Stretched octaves

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!

Inspired by the multiple tuning & temperament discussions, I remembered and activated a tuning app which has the capacity to measure and quantify the inharmonicity and relative amplitude of up to 16 partials of a note.
What it makes clear is that the real behavior of a vibrating string on a resonant instrument is very complex and sometimes contradictory of simple textbook descriptions of vibrating strings.

For example, it is unable to detect the first partials of the lowest notes on my five octave harpsichord, but it can detect most of the higher 16 partials. To my ear the fundamental is so loud and clear that I just can’t believe it is an artifact of my own hearing (though I can demonstrate on the piano that a low string very visibly moving in its first partial mode does not produce an audible sound until higher partials are agitated).

Much odder is the frequency with which the app displays negative inharmonicity in lower partials of both harpsichord and lautenwerk (fluorocarbon) strings. In all cases the ear does a beautiul job of coordinating the slightly irregular (?) partials into a clear and beautiful sound.
making these strings sound together harmoniously is a task of such complexity, yet if we just listen, it can almost always be done.

However you set the temperament and tuning, it isn’t complete without a careful listen and adjustment…just in case… One good approach can be to tune double octaves down from the treble to the bass, then adjusting the tenor octave to work with both notes, above and below.

This was amazing. Thank you.
Can’t wait to try the double octave technique!

@Ed Are you going to tell us what this app is? A mere description is interesting, but without knowing what the app is it is not much use.

The app is Cybertuner. $999 purchase plus $85 annual “subscription fee.” The overtone analysis function works even though I’ve dropped the subscription.
I believe Pianoscope can do something similar.

My intention was not to recommend use of the app, but rather to recommend using human ears for final refinement. I find it lovely and fortunate that our hearing manages to make beautiful sounds from situations which, upon close examination may be a bit more erratic than we would think. Most commendable earwork!
Especially when we use them to play music.

I am intersted to know as this ties in to my topic on request for requirements for a new tuner app that I am starting to develop. Perhaps there are features in that app worth having - in something more reasonably priced!

All the store links on the site are broken. Is this yet another good tuning app that is defunct?

Certainly a most impressive bucket load of features for pianos and ET.

Cybertuner is not defunct. Try the Apple App Store.
I’m not recommending it for harpsichord tuning, was just referring to some sample readings from the function that analyses partials of a note.

So far as I know all tuning apps start with either a simple list of equal tempered frequencies, or with a calculated curve for equal temperament adjusted for sampled inharmonicity in the particular instrument. This may involve averaged adjustments for multiple coincident partials.
Historical temperaments are then calculated from offset tables giving the supposed differences from equal temperament.

Would there be any value in creating a tuning app which, somehow, came closer to aural tuning techniques? For example, quarter comma Meantone thirds could be calculated by tuning the fourth partial of the upper note to the fifth partial of the lower note (or ideally by averaging the relative amplitudes of the 4/5 and 8/10 coincidences? See, it ain’t easy duplicating what the ear does easily!)
From there you could extract appropriate partials for tempering the intervening fifths.
Then a comparison could be made to see if there is any difference between “offset from equal” Meantone and directly calibrated Meantone.

Or you could just tune a given program’s Meantone and tweak the thirds to see if you can make them better.

I chose quarter comma Meantone because the pure thirds can be used as an “acoustic absolute” forcing tempering of other intervals. I don’t know how you’d calculate other temperaments.

At this point I wonder if this really matters for tuning harpsichords to play music. One objective test could be a “threshold analysis” of human perception of pure thirds, i.e. “How far off does it need to be for a person (musician? tuner? anybody?) to say ‘That’s not pure.’”

While such accurate tuning devices have brought about a very valuable revolution in piano tuning, it is important to remember that if such accuracy was necessary for playing music, music as we know it would not exist.

[For years my fine tuning fork and I were inseparable. It was a slow process to admit that I could serve my customers better with Cybertuner. This is not a matter of a necessarily “better” temperament and tuning, but that an advanced program gets you there faster with minimal disturbance to the piano and produces a tuning more likely to hold for six months. It is also far easier on the hands.]