I may be mistaken, but I get the impression from the meantone topic that there are those who use stretched octaves in harpsichords, unless I have just read things all wrong. I am, to say the least, very surprised about this. I have never seen (or rather, heard!) the need to do this on any instrument I have encountered.
I have always thought that although there is naturally a small degree of inharmonicity in harpsichord strings, that it is never enough to force stretched octaves.
Discuss!
| andro Andrew Bernard
September 14 |
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I may be mistaken, but I get the impression from the meantone topic that there are those who use stretched octaves in harpsichords, unless I have just read things all wrong. I am, to say the least, very surprised about this. I have never seen (or rather, heard!) the need to do this on any instrument I have encountered.
I have always thought that although there is naturally a small degree of inharmonicity in harpsichord strings, that it is never enough to force stretched octaves.
According to Michel Corrette, Le maître de clavecin:
‘For the greater perfection in tuning the harpsichord one must keep the octaves of the upper notes a little sharper [wider] than the others and the opposite for the ravalemens below, although this should be imperceptible.’
Translation after Edgar Hunt, ‘Corrette on Stringing & Tuning’, English Harpsichord Magazine vol. 2 no. 5, 1979.
Michel Corrette, Le maître de clavecin pour l’accompagnement: méthode théorique et pratique. Author, Paris, 1752, 1753, 1775.
Reprints Georg Olms Verlag, Hildesheim, 1974. Minkoff, Genève, 1976, 130 pages. Broude Brothers, New York, 1976.
See also Michel Corrette, De la manière d’accorder le clavecin et l’orgue. Paris, 1753.
Sharper but imperceptible? I’m not convinced. That sounds like a contradiction to me. If imperceptible you can’t hear it, so how do you tune something you can’t hear? [Perhaps a poor translation?]
By this logic every interval is stretched, not just octaves.
I am referring to what I thought stretching is which is perceptible sharpening of the octave interval. Isn’t this what piano tuners do? @EdS would be the man to say.
September 14 |
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Sharper but imperceptible? I’m not convinced. That sounds like a contradiction to me. If imperceptible you can’t hear it, so how do you tune something you can’t hear? [Perhaps a poor translation?]
This is what Michel Corrette published (Le maître de clavecin pour l’accompagnement: méthode théorique et pratique. Author, Paris, 1753, p. 85):
‘Pour la grande perfection de l’accord du clavecín il faut tenir les octaves de dessus un peu plus fermes que les autres[,] le contraire pour les ravalemens d’en bas, mais que cela soit imperceptible, ceque les hábiles facteurs observent très bien.’
This hinges on the intended meaning of fermes. Does it connote firmness or, as in the modern fermées, closedness? (The translation ‘sharper’ came from Hunt (1979).)
Unfortunately, in five pages devoted to tuning the harpsichord, in which temperament might modifier, diminuer or modifier intervals, and intervals are variously described as diminué, juste, plus forte, trop forte, and foible, Corrette does not use plus fermes again.
Le 14/09/2023 14:28, Lewis Jones via The Jackrail écrit :
‘Pour la grande perfection de l’accord du clavecín il faut tenir les octaves de dessus un peu plus fermes que les autres[,] le contraire pour les ravalemens d’en bas, mais que cela soit imperceptible, ceque les hábiles facteurs observent très bien.’
This hinges on the intended meaning offermes. Does it connote firmness or, as in the modern fermées, closedness? (The translation ‘sharper’ came from Hunt (1979).)
If this means octave stretching in the treble (and I think this is most
likely the meaning of “fermes”), then it also implies octave shrinking
in the bass, which is rather surprising.
If “fermes” means “closed”, i.e. shrinked, narrow, this implies octave in the bass more “open”, wider. This would be in accordance with octave stretching in the bass, no?
“Fermes” is not “fermés”
It means “firm”. It implies more energy. That means somewhat sharper, but not to the point of being higher, noticeable.
In the low register, he says it should be the opposite : it means the low notes should be on the slack side, on the lower edge.
Le 14/09/2023 18:45, Martin Gester via The Jackrail écrit :
In the low register, he says it should be the opposite : it means the low notes should be on the slack side, on the lower edge.
