understand you correctly, this is the “Chas Preparatory Tuning” which when after the unisons are tuned, produces equal beating 12ths and 15ths."...

Yes.

..."I did make a post a while ago about a possible explanation for how the tuning could change when tuning unison,"...

Sorry... maybe if I had read that.

..."but since I have never experienced this I am going to continue to consider this to be an “Indulgent Mystery.”"...

Wait Jeff. The "Indulgent Mystery" may be how ET octaves can not be progressive and how ET 12ths and 15ths can routinely (and out of rule) be inverted in the high register, i.e. what has been repeatedly written in Chas main Topic.

Also an "Indulgent Mystery" may be how 4ths and 5ths should be tuned when tempering what ever ET temperament-module, and down C3, where I'm stating that Chas 4ths invert.

Anyway, today I think I was told about quasi-ET, so for me it is not really a mystery anymore. If I may suggest, do experience the Prepare-Tuning.

a.c.

Alfredo:

Look at my post on 21.12.09, this Topic.

"S-shaped octaves" do not tell me much. But saying if the fifths become wide of just intonation does. Do the fifths become wide of just intonation or not???? Some of your posts seem to say one thing and some another. If the fifths become just, then the 12ths are wide of just unless only some octaves are narrow which would then mean that it is probably not ET.

And I am the one that gets to choose what I consider to be an "Indulgent Mystery."

http://home.broadpark.no/~rbrekne/beats.html

Have an ear at what is presented as correctly tuned beat rates for 3 octaves C-4-5 played together :
http://home.broadpark.no/~rbrekne/sounds/coctpart.mp3

(This is just an aside\interruption, but one that I hope I can make here for the people who are experimenting with Pianoteq. It's available at an academic discount--if you are affiliated with a school or university, there's a different pricing scale. I don't know what the adjustment is. There's a form to fill out at http://www.pianoteq.com/faq?pianoteq=e76fed63871b9bef6603314640867334 . I'm not part of Modartt, by the way. Just a user and fan. The program seems to be a natural match for these discussions. Cheers.)

Jeff, you ask:

..."Do the fifths become wide of just intonation or not?"...

Yes, on centre strings Pre-Tuning, very slowly-progressive wide. But after unisons you want 5ths to sound just.

Then, it is better to distinguish what may be needed for the piano to release Chas, from what Chas Form is, which is the point of this thread.

Whether Chas theory can be conventionally said to be ET I'd say yes, since all semitones are numerically equal in size. And in practice too, RBI are "ET" progressive.

For tuning this ET you may start following some "technical" instructions, even if in bits and peaces.

..."And I am the one that gets to choose what I consider to be an "Indulgent Mystery."...

Ok, but since it is a patent, you'll have to correspond the partials rights, 3 and 4, all together US $7.00.

- . - . - . -

...People who are experimenting with Pianoteq. It's available at an academic discount--if you are affiliated with a school or university, there's a different pricing scale.

Thanks Jake for this information and for the link above.

Regards, a.c.

Alfredo:

”Ok, but since it is a patent, you'll have to correspond the partials rights, 3 and 4, all together US $7.00.”

I will gladly pay your price for the patent rights on the term “Indulgent Mystery” next time I am in Augusta Bay. Perhaps in liquid refreshment at one of the cafes I fondly remember?

I'm still trying to learn more about the unison technique. I know that you and Kamin have explained it, and that it has a history. I'm sorry if I seem to be asking the same question several times, but:

1. If the unisons are pitched very slightly higher, so that they have partials that beat equally with partials on the center string, is their fundamental also beating against the fundamental of the center string?

2. Assuming that the answer is yes, is the perceived pitch of the "note" raised to the pitch half-way between the pitch of the center string and the pitches (which may differ) of the unisons? Which means that the perceived pitch emerges from the beating fundamentals and partials of the three strings.

3. Is it thus true to say that, in this method of tuning, there is no one string in the trichord that, if plucked, would be at the same pitch as the pitch heard when all three strings are played together?

4. The 12'ths are slightly flat across the keyboard, if I understand correctly. Should they, after the unisons are tuned in this way, be heard as just? Should some of them, at least, such as above A440?

5.Are the two outer strings usually in unison with one another (as just as possible), or are they pitched to beat with different partials on the center string. Or does this vary, according to the piano and overall tone desired?

Thanks Alfredo and Kamin. Love the sound of the pianos.

Jake:

I know your questions are to Alfredo and Isaac, but perhaps I can give another view point.

If any one partial of two strings in a unison are at the same frequency, then all the partials of the two strings of the unison are at the same frequency. This is because the strings have the same physical characteristics, and should have the same inharmonicity.

