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All:

When you think about "NIST traceable standards", the idea is to have something more accurate than what you can calibrate. So I agree with Kees. Since progressive M3s and M6s is easily definable yet apparently unatainable, it makes it a good standard.

Now the question is how unprogressive can they be and still be considered ET and not UT? The demonstrated tolerance seems to be +/- 3 semitones. (F-A might beat the same as G#-C but not A-C#). Or perhaps there would be a weighted average sort of thing. Like not more than 2 RBIs 3 semitones out of progression.

I would hate this to become what the PTG exam seems to be: a graded curve. It would be like "relative morality". But I don't know at what point an ET becomes a UT. The idea of Musically Significant Intervals comes up again...

Another recording. I think I got a lot closer... definitely need to work on getting those fifths more even though!

https://soundcloud.com/phil-dickson-1/yamaha-c110a-tuning

I don't understand why that is better "Apparently equal beating" is subjective. Apparent to whom?

As a preemptive strike: I don't know what "virtually equal" means either.

"Approximately equal to such and such tolerance" is honest terminology IMO.

Kees

Would "approximately equal beating" be OK, then?

But really, the M3/M6 test is redundant to progressive M3s and M6s. Like saying fence posts are 4ft apart and every other one is 8ft apart.

I agree. Before leaving the subject of the M3/M6 test let me mention that many unequal temperaments, ebvt3 specifically, also have M3/M6 tests but instead of being a whole tone apart at different intervals (e.g., semitone, m3) depending where you are in the scale.

Kees

I just dont get that

What is the "congruence" and/or "clarity" of a note? Those terms mean nothing to me. Can you give a specific example, say a chord, to clarify your concept?

Kees

The OP asks about a tuning standard, not a piano tuning standard, though that is likely what he meant. It is rare for large groups of pianos to be played together. Orchestras, however, do this regularly. Defining a tuning standard based on some progression of M3/M6 intervals is not likely to help the bassoonist play "in tune". Does the OP hope that some particular temperament scheme will be selected as the universal standard for all performing groups where a bassoonist can play an ascending scale in any key and know that it will be in tune with the cellist?

Here you go. There are a few instances where I can neither hear not see any beats.

M3

C#3F 5.1
DF# 5.5
D#G 7.0 (beats very faint)
EG# 6.5
FA 6.6
F#A# 7.2
GB 7.6
G#C 8.8
AC# 9.0
A#D 9.4
BD# 8.4
CE 10.5 (beats very faint)
C#F 11.2
DF# 12.0
D#G 12.1
EG# 13.8
F4A 14.1

M6

C#3A# (can see no beats)
DB 7.2
D#C 7.5
EC# 7.6
FD 7.7
F#D# 8.2
GE 8.6
G#F 9.5
AF# 10.4
A#G 10.5
BG# 10.3
C4A (can see no beats)

Kees

Individual notes are reinforced by the amount of partials they trigger up and down.
I suggested slow beating intervals are more effectively doing so. (then FBI also but they are higher in the partial range and are less active for that part of the job...

I suppose the recording and concert industries are the main keepers of what standard there is. We are flexible, though, given the right circumstances.
I was talking with a colleague who understands UT's and had tuned a piano in Kirnberger lll for a modern piano concerto that specified Kirnberger lll. The pianists' only comment was that the piano didn't sound out of tune enough!!! After a good laugh, we discussed it more seriously. I wonder If this typifies the real underlying thinking of pianists in this matter?

Yes, as the ear is not accustomed, the effect can turn to be too addictive and common musical sense lost at some point.

(Better keep it, be it because the vast majority of listeners are accustomed to hear more evenness than "out of tuness")

I for one just believe that the tuning on piano does not need so much "acoustically pure" intervals to go to the point any "out of tuness" is really noticed.

Now if it is the goal is to play an old instrument with a less even tone, more variations are probably allowed.

