another DIY video tutorial: starting any regular temperament accurately, on harpsichord

[Brad Lehman]

I wrote about a general tempering technique:
 > My little shortcut to establish the G *exactly* where it belongs
 > halfway between F and A: use a C that's temporarily pure below F,
 > and a D that's temporarily pure below A.  From that C and D, get
 > the G going so the C-G 5th is making a duplet beat against the
 > triplets of the D-G 4th.  Voila.  Then, average out the C and D
 > later (within F-C-G and G-D-A).
 > Explanation:
 > http://www-personal.umich.edu/~bpl/larips/practical.html
 > http://www-personal.umich.edu/~bpl/larips/tetrasect.html
 >
 > Maybe I'll do a short video sometime on that technique, too,
 > since it's useful to set up any type of meantone or
 > modified-meantone temperament accurately.  It gets the core
 > 5ths/4ths to be evenly spaced (properly) in just 2 or 3 minutes,
 > with no guessing.  Any interest?  Anybody else here already use
 > such a technique with two temporarily-pure notes as markers?


Went ahead and did it, since an aural demonstration is worth a
bazillion words:
http://www.youtube.com/watch?v=21eocx96sGM

Harpsichord tuning: building a scale by ear - Bradley Lehman

Tuning a harpsichord from the reference of a single starting note.

In this demonstration we start from an A, and then we derive all the 
notes of a pentatonic scale from it: F, G, A, C, and D.

The title of this demonstration could also be: "Starting any meantone 
temperament accurately, by ear." The notes and intervals are adjusted 
carefully until they are deliberately impure by the right amounts 
relative to one another.

Despite some perhaps arcane terminology used here, this is merely a 
simple listening skill of controlling the relative pitches carefully. 
With practice, and knowing what to listen for, this skill can be 
developed by any reasonably musical teenager working hands-on at a 
harpsichord.

The basic technique here is to set up four consecutive 5ths (such as 
F-C-G-D-A) with exactly the same amount of tempering (impurity) in each 
interval, deliberately. The 5ths all have to be made slightly narrow, or 
else we would end up with a major 3rd that is unpleasantly wide and 
ugly. Tempering is always a series of trade-offs.

In this demonstration a size of major 3rd is chosen first, as boundary, 
and then the intervening 5ths/4ths are fit equally into that confined 
space. Here we have chosen to start with a pure major 3rd, for 
simplicity, but the technique works similarly with any other reasonable 
size. We could have used a slightly wider major 3rd tastefully, 
according to the milieu and the keys of the music we plan to play.

The resulting layout is called "meantone" because the whole step (the 
tone) makes an equal and average size within a given size of major 3rd. 
That is, for example, F to G being the same size step as G to A, within 
the major third F-A as illustrated here. The G's frequency is at the 
geometric mean between the other two frequencies.

This hands-on tuning method at the harpsichord is entirely 
geometric/analog, not involving any calculations or any technology 
invented later than 1600. (Well, OK, the tuning fork was 1711, but it's 
not necessary even to have a tuning fork; just some suitable way to 
assign a resonable pitch to the first note.)

This is the basis for most of the historical keyboard temperaments used 
on harpsichords, clavichords, organs, and pianos: at least among the 
natural notes (white keys on a piano), having all or most of them 
equally spaced in a "meantone" relationship.

After watching the video several times, taking notes if necessary, it 
might be useful to go through it again only listening closely to the 
sound (i.e. not looking at the picture or the captions). It might be 
easier to comprehend in that way, since the technique being taught is a 
listening skill...not a reading skill.

Of course, nothing substitutes for trying it out oneself at a 
harpsichord, to get a feel for the types of adjustments necessary.

With enough practice, and using temperaments that are built like this, 
the whole harpsichord can be tuned accurately by ear in about 7 to 20 
minutes.

This same triplets-to-duplets listening skill is also useful in checking 
the purity of octaves, especially when working on the treble notes. I 
use it all the time to make sure my 5ths and 4ths aren't getting too 
gamey, or conversely too nearly pure where they're not supposed to be!


Dr Bradley Lehman
http://www.larips.com
Tuning resources and CDs