But when two or more strings of a unison are not at the same frequency when played separately, but very close, when they are played together they can "couple" or "pull' each other into vibrating in phase and at the same frequency. This can give a certain color to the tone, especially at the attack when the coupling takes place. And since the piano is really a percussion instrument the mind remembers this color and attributes it to the decay portion of the sound as well.

Jeff, good that you took me back to that post of yours.

You wrote:..."I understand that measurements of frequencies of single strings have been compared to a tuned unison with all three strings sounding together."...

Actually, beats have been compared, not frequencies. I've observed the effects of my unisoning on beats, in different registers.

..."A drop in pitch has been observed."...

Yes, like when you do voicing, in any range. Check yourself: compare a 5th (or an octave), say C5-G5, tune pure on centre strings, then unison and listen to your 5th. Is it still pure?

..."But since a higher partial is measured, I am not sure if it is the fundamental frequency that changes or if it is the effective iH of the strings that change"...

Indeed, when I unison I reinforce the pitch of the centre string. As I've explained, I go for a beam, made up by the mid-string's foundamental and its 2nd partial, gained with the outer strings outcome. In a way, the outer string can syntethize the centre string's pitch, i.e. foundamental + partials. Then, I'd say that both the foundamental frencency and the iH of the strings change.

..."and therefore the frequency of the partials and the beat rate of the tuning intervals."...

It may as well be the strengh/precense of the partials and the overall pitch.

..."This effect is an argument for tuning unisons as you go and for adding a bit of extra stretch when tuning an octave so that when the other strings of the unison are tuned the pitch will settle where it belongs."...

Yes, the pitch has to settle where it belongs, beat-wise.

..."Perhaps this is what you are experiencing rather than the piano’s tension equalizing."...

I talk about piano settlings, considering the sum of those two factors (plus the strings adjustements on their three lenghts). Increasing the string's tension involves the change of loading onto the bridge, maybe very very little but for me and Chas form it is still meaningfull. I need to control unisoning effects on closed notes too.

Fine and coherent voicing solves most problems related to the partials outcome. Thinking of a sound, can coherent timbre proportion the relevance and presence of partials? How would that effect your tuning?

a.c.

EDIT: more has been posted, I'll hopefully reply this evening.

"How would that effect your tuning?"

For the typical middle aged consoles and the old aged uprights, which is about all that I tune, not a bit. I concentrate mostly on stability and general octave stretch. The hammers are rarely in any condition to worry about tuning tone into the unisons. I just mention these things because others are also interested, not that I have much of an opportunity to use them.

But really, I don't know what you are babbling about, and please don't try to explain.

Hi Jake, you write:

..."1. If the unisons are pitched very slightly higher, so that they have partials that beat equally with partials on the center string, is their fundamental also beating against the fundamental of the center string?"...

You might have read my previous post about unisons.

Anyway, I've not mesured the partials of an outer string, after my unisoning, and compared with the partials of the centre string yet. This may answer your question.

Jeff's statement that if one partial meets, then all partials should meet, may be true in theory. In my opinion each real string has its own "irrational" story. What I know for sure is that I can reinforce the centre string's pitch, by gaining the 2nd partial of the centre string.

In other words, in the unison there is a very precise point where you hear the foundamental and its 2nd partial, the latter going absolutely straight, like if it was surfing on the foundamental. That beam gains the longest sustain.

..."2. Assuming that the answer is yes, is the perceived pitch of the "note" raised to the pitch half-way between the pitch of the center string and the pitches (which may differ) of the unisons?...

Half-way, I do not know. Generally, those unisons raise the pitch.

..."Which means that the perceived pitch emerges from the beating fundamentals and partials of the three strings."...

Definitely, the perceived pitch emerges from the fundamentals and partials of the three strings, it emerges from what is beating and what is not.

..."3. Is it thus true to say that, in this method of tuning, there is no one string in the trichord that, if plucked, would be at the same pitch as the pitch heard when all three strings are played together?"...

True. There is a sum-effect that raises the pitch of the whole trichord. Take this with a POS, as it comes only from my empirical, aural survey.

..."4. The 12'ths are slightly flat across the keyboard, if I understand correctly."...

Correct. Delta-flat all across the keyboard.

..."Should they (12ths), after the unisons are tuned in this way, be heard as just? Should some of them, at least, such as above A440?"

No, after the unisons are tuned, all 12ths must be heard delta-flat.

..."5. Are the two outer strings usually in unison with one another (as just as possible), or are they pitched to beat with different partials on the center string."...