While looking for that old recording of Nelson Freire at 13 , I find that one at 20, in 1969 (let you do the math guys, if of some interest
F#major Chopin barcarolle (dedicated to Mr Stockhausen - was not the same you think about guys )

I would call that "French style" of tuning. Hear that enough to recognize some characteristics. Unfortunately even after 30 years tuning I cannot link that to any particular method or temperament.
(The Steinways where different at that era, also..)
[video:youtube]q-xNeRG_KU4[/video]


P.S food for though : the F3 F4 ladder of M3 is long time used in France, and was known as "Pleyel temperament", while I cannot put a date on it unfortunately.
That probably accounted for some evenness in tuning.

I like that one, for instance :

[video:youtube]-1s8IapSY-A[/video]

But in that other recording, the piano is just out of tune, to me :
[video:youtube]50IluxYCUY8[/video]

While the Bach Busoni sound nice, many other pieces are just sounding uncomfortable to me.

The second recording has a lot of flutter.

Yes , that may influence pitches indeed.

But unison also are terrible , I am talking justness, nowadays.

Not much "advantage" the pianist can use while playing, I mean... considering this he does very well.

the 4th F- C is extremly large while C3 C4 is large too (could it be a C3 C4 based temperament ?) I guess so, with a pure FC 5ths somewhere in the scale (reported to the basses it is clearly noticed)

Got the concept. Are you trying to maximize or minimize that reinforcing effect? As a player of mainly contrapuntal music I would like to minimize it. How does that prevent you from having progressive M3/6's?


Kees

I'd like to give a precise answer to that.

I use the amount of consonance at the individual note level to decide where my octave or unison is good but it works also for 5 ths.

I do not believe it prevent me of reducing the progressiveness of FBI, unless I do not strive for that as an absolute priority , as I did recently.

I am more interested to keep some congruence in the 5ths, meaning if I have a slight difference of warmness for one, I like to find the same along the scale.

BTW I do not see why it would be a trouble to contrapuntal music to have the individual notes enhanced by others. It gives the tone more presence, does not seem to lower the musicality, on the contrary it allow the pitch perception to happen sooner in the tone (crispness of the attack), so it may help to shape the voices. (on the acoustical part of things)

the 5ths can be tempered well and have some slight difference in venue, seem to me, that may be interesting, particularly if it is also something that is within the natural spectra of the piano.

I believe that the sort of phantom note that we hear in the 5 th upper note , due to the difference between the 2 fundamental pitches, is a part of what I hear as the 5th characteristic.

It mixes with the 3:2 beat and the 5th begin to be more interesting .

I feel the permanent raising of speed in fast beating intervals easily induce a sense of permanent tension, it is not so easy to have at the same time quietness and that raising tension that push the ear toward the treble. One need excellent instruments.

Pianists seem to like the way the enhanced unison make the piano sing. This is so strong it hide the inbalances that would strike the ear if the tone was more dull.

It is mostly based on the 12- 15 balance and CHAS style shape, while the imbalances in the tempering make chord differences more present, avoid too much predictability. That allow to go a little farther in direction of acoustically pure, without being obliged to attain it.
I hardly can obtain a mean to control that, at the moment. WHat I know is that I can avoid intervals sounding too badly, without making too much corrections., Just tuning where I feel the pitch is right and listening to the answer from the rest of the piano.
This is then absolutely linked to any flaws in my listening.

Musical behavior is not granted by an absolutely even progression of FBI, I mean, use an ETD with fixed curve, and you have something that sound tuned, but does not sound so much right.

The "answer" from the notes of the partial scale is so strong it allows to have good double and triple octave and even more, without the need to check them. I trained to listen to the strength of the coupling when I tune a new string, this does not give absolute justness, but it is abig help.

There is a certain amount of progressiveness, its curve shape is not too steep nor too straight

Hi Kees,

There I was replying to Isaac. As a standard, I would propose Chas as the (theoretical) "optimum" and non-beating 12ths as the ante-room (does that word exist?), say something that we can check easly, provided we get non-beating 12ths by establishing progressive RBI's and SBI's. In order to do that, you need to invert 4ths and fifhts.