So, the octaves are imperceptibly stretched in the treble and the bass.
I fully agree with Dennis. With some details: it is true that Corrette advocated a minimum of octave stretching in the treble, but his advice is too late to influence the tuning in the heyday of the harpsichord c.<1755.
Also, although arguably in the extreme treble the ratio diameter to length is greater and therefore the worsening of the “perfect string”, the offending harmonics are so high that are mostly part of the “formant” and will not be heard as offending.
This said, testing octaves, by fifths and fourths as suggeted by Bradley or by using other intervals, (in my U.T. book I suggest checking octaves and unisons in two-manual instruments), are mainly for use in the extreme bass. It is there where the diverse inharmonicity in the two 8’ choirs causes trouble.
Experiment everybody knows. Have a perfect-unison of the two 8’ choirs in the note G. Now in the upper manual tune GG by perfect octave. Do the same in the lower manual. The two GG strings should be in unison, but in many instruments they are not, and in most cases the upper GG is minimally higher in pitch. This makes perfect sense. In both octaves there is inharmonicity in the 2nd harmonic, only the amount of inharmonicity is different. The effect is audible, but the difference is not great, and the skilful tuner just compromises, both revising octaves and minimally flattening upper GG, until both octaves and the unison are heard pure.
I also suggest for the extreme bass to check using the 4’, which has hardly any inharmonicity there.
This said, the minute differences observed just help to have a perfect GG unison. Measurement of pitches hardly qualifies for “octave stretching”.
Seems to me that in this discussion of inharmonicity and stretching, one should take care to specify which harpsichord is meant (and from which century).
Strings generally tended to get thicker, which exacerbates the inharmonicity in a non-linear way.
Also, consider that the strings which are most susceptible to sounding bad if no stretching is done, i.e., the bass strings (because more octaves of partials are within hearing range), are also the ones which are almost invariably foreshortened in most harpsichord designs.
Someone with access to a “real” harpsichord could add some worthwhile data to this discussion, by making sure the instrument is in perfect tune (by ear), and then testing with an electronic aid: is there enough “stretching” to show up consistently on the tuner?
Personally, with my experimental instrument with relatively thin strings and a narrow compass of four octaves starting at C, I just tune it with an electronic tuner and I can’t personally perceive any problem with the tuning, but I am no expert and my ears are mostly raised on equal temperament and guitar music.
–Benjamin
Nowadays in piano technology at least some tuners distinguish between “natural” stretch, i.e. the extra bit of frequency beyond a simple 2X octave and “artificial” stretching, i.e. adding even more for an intentional effect.
The realities of this can vary considerably from piano to piano, since inharmonicity makes it virtually impossible to tune an octave with absolutely perfect agreement of all audible coincident partials. BUT, in a well-scaled piano, there may occur a kind of cancelling of opposing beats, such that the not quite perfect coincident partials seem to obsure one another. Similarly, slightly blurred unisons can also obscure imperfect octave coincidences.
Add to this that there are competing theories about the “right” may to listen to intervals. Some tuners are opposed to focusing on individual partials, promoting what is now called “whole tone” tuning.
My sense is that all these approaches make plenty of sense when you’re tuning the right piano, not so much sense if you’re tuning a wide variety of conditions and designs of pianos. In any case, the only possible absolutely absolute pure interval on the piano is perhaps the unison…when everything is perfect.
Another issue that comes up is the different ways of perceiving wide intervals. When intervals are played melodically, there is a tendency to want them to be somewhat wider than what would be preferred as harmonically played intervals.
The most advanced digital piano tuning programs are capable of remarkable measurement and calculation, often taking into account compromises involving more than one pair of coincident partials. The most interesting discovery has been the development of “Perfect 12th” tuning, which takes advantage of the strong third partials of modern pianos. This produces a “natural stretch” which is a little bit less than what was typical of many octave/double octave stretched tunings. Perfect 12th temperament is very difficult to set by ear, though once the temperament 12th has been set, it’s easy to expand. This has become more common because of digital piano tuning.