I tune them to that beam, and I've never checked outer strings one another.

..."Or does this vary, according to the piano and overall tone desired?"...

In my tuning, I happen to pitch with different partials on bichords, or grands trichord, when I find odd strings.

..."I'm sorry if I seem to be asking the same question several times"...

You are welcome. a.c.

Thank you, Alfredo. I hope you do understand that I'm asking these questions about the unisons because I like the sound of the tuning so much.

Please dont quit, Jeff, the fact that you have to tune less than first grade instruments does not mean you cant benefit of that raised harmony. In fact I just believe the opposite, it may well give you some fun, as even uninteresting pianos get something with Chas.

The method with the felt mute and "preparatory tuning is a very good one, if you ever use a EDT you can see very easily how the strings settle and the pitch change when you are going thru the scale (unisons tuned or not).

The way you are yet tuning makes me think that you ar yet using some "auto settling" property of the tuning (be it with th 5th s or with the 12the, the instrument seem to find its correct place when it is pushed in the good direction, then tuning Chas means only using RBI to have more precision or evenness, the raised resonance put you more easily than expected in the correct pitch region.

The emphasis of 2nd partial is a help for resonance, it is just a way to listen that allow you to thicken the tone without using beats in unison (just a coupling question, to me).

I suggest you experiment on the relations of the 2nd inversion of the minor chord with the double octave of the second note. You may find some interesting thing....

Besty regards

To Jeff

I recorded ..

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

There you have an idea on how the beat rates are progressing, tuned on one string, and how the top note can be tuned only in the resonance of the octave, and fall in place well.

It is quiet to listen, even on a small vertical (but one need to have a thin enough strip mute there, to mute up to C6)

The piano is a120 cm vertical, good tone, Ciresa soundboard. I will record the job on a bad piano someday...

I've been making notes about tuning to CHas (an actual tuning, as opposed to the model), trying to create a list of general requirements. This list is just meant to recapitulate what I've gathered. Corrections and additions would be appreciated:

1. The bearing is set over two octaves. (NO: See below.)
2. The intervals of the two octaves are divided up equally, (NO: See below.)as much as possible, although of course iH on some pianos may require repitching some notes slightly.
3. The lowest possible partials are listened to when checking beat rates:
octaves at 2:1 , doubles at 4:1, 12ths at 3:1 ; 5ths at 3:2 not using the checks that compare 2 fast beating intervals, as the M6 M17th to check the 12th size.
4. Double octaves and 12ths beat equally.
5. Double octaves are very slightly wide.
6. 12ths are very slightly narrow from A4 to the top. (NO: See below.)
7. Octaves beat very slightly wider as they move to each end of the keyboard. (NO: See below.)
8. But the 12th's remain slightly narrow from A4 to the top. Moving towards the bass, they widen. (NO: See below.)
9. M5's become just or nearly just in the upper regions.
10. 4ths become more narrow as they approach the top. (Not exactly: See below. They become less wide.)
11. Unisons are often very slightly wide to reinforce the 2nd partial.
12. Resonance is to be preferred to power: Although the bearing\temperament octave (three octaves in CHas) is slightly wide of theoretical ET, the upper keyboard is often "milder," than many contemporary ET's, since lower partials are listened to for beats. (Partly right. See below.)

Hi Jake, thanks for this list, a valid contribute. Since I do not know how to control the editing, I'll write some CORRECTIONS/ADDITIONS with capital letters.

..."I've been making notes about tuning to CHas (an actual tuning, as opposed to the model), trying to create a list of general requirements. This list is just meant to recapitulate what I've gathered. Corrections and additions would be appreciated:

1. The bearing is set over THREE OR MORE octaves (FROM C6 DOWN TO STRINGS CROSSING, ON CENTRE STRINGS).
2. The intervals OF THESE octaves are divided up equally, as much as possible, although of course iH on some pianos may require repitching some notes slightly.
3. The lowest possible partials are listened to when checking beat rates:
octaves at 2:1 , doubles at 4:1, 12ths at 3:1 ; 5ths at 3:2 not using the checks that compare 2 fast beating intervals, as the M6 M17th to check the 12th size.
4. Double octaves and 12ths beat equally.
5. Double octaves are very slightly wide, CONSTANT ALL ALONG THE KEYBOARD.
6. 12ths are very slightly narrow, CONSTANT ALL ALONG THE KEYBOARD .
7. Octaves beat very slightly (PROGRESSIVE) wider as they move to each end of the keyboard.
8. But the 12th's remain slightly narrow, AND CONSTANT ALL ALONG THE KEYBOARD
9. M5's become PROGRESSIVELY just or nearly just in the upper regions.
10. 4ths become LESS WIDE as they approach C3.
11. Unisons are PREFERABLY very slightly wide to reinforce the 2nd partial.
12.(SUSTAIN) Resonance is to be preferred to (ATTACK) power: Although the bearing\temperament octave (THREE+ octaves in CHas) is slightly wide of theoretical ET, the upper keyboard is often "milder," than many contemporary ET's, since lower partials are listened to for beats."

