Re: [Harp-L] 19-limit Paddy

[G <gigs@xxxxxxxxxxxxxxx>]

Date: Sun, 1 Oct 2006 15:54:43 +0200
From: "mOx" <mox1@xxxxxxxxxxxxxx>
Subject: [Harp-L] 19-limit Paddy
To: <harp-l@xxxxxxxxxx>

>Recently, for certain tunes in A minor (Shady Grove), I've been using a
>'C' Paddy Richter tuned Golden Melody that I've modified myself.
>O.K. as far as that goes, but I'm not yet satisfied with Equal
>Temperament so maybe 19-limit would do the job..
>So before posting I checked the archives
>( http://harp-l.org/mailman/htdig/harp-l/2005-March/msg00365.html)
>& found this:
>>blow: +00  -14  +04  +00  -14  +04  +00  -14  +04  +00
>>hole: 001  002  003  004  005  006  007  008  009  010
>>draw: +02  +04  -10  +02  +03  +06  -10  +02  +03  +06

Hello Mox, 
  The tuning chart is intended for German Major diatonic harmonicas.
But, with all due respect to the author, the above chart is entirely
wrong:
* Perfect fifths are about 702 cents higher than tonic, not 704 cents,
so blow holes 3, 6 and 9 are 2c too high.  Draw holes 6 and 10 would
also be 2c too high too, except...
* Draw holes 1, 4 and 8 (fifths to draw 2, add 702c to tonic) are all
flat by 4 cents compared to the tonic draw hole 2.
* 19 limit sub-minor third is 298c higher than tonic, not 301c. So draw
holes 5 & 9 are also incorrect.
* The major thirds, however, are correct: 386 cents above tonic.

The problem with tuning charts is without a deeper understanding how
these charts are created, it's very easy to make a lot of mistakes -
especially if you forget the values, or start trying to apply it to
other tunings.

Pat Missin has explained harmonica tuning extensively, starting here
http://www.patmissin.com/tunings/tunings.html

With that in mind, a 19 Limit JI German Major diatonic harmonica tuning
chart usually looks something like this:
blow: +00  -14  +02  +00  -14  +02  +00  -14  +02  +00
hole: 001  002  003  004  005  006  007  008  009  010
draw: +04  +02  -12  +04  +02  +06  -12  +04  +02  +06

Now onto your question about 19 Limit JI Paddy Richter tuning...

>Now my question is :
>As the 2 Blow has been raised a wholetone should I now consider it as :
>a) The tonic therefore +00 cents
>b)A sixth and adjust the fine tuning to +06 cents?
>c)Or as a second, +02 cents?

With Paddy Richter, blow hole 2 remains a major third up from the tonic
blow hole 1 - instead blow hole 3 is raised a semitone.  On a key of C
Paddy Richter harmonica the note layout is

blow: C_ E_ A_ C_ E_ G_ C_ E_ G_ C_
hole: 01 02 03 04 05 06 07 08 09 10
draw: D_ G_ B_ D_ F_ A_ B_ D_ F_ A_

I'd recommend tuning it as a major sixth/minor third to the harmonica's
tonic, however there are a number of problems with this.

Pat Missin's article on approaching Melody Maker(TM) tuning is relevant
since it has the same blow notes as Paddy Richter tuning:
http://www.patmissin.com/tunings/tun4.html

He recommends tuning it a perfect forth (498c) above the maj third (E).

So a 19 Limit JI Paddy Richter diatonic harmonica tuning chart looks
something like:
blow: +00  -14  -16  +00  -14  +02  +00  -14  +02  +00
hole: 001  002  003  004  005  006  007  008  009  010
draw: +04  +02  -12  +04  +02  +06  -12  +04  +02  +06

>Also, should  I decide to go one step further & raise the 5 Draw by a
>semi-tone would you advise me to treat it as a Major 7 (i.e. -10 cents)

>or, as a #4/b5 as in the tri-tone between 5 & 7 draw (i.e.-13cents)
>What would you advise?

If you raised draw 5 by a semitone you'd tune it as a major third to
draw 4 (add 386c) or major seventh to draw 2 (add 1088c) which gives the
same result - it's a 5 Limit interval.

hole: 001  002  003  004  005  006  007  008  009  010
draw: +04  +02  -12  +04  -10  +06  -12  +04  +02  +06
(keep in mind draw 9 is being left as is, a 19L interval)

>Thanks in advance
>Mox

Cheers,
-- G.
http://harmonica.7p.com