Re: Set up Just Intonation with Chromatic Tuner

[Pat Missin <pat@xxxxxxxxxxxxx>]

Bernhard Fischereder wrote:
>
>The last few days i spent a little time with just intonation tuning theorie.
>I read the article (Just Intonation by ear) from pat mission about this. 
>Additionally you can find some theory on 
>http://home.earthlink.net/~kgann/tuning.html
>
>I now have some troubles/questions:
>
>1. If you have a harp key of C. What key would you tune in Just Intonation?
>   C, G or D if you play mostly 2. Position (sometimes 1. and 3.)
>   Pat Missin starts to tune the 1b +/-0 cent sharp. So i could assume, that
>   the JI-tuning is for C? 

OK. I've said this numerous times before, but it bears repeating:

Just Intonation is not a scale (or a set of scales), it is a system.
There is no such thing as "THE JI scale in the key of C", or whatever.

JI can be used to generate an infinite variety of scales that can be
transposed to various pitches, but more often (particularly with the
harmonica) it is more concerned with harmonic considerations rather
than melodic (scalar) aspects.

>   He than goes on with the oktaves e.g. 4b 2cent sharp (oktave stretched).
>   Rest is mathematics: on richter C tuning 2b is a E, therefore it is four
>   halftones from C. The ratio for this intervall is 5/4 and so 
>   1200*log2(5/4)=386,31cent=~14cent flat.
>   For 3b on a richter C tuning it is a G, therfore it is seven halftones from
>   C. The ratio for this intervall is 3/2 and so 1200*log2(3/2)=701,96cent=
>   ~2cent sharp (both calculations without considering the little stretched oktave)
>   ...for higher oktaves in equal ways...

OK.

>2. Now i have a problem: what key to use for the draw notes? In my opinion
>   the draw notes must be tuned for the same key as the blow notes. But if this
>   is so, why does p.missin starts to tune the draw notes with 1d? He says,
>   drawing notes sound cause of natural intonation a little bit flater than
>   blowing notes and therefore he adds an offset from about 4cent sharp.
>   So long so good. But should i tune the draw notes relativ to C just intonation
>   or D Just Intonation?

Forget about JI being in a given scale (see below). Also, I tend to
start tuning the draw notes with 4 draw, rather than 1 draw. 4 draw is
a much more stable note and after I get it in tune, I tune 1 draw so
that it makes a good octave with 4 draw at a variety of playing
pressures. I then tune 2 draw so that it makes a good sounding fourth
above 1 draw and a good sounding fifth below 4 draw. I then tune 3
draw so that it makes a smooth major chord with 2 and 4 draw, etc.,
etc.

Likewise, I tend to start tuning the blow notes from 4 blow, again
because it is an easier note to tune to a reference point than the
lowest blow note. The lower notes (particularly the lower draw notes)
tend to flatten more with increased pressure than the higher notes do,
so they usually need to be set a little higher than their theoretical
value. This is one of the reasons that I always say that you need to
learn to use your ears, rather than relying too much on an electronic
tuner.

>3. If i am playing mostly 2. position. Isn't it a good choice to tune a harp key
>   of C into G Just intonation rather than C? So i can reach pure chords in G.

OK - forget about scales for now. The best way to get pure chords is
not by tuning to a given scale, but by tuning the chords themselves.

Tune the draw notes so that they form the smoothest possible chords,
without worrying too much about their relationship to the blow notes.
You can't play blow notes and draw notes at the same time, so they do
not need to be as precisely tuned. Also, the ear is much more
forgiving of melodic intonation than it is of harmonic intonation. A
note that is a few cents sharp or flat might sound perfectly fine in a
scale (depending on your accompaniment), but perfectly horrible in a
chord.

Set your 4 blow note to wherever you choose (I find that tuning it to
+/- 0 cents with your tuner set to A=443 Hz works well, as this means
that none of the blow notes fall much below their 12TET value relative
to A=440), then tune the rest of the notes relative to that one, so
that they form the smoothest chords. The tuner is useful for getting
the notes to their approximate values - on a C harp, the E should be
14 cents flatter than its tempered value and the G a couple of cents
higher (as you mention above). However, tuning each individual note to
a given number of cents above or below the 12TET version does not
really give you the best results. As the goal of tuning in JI is to
get the smoothest possible harmonies, then in order to achieve that
goal you need to learn to hear the beats caused by impure intervals
and the intervals so that the beating disappears. This also allows you
to compensate for the different degrees to which different notes will
react to increased and decreased playing pressures. It is almost
impossible to achieve this with a tuner, working on each reed
individually.

Tune the draw notes similarly. Set 4 draw to your chosen start point
(I find that =4 cents on a tuner set to A=443 works well), then tune
the other notes relative to that one. You do have some choices to make
when it comes to 5 and 9 draw, depending on what you want from the
harp. I cover all of this in Altered States (free download from
www.patmissin.com/tunings.html etc., etc.)

If you have any further questions, I'd be happy to try to help.

 -- Pat.