Tuning meantone by ear

A video on tuning meantone by ear:

As an aside 395 Hz is an odd setting, but who am I to argue.

A lovely video, but makes me wondering. He only tunes fifths, guessing how much to temper. If done precisely, it then produces the requested pure thirds. Though, he doesn’t check for them. Of course he is very good at tuning (the result is very pleasing indeed), but isn’t the aim of meantone to have pure thirds? So wouldn’t it better (and easier) to tune pure thirds first and then the fifth are what they are?
For example, he tunes C-G, G-D, D-A, A-E, and then the all important third C-E should be pure as a result. Wouldn’t it better to set an absolutely pure C-E and then to fit the 4 fifths inside? I mean, a tiny error with the latter approach would lend to non-perfectly tempered fifth. But with the former approach a tiny error would lend to a non-pure third.

My personal approach to meantone is:
C-E pure third.
Fit G, D, A inside that third.
From now on I only tune pure thirds:
From A, I tune F and C#.
From E I tune G#.
From D I tune F# and Bb.
From G I tune B and Eb.
Then I check if the wolf is indeed a wolf, and I’m done.

Am I wrong? how you tune meantone usually?

Indeed!

Le 12/09/2023 13:14, Domenico Statuto via The Jackrail écrit :

Am I wrong? how you tune meantone usually?

I do exactly the same. I can’t imagine any other way. Of course, if I
only had an A tuning fork, I’d start with F-A, but never with the fifths!

@hpschdNU gives his technique for tuning meantone - with thirds - very nicely expressed, but due to the dated structure of his website you can’t link to specific pages.

I do the same as Dominic. I should have thought tuning by tempered fifths can only lead to an accumulation of errors, though on a good-ish day they might cancel out… However, I cannot understand why one would not check the pure thirds.

David

I posted the link to await the inevitable replies!

The video provides an excellent, very didactical basic teaching into harpsichord tuning.

Let me just comment about a few details, some already observed by Dennis, David and others in previous posts.

CIRCLE OF FIFTHS. The vast majority of modern writers use the Circle with C on top. He turns it around 3 positions and places A on top.

TEMPERAMENT RANGE. He tunes in the centre of the keyboard, and the result is that beats are too fast and sometimes he needs to tune an octave down to check for fifths. The time-tested traditional way of tuning the harpsichord, both in ancient and modern writings, is to use the F-clef region.

FINDING THE TUNING PIN. Especially in an instrument with the typical disposition of hitchpins in separate rows for naturals and accidentals, finding the hitchpin corresponding to a key and choir is easy by visual similarity with the keyboard layout. There is no need to touch the string with the tuning hammer tip, as the video suggests.

THE SCARY PART. How to split the pure major third F-A into 4 similarly tempered fifths. He does it the “traditional” way: tune every one slightly smaller, hoping to achieve a “similar impure quality” in all of them. Let me note that there is a way to do this with much more accuracy, following a procedure already described by Fogliano in 1520.

EXTENDING THE TEMPERAMENT. There are two ways: (1) tune by fifth and check the major third, (2) tune by pure major thirds. Harpsichord era sources mention both things: “tune a small fifth so that the major third is pure”. The video prefers (1), which provides a good test in case the initial 4 fifths were not similarly tempered. However, provided these 4 fifths were accurately tuned, tuning by successive pure major thirds is faster, it will repeat the fifths’ temperaments, and their testing is unnecessary.

When fitting the 4 fifths into the endpoints of a known major third, it’s not necessary to guess at them.

Do the same thing you would do when tetrasecting an angle on paper, using only compass and straightedge. Bisect it first, and then bisect each of the pieces.

If you prefer origami: Fold your piece of paper in half, and then in half again.

To fill in the fifths of C-E:

  1. Set the C-E to whatever size it needs to be.

  2. The next note is D, the “mean tone” (average) between C and E. To hear where it belongs: Temporarily tune a pure fourth from C down to G, and a pure fifth from E down to A. Use those endpoints of G and A to place D halfway between C and E: the G-D fifth and the A-D fourth are the same quality as each other. Check your C-D and your D-E melodically, to confirm that these whole steps are the same size.