Hi Jeff,

I do not have time to quote your post, where you were mentioning "breaks"; on top of having to "see" a whole_form, I would like you to check one more "scaling" factor, namely how you set the picth in relation to the pin and the string's tension. In my experience, the partials scaling (leave the piano scaling aside) may variate significantly... to the point that pin/string setting might be the problem, more than the piano scaling itself. You would focus on progressive 6ths, but a 6th is... a 4th plus a M3.

Hi Isaac,

I could only listen to the first recording you posted today, French tuning or whatever... that piano could sound better :-)

Hi Phil,

I only looked at Kees' numbers, it seems you have done a very good job. Do you have discretional access to a piano, in London?

Regards, a.c.
.

Ciao Isaac,

I too feel like wanting to understand your priorities.

..."I use the amount of consonance at the individual note level to decide where my octave or unison is good but it works also for 5 ths."...

Do you mean that you go along your musical ear and sense of "in tune"? That you let your ear "drive" you, more than considering beats?

..."I do not believe it prevent me of reducing the progressiveness of FBI, unless I do not strive for that as an absolute priority , as I did recently."...

Do you mean that your ear calls for progressive FBI's? Or..., for you progressive FBI's are not the "absolute priority"?

..."I am more interested to keep some congruence in the 5ths, meaning if I have a slight difference of warmness for one, I like to find the same along the scale."...

I like how you describe intervals, I think I am more simplistic... If I consider a fifth on its own, say A3-E4, it could sound beatless or have a (narrow) 0.5 bps and my ear may still accept that; though with other notes it would become a problem. What makes a fifth warmer for you, does it mean purer or narrower?

..."BTW I do not see why it would be a trouble to contrapuntal music to have the individual notes enhanced by others. It gives the tone more presence, does not seem to lower the musicality, on the contrary it allow the pitch perception to happen sooner in the tone (crispness of the attack), so it may help to shape the voices. (on the acoustical part of things)"...

Well, I do not know what Kees meant.

..."the 5ths can be tempered well and have some slight difference in venue, seem to me, that may be interesting, particularly if it is also something that is within the natural spectra of the piano."...

Yes, I think I get what you mean, but "that" particular 5th will also have to work as any other interval, so... what is (where do you find) the leeway?

..."I believe that the sort of phantom note that we hear in the 5 th upper note , due to the difference between the 2 fundamental pitches, is a part of what I hear as the 5th characteristic."...

That may well be, and I look forward to experiencing that.

Hmmm... I have to postpone the second half.

Have a nice Sunday,

Alfredo

Thanks Isaac for that explanation.

Am I correct in assuming voicing is also part of your process of what you call "congruence"? In other words, do you consider "tuning" and "voicing" not as completely distinct processes?

I have always wondered why proponents of UT do not also advocate unequal voicing. For example the baroque flute has very unequal voicing as accidentals are handled with forked fingerings, hence difference keys have their own character, independently of the tuning. The modern flute equalized all that with all those keys.

Anyways, with such an artistic approach to tuning as you seem to advocate, having a standard for tuning would be like having a standard for playing Bach.

Kees

Hi Ian, good question.

Perhaps the first distinction is to be made between the 12-Tones ET and one ET amongst modern ET models.

I would discard the well known 12TET (12 root of two) in that it is of no use at all, not really (or not only) because of inharmonicity, but because (in theory) it doubles all beat-rates every other octave, and because in practice a zero-beating octave does not exist.

Modern ET's include "pure fifths" (proposed by Serge Cordier), which encompasses 7 tones, "pure 12ths" (proposed by Bernhard Stopper), which includes 19 tones, and Chas which encompasses 24 tones.

We might decide to go for one of these ET's, in which case - for obvious reasons - we would need to add the respective theoretical constraints.

Chas represents an exception: when it comes to aiming at the target into practice, it suggests the tuning of a sharper curve, which ever curve we may need in order to counter-balance (anticipate?) hysteresis.

Other requirements might be needed, in consideration of specific interval beat-curves, I do not know if you were also asking about that.

Best wishes,

Alfredo