But for harpsichords…if inharmonicity matters, it might be obvious in revival instruments with wound bass strings. Beyond that, I believe there is a bit of forgiveness is octave tuning. There is a range within which it will sound wonderfully clean, even though, microscopically it is less or more than perfect. And someone might want to tune “just a little more, but not really enough to hear it when you play.”
I could go on and on without reaching any conclusion. It’s good to have a deadline so you can stop and play music. That’s the wonder of 1x8’x5 octaves.
This is exactly what I was talking about. Perceptible sharpening. I do not regard ‘imperceptible stretching’ as stretching.
Le 15/09/2023 01:28, Ed Sutton via The Jackrail écrit :
But for harpsichords…if inharmonicity matters, it might be obvious in revival instruments with wound bass strings.
According to Wikipedia, on the contrary: “A wound string generally
exhibits less inharmonicity than the equivalent solid string, and for
that reason wound strings are often preferred.”
Stiffness adds to inharmonicity, and wound strings are less stiff than
solid strings.
Le 15/09/2023 00:12, Benjamin Ketcham-McGrath via The Jackrail écrit :
Seems to me that in this discussion of inharmonicity and stretching, one should take care to specifywhich harpsichord is meant (and from which century).
It also is very dependent on the type of strings. I just restrung a
three-rank instrument with Stephen Birkett’s historical wire, and there
is obviously less inharmonicity than with the Rose iron and Little Falls
brass that was on it previously. Which makes it much easier to tune,
especially the highest notes. Anyone who has tried his wire will
probably confirm this.
Yes but Ed was speaking of revival harpsichords, whose bass strings are so severely foreshortened that they would lead to unbearably thick strings. In order to avoid strings too thick, they must use wound strings. Better than solid - very thick - strings, but still more inharmonic than the moderately thick strings one can use on a historically scaled harpsichord.
Where possible,- not unlike when tuning unisons- when tuning octaves I listen to get rid of any beats at the fifth, on the partial which they have in common. If there are offending beats, they are faster than those pulsing at the octave, and so can be easier to fix than very slow beats.
Apologies, you can please ignore my last mail (which thankfully Andrew truncated)- my email server removed virtually all of the conversation, so it is completely out of context. Time for me to use the Jackrail site in future.
In the case of wound bass strings, generalities don’t help much. As the tension on the solid string, or in wound strings, the core string, approaches the breaking tension of the string, the inharmonicity decreases.
So, for example, lowering the pitch of a harpsichord from A440 to A415 will increase the inharmonicity-how much, I don’t know. That will depend on the % of breaking tension of various strings at those pitches.
That is also why the highest brass string in the bass sounds so clean and breaks so easily.
A problem with wound bass strings is that the core wire %s of breaking tension become skewed irregularly, producing a warped network of higher partials. In the low bass of the piano we hear very little, often none , yes, NONE of the sound of the first partials. The low sound we hear, if we hear anything, is an auditory system response to the higher partials. In wound piano bass strings designed with up-to-date scaling programs we can hear a clear half step progression all the way down to A0, but, again, it is not the fundamental we hear, but rather a response to the well-designed overtones of the strings.
Stephan Paullelo offers piano wire in a variety of breaking strengths. When the % of breaking tensions of each note are controlled as part of the scale design the piano tunes more smoothly and small pianos take on the inharmonicity curves of larger pianos.
Simplifying: the problem of inharmonicity in bass strings lies not with the fundamental of the string, but with how well, or poorly, the partials of the low string can match with partials of the mid-range notes that are so often played harmonically with the low bass notes. Getting beyond tuning theory, it may be worthwhile to look at the “big” concordances of the music we are playing, at the octaves, double octaves and 12ths in significant progressions that show harmonic beauty (whatever that means to you). These harmonies can be tested as the conclusion of whatever tuning method is used, and corrections can be considered if needed.
It’s probably worth learning to hear the multiple coincident partials involved in perfect intervals, as this is where irregularities of scaling will be audible.
Compared to piano tuning, harpsichord tuning is a very straightforward endeavor. Harpsichords are naturally wonderful. Pianos are overloaded contraptions. I am so glad to be a RETIRED piano technician. Whew!