  3. Use C and D to put G at the correct place (which is slightly lower than the temporary G from step 2).

  4. Use D and E to put A at the correct place (which is slightly higher than the temporary A from step 2.)

  5. Check the qualities of C-G-D-A-E, which should be all the same as one another.

  6. (etc) Now that you have these 4 example fifths or fourths that are all the same as one another, copy that same quality to wherever else your temperament needs it.

This process works fine when your starting major third C-E was some size other than pure, too.

It can be started from F-A, if you prefer. Temporary C below the F, and D below the A. Place the midpoint G. Correct your C and D.

It’s much faster, and more accurate, than guessing and then having to go back and fix the misguesses.

Once you have the technique of tuning the thumb’s note of your left hand, equally spaced over the notes played by fingers 4 and 5, you can use this to check your fifths everywhere that they are supposed to be the same as each other.

I use it to check my octaves in the treble. For example, when working on A, I make a good guess at a pure octave A-A. Then, I quickly check that high A against both the D and the E within that octave, knowing that it’s supposed to have the same quality from both. I fuss with the high A until I am happy with all three of its relationships with A, D, and E.

Checking my octaves in the bass, I test with fingers 1 and 2 the note that I am confirming at 5.

Once practiced, all of this is so fast that it doesn’t take any conscious thought. Any temperament that is really internalized doesn’t take more than 10 minutes to set up the whole register of 50 to 60 notes, including all the octave checks. Whatever qualities the various fifths and fourths are supposed to have, they can demonstrate either directly or in pairs when our octave is good enough to move on to the next one.

My old web page about this, from 18 years ago:
https://www-personal.umich.edu/~bpl/larips/tetrasect.html

Bradley Lehman

Le 12/09/2023 16:18, Bradley Lehman via The Jackrail écrit :

I use it to check my octaves in the treble. For example, when working on A, I make a good guess at a pure octave A-A. Then, I quickly check that high A against both the D and the E within that octave, knowing that it’s supposed to have the same quality from both. I fuss with the high A until I am happy with all three of its relationships with A, D, and E.

I find this rather unusual. I think pure octaves are much easier to
judge than “equal quality fifths” and don’t require and guess-work. Once
the temperament is set, I see no need to do any more checking.

If one is a grandmaster in tuning then you can temper the fifths A-D-G-C-F in such a way that A-F is a pure third. I prefer to cheat: I make A-F a pure third and then do my utmost best to have the fifths in between equally “wrong”. It’s easier than you think. A tuning app can help you verify but after a while you’ll notice that you have the beating of the intervals stored in your ear.

As Dennis said: tuning a pure octave should be the first (and easiest) skill to master. Second most easy is a pure fifth (even violin players can do it). From there, it’s a small step to appreciate the warm sound of a pure third.

This is a great trick. I’ll use that. Unfortunately I only tune meantone rarely (I only am able to tune by ear meantone, werckmeister III and Kirnberger III)

I’ve used the following as a demonstration to beginning tuners:

  1. Tune C4-E4 as a pure third (demonstrating tempered and pure thirds)
  2. Tune C4-C3 pure octave and E4-E5 pure octave.
  3. Tune C3-G3 pure fifth and E5-A4 pure fifth. (Opportunity to demonstrate pure and tempered fifths, ending with the two pure fifths. Show that pure fifths sound similar to pure octaves.)
  4. Show that you can’t tune D4 pure with G3 and A4.
  5. Split the difference. Tune D4 to be equal beating with G3 and A4. Maybe the very tiniest bit faster with A4. Since each is a half-comma fifth, it’s pretty easy to hear. You’re trying to make each fifth equally noisy.
  6. Now split the difference between C3-G3/GC3-D4 and D4/A4/A4/E5.
  7. Tune octaves to these notes, beginning to fill the two octave range.
  8. Tune appropriate thirds above and below the tempered fith notes.

I don’t know of a historical precedent or this, but it “lays out” the problems and their Meantone solutions rather clearly, and helps learners to hear that tempering is not about one note, but always about relationships between notes for musical purposes.