- . - . - . -

I do not know if Point 12 is correct. I could say … “Although the bearing\temperament octave (THREE+ octaves in CHas) is slightly wide of theoretical (historical?) ET, the upper keyboard is often "milder," than many (?) (there seem to be two, Cordier's and Stopper's) THEORETICAL contemporary ET's, since the Chas octave is less stretched.”

Unfortunally, I do not know which partials would Cordier or Stopper listen to, I could not get their aural tuning sequence either.

Regards, a.c.

Hi Alfredo,
I attempted implementing your above techniques as closely as possible during my tunings on Saturday on both upright and grand pianos.

The most difficult part I found was controlling the openness of the unisons against the openness of stretch I chose for the octaves up the register.

The bearing section I expanded was C3-C4, using A-440 as the mark. Normally, I use F3-A4.

After the tunings, I played several different pieces of music and on each different piano, the salesman in charge of the showroom commented very positively, that he liked it. Because I had been using a different method, CHAS felt different, sounded different. When I was at the piano playing, it sounded in-tune, but loose to me. When I was at the other end of the showroom and the salesman was playing - the tuning sounded very lively, pure and most of all, musical and resonant - a whole piano sound, not just intervals strung together (which as a novice tuner I've been consumed with)

My preference is for a slightly tighter sound, but this method allows me to experiment with the piano's "whole sound", rather than simply listening to intervals. I still check outside 6ths against inside 3ds, then a quick check of 10ths and 17ths up the register as it pertains evenness of the stretch. The precise evenness of beat progression up the register is sometimes altered by the piano itself, I suppose inHarmonicity, false beats, and lack of experience on my part, are the culprits.

Did you receive my tuning sample with checks? Thanks for the descriptions of your methods.

Glen

Many thanks, Alfredo.

Hi Glen,

I'm glad for your positive feedback. And your approach, trying different techniques, can only open to the best for all of us.

Though my tuning routine is related to strings loadings onto the bridge, I do not think it is a must. What is important is to know what to go for and why.

For instance, the little variations in loadings could be evaluated in other ways, depending on your idea of the sound-board's elasticity or your strings and structure settlings technique. My evaluation is not proposed as the best.

..."The most difficult part I found was controlling the openness of the unisons against the openness of stretch I chose for the octaves up the register."...

Unisons raise the pitch, but the increase in strings tension does load more onto the bridge, so eventually experience will help.

..."The bearing section I expanded was C3-C4, using A-440 as the mark. Normally, I use F3-A4."...

Did you mean C3-A4?

..."After the tunings, I played several different pieces of music and on each different piano, the salesman in charge of the showroom commented very positively, that he liked it. Because I had been using a different method, CHAS felt different, sounded different."...

Still today I'm surprised by the effects of this beating form, both for the "in tune" feeling and the resonance power. A small piano too gains so much brightness and volume, like if it was double in lenth.

.."My preference is for a slightly tighter sound, but this method allows me to experiment with the piano's "whole sound", rather than simply listening to intervals."...

Yes, the whole sound is relevant. Today I do not make a distinction between the first temperament-octave and the whole keyboard.

..."The precise evenness of beat progression up the register is sometimes altered by the piano itself, I suppose inHarmonicity, false beats, and lack of experience on my part, are the culprits."...

If you are tuning with beats, do not submit to iH. You'll be able to lay down your favorite tuning form by imposing beats coherence for all intervals.

..."Did you receive my tuning sample with checks? Thanks for the descriptions of your methods."...

I did receive your samples and listened to them. Progressions can be improved, but they are already good standard. One point: when you check the intervals progression go slowly and regularly, do not change the choromatic sequence's rhythm, you risk to confuse the increasing (or decreasing) beat rate you want, with your increasing (or decreasing) playing rhythm.

Our tendency (O) is to hear what we would like to hear, being sort of "generous" with ourselves. If you can, be severe and always ready and willing to perfect your Real beat hearing. Choromatic 12ths are easy to evaluate, and vivid and reliable too.

Let us know. a.c.