P12 in Tunelab Pro

[Richard Brekne]

Bernhard Stopper wrote:

>Ric said:
>  
>
>>Taking the 19th root of the 3rd harmonic (or any partial for that
>>matter)  for 19 semitones by the way... is not the same thing as spacing
>>those same 19 semitones the way I do with the aid of Tunelab. Nor is it
>>likely to result in exactly the same <<pure 12th>> unless it in turn is
>>based on a 12th in which the 3rd partial of the lower note is identical
>>to the fundamental of the higher.  That said... the basic and general
>>spirit of basing said spacing on a perfect 3:1 12th is much the same.
>>    
>>
>
>Yes Ric. But the differences we speak here about are ONLY caused by
>different ways of discretizing the inharmonicity effect.
>  
>
Thats very true.  And as such they represent variations on the theme. 
You could take this logic further you know Bernhard.... conceptually ET 
was thought of 5000 or so years ago by the Chineese... or some such 
people.  Since then nothing really significant has happened... if you 
get my meaning.

Point being, a generalized conceptualization, and a given application of 
that are not really the same thing.... tho it is true that different 
applications of the same idea do indeed have in common the idea itself.

>Taking the 19th root of 3rd harmonic valids surely only for the special case
>where the inharmonicity slope stays constant.
>I did not figure out more precisely at this point for not complicating the
>things more than necessary. Since you see this immediately, more
>discretizing is necessary now ;)
>For example in the old Mensurix Versions 1,2,3 and 4.0 the frequencies were
>calculated on a P12th tuning where i calculated the inharmonicity curve in
>that way that i took for each consecutive P12th the frequency of the 3rd
>harmonic and did a spline smoothing on the resulting 19th root factors. So i
>think what we are doing is not as far away than that what other tuners are
>doing by tuning octavely. (No matter what Octave ratio is used, perhaps a
>6/3 may come in the case of a good inharmonicity curve most closely to
>P12th.)
>  
>
I agree that what the P 12th tuning is very similiar in most regards to 
what the octave chasers get.  You will find a marked difference in the 
upper treble / lower diskant range.... somewhere around that A5 to F6 
range.  If you look at Reyburns <<preview curves>> you'll see how the 
3:1 12ths develope there when his octave types are used to construct a 
curve.  Holding the 12ths pure instead of course turns the tables on the 
relevant octave types.  Still, all in all the real difference is small, 
tho perhaps large enough to account for comments that go along the lines 
of the P 12th tuning giving the impression that it has a higher stretch 
figure then it really has.

>again Ric:
>  
>
>>I find them very useful myself.  Tuning, one way or the other, is not a
>>matter of simply taking regard to the fundamental frequencies of
>>strings. Nor is it a simple matter of dealing with the lowest partial
>>pairs in any intervals. Most of our aural octave tests are actually
>>dealing with differing octave types for different registers of the
>>piano. Being able to refer to these directly as well as referring to
>>aural tests allows for a degree of communication among tuners that
>>otherwise becomes difficult, clumsy, and less then dependable.
>>    
>>
>
>I did not say that i tune only the fundamentals. Since i tune aurally, if i
>set M6th and m3rd and M3rd and double 8th+M3rd, i always keep in mind of the
>higher partials ( i think i must not figure out more precisely here).
>I only said i do not use any higher P12th ratio than the first 3/1. (you
>also stated to Isaac that the 12th should in no case be wider than straight)
>  
>
Ah.. I see.  well then.. we are in agreement here as well then.  I had 
considered (and tried) employing a graduated move to a 6:2 12th in the 
base... but found it easier to use a 6:3 octave instead... which by the 
way ends up being a 6:1 octave and 12th.  So in reality there... down to 
D#1 there are perfect 6:3:1 coincidents.  In practice tho.. I find that 
the bass is a bit less predictable. Some pianos just plain seem to want 
a bit more stretch down there.

>And since i built my tuning only with the help of the beat structure net,
>i don´t matter whether my octave is a 4/2 or a 6/3 or a 8/4 or somewhat
>between that.
>  
>
I am not entirely sure what you mean by <<beat structure net>>  But if 
it means just using the lowest coincident pair I at least understand 
that much.  But why the term <<beat structure net>> then ?

>This is a straight consequence of tuning really straight P12th throughout
>the piano.
>But ok if someone remains in thinking or hearing "octavely" or for handling
>the discretized absolute frequencies with ETD´s it might be helpful to
>describe the octaves relating to a higher partials ratio.
>  
>
This ends up being the case.  But it also means that curves utilizing 
more then one set are making trahsitions chromatically in which at one 
point in the scale they have their sights on just 6:3 types... and at 
another just 4:2 types, and at higher areas just 2:1 perhaps as well.  
Not to mention some curves go all the way for a just 12:6 in the bass. 

These transistions from one type to the other progress differently then 
if you force the 12th to remain pure. I havent gotten around to 
figureing out a theoretical chart plotting this progression yet.. but I 
imagine that P 12ths will cause the devoloping  width of the octaves to 
change directions for a small area in that upper treble area.  I.e. 
octaves would be getting increasingly narrower until around A5... then 
until about F6 get slightly wider, for to resume getting narrower the 
rest of the way up.

>don´t let´s forget we are talking about a tuning we are both convinced of. I
>agree with every statement you have said about its sound impression.
>
>  
>
THAT !! my friend... has never been in question. :)

>regards,
>
>Bernhard
>
>  
>
Best

RicB