I can’t understand why you would make a ‘good guess’ at an octave interval, unless I don’t understand the prose. A pure octave is the easiest of intervals to hear, and even non trained people can hear it. That statement has me puzzled. Unless you are suggesting octave stretching, or not having perfectly pure octaves. I don’t think anybody does that on harpsichords?

@andro So many people now expect swipey-feely websites to view on their phones. Apologies to all that I’ve so far managed to resist updating my gigantic archaic website. It continues to use old technology like frames, and is specifically designed for viewing on a real desktop computer. My site remains secure, extremely fast loading as it only pulls data from my domain server instead of multiple locations, and does not set cookies.

If you must use your phone, please turn your screen sideways to maximize viewing width, but still be prepared to scroll.

You can, however, easily link to specific pages by two methods:

  1. [Advanced] Copy the canonical link appearing in the HTML source code, which displays the direct route to the page.

  2. [Simple] Ensure your browser preferences allow display of the complete URL rather than just the domain, and copy that. The result is lengthy because when a direct URL from my site or search engine is entered, javascript parses that to load the result into a frameset, pulling content for the top banner frame, along with content for the lefthand navigation frame.

The specific page on Quarter-comma Meantone in my Technical Library can be found here:

Regards

Carey

In your step 5,
“Split the difference. Tune D4 to be equal beating with G3 and A4. Maybe the very tiniest bit faster with A4. Since each is a half-comma fifth, it’s pretty easy to hear. You’re trying to make each fifth equally noisy.”
Not equal beating, and not “the tiniest bit” faster. The beats here should be in 3 to 2 proportion (triplets against duplets) because the frequencies are a fifth higher.

Equal quality (half comma each), not equal beating.

For everyone perplexed by my comment about testing octaves: test your octaves! The fifth and the fourth will tell you if your new note is in fact too high or too low to be a pure octave, even if it seemed to be a pure octave as intended. Octaves are so supposedly “easy” that it is easy to have a beat too slow to be bothersome. Then, these cumulative errors that weren’t noticed make a mess elsewhere.

Bradley Lehman

I fully agree with Bradley Lehman re the usefulness of octave testing via fifths and fourths. For centuries used by piano tuners due to the modern piano inharmonicity, it is also useful in the harpsichord in the extremes of the range.

| bpl Bradley Lehman
September 13 |

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In your step 5,
“Split the difference. Tune D4 to be equal beating with G3 and A4. Maybe the very tiniest bit faster with A4. Since each is a half-comma fifth, it’s pretty easy to hear. You’re trying to make each fifth equally noisy.”
Not equal beating, and not “the tiniest bit” faster. The beats here should be in 3 to 2 proportion (triplets against duplets) because the frequencies are a fifth higher.

Equal quality (half comma each), not equal beating.

To temper the four quarter-comma fifths between C and the E a pure (4:5) third higher, with gradually and smoothly accelerating beat frequencies, alternate ascending fifths and descending fourths: C3, G3, D3, A3, and finally, as a check, the descending fourth from A3 to the already established E3.

Each interval should beat slightly but perceptibly faster than the preceding one (so C3:G3 slowest; E3:A3 fastest);

if the progression of accelerating beat frequencies is even and smooth, the temperament is good.

Some people find this easier to learn/achieve than the sesquialtera proportion between the frequencies of, for example, C3:G3 and G3:D4, and it helps to stay within a narrow ambitus (a sixth in this example), thereby avoiding needless octave leaps.

I use your website all the time and have no problems with it. It has been helpful in the extreme.

Many browsers have a browser setting for ”View Desktop Page.” If you prefer portrait mode on your phone, just go to the desired page, and then change your browser setting to ”View Desktop Page.” On my phone, the Microsoft Edge for Android browser reduces Carey Beebee’s index until it’s almost illegible, and reformats the rest to fit the page.

I’ll take this opportunity to thank Carey Beebe for his generosity in making his superb site available to the public. I for one have spent many happy hours learning from him over the years.

Bob