temperaments

[Richard Moody]

Thanks for the response, replies inserted .....  ---ric m 
 

> -----Original Message-----
> From: pianotech-bounces@ptg.org 
> [mailto:pianotech-bounces@ptg.org] On Behalf Of Ron Koval
> Sent: Thursday, April 08, 2004 8:42 AM
> To: pianotech@ptg.org
> Subject: temperaments
> 
> 
> Hi everyone,
> 
> I just had to respond to this again.
> 
>> ric wrote:
> Don't forget the first instrument that had to be constructed 
> to ET in order to exist as a musical instrument, the lute and 
> later the guitar. The proportional spacing of the frets 
> results in ET or is ET depending on how you want to think 
> >about it. <snip>
> 
> Yes, of course you are right.... except when you realize that 
> many times the 
> tuning of one string to another is tuned pure by many 
> guitarists, .......

Yes but many other guitarists for the last 50 years used tuning machines
to tune their guitars which means the strings are in ET rather than in
pure,to each other. Is it 90% of all guitar music you hear recorded and
performed coming from instruments tuned by machine, with exceptions
being in classical? (since 1950?)  
> 
> 
> ric again:
> all the orchestral fixed pitch instruments, which 
> includes flutes, woodwinds, saxophones, xylophones, marimbas, 
> glockenspiels, orchestra bells, tympani etc. 
> 
> You mentioned you are a bassoon player.  Is your bassoon 
> designed in Et? If not, what? <snip>
> 
> ARRRRRG! (sorry for yelling)  There are no orchestral fixed pitch 
> instruments, except in the percussion section. 

Ok maybe I am using the wrong term.  But what are the holes for in the
bassoon? To give a pitch? Why is that not called a fixed pitch?  Because
the player can "bend" it?   What term should be used then, to
distinguish the pre determined pitch of the bassoon and the variable
pitch of the trombone?    Also I would like to know how your bassoon was
actually made.  Did the  craftsperson sit at a bench and file the holes
so that the pitch agreed with an electronic tuning machine?  If so then
your bassoon is in ET. Or if not then what pitches were designed will
tell the anti ET trio what to say about anti ET. 

> And  what does the 
> width of the octave have to do with the necessity of ET?

It means that every note in the octave can be expressed as powers of 2. 
It can be seen on a monochord.  Divide the string in half and you have
the octave.  
But how to divide the string into 12 equal parts within that octave? 
ET is expressed by the mathematical concept of 2^(1/12), or the twelfth
root of two which means 12 notes are of equal proportion within the
octave or a proportion of two to one.
There are other ways of expressing the proportion of the notes again
illustrated by the monochord.
The 2/1 width of the octave and the "necessity of ET" is a bit of a
stretch but consider what is available in reality.  What system is 1/1?
So what is the next system,,,,2/1?   It turns out 2/1 is the octave of
music.   What about 3/1?  What about 5/1?   What about 10/1?  10/1 is
our counting and number system.   Every number of our system can be
expressed as a power of 10.  Every musical note can be expressed as a
power of 2.  2^(1/12) expresses C#.   2^(2/12) signifies D. 
 
 
> 
> ric again:
> The only "norm" I know in music among players is to match 
> pitch and "make pleasing harmonies".  There is no temperament 
> in these situations unless you are playing a tempered 
> instrument.  It a matter of tempered instruments matching 
> pitch with free pitch instruments, and the job of the 
> musician is to make his/her instrument sound good with all the others.
> >
> Ps  If you want a keyboard instrument tuned to a different 
> temperament that is OK, but why is the "norm" of ET for 
> keyboard instruments for the last 200 years so hard for some 
> to acknowledge? <snip>
> 
> Now we're actually getting somewhere. This was my point, that 
> in reality, ET 
> is pretty rare.

Well so is the perfect performance.  But the proximity to ET since 1800
has been closer to "the norm" than certain publications and posts here
endeavor to say otherwise. 


>



 In fact, what is the 
> "litmus test" 
> for ET? 

It is what my teacher told me, and what another master tuner told me,
and another master tuner told me.  At any PTG convention you can get an
idea of what tuning is a "litmus test" of ET.  



 I commonly use a temperament that has a maximum 
> offset from ET of 
> only 1.2 cents.  Yet, to another skilled tuner who would test 
> the thirds in 
> chromatic order, it is easily heard to be not ET.

Why do you not want to tune ET?  Do you do this by ear or by machine? Is
it the same every time. How did you learn this?  When you play are you
constantly reassured this "offset" does indeed sound better than ET.
Can you perform and demonstrate this? If so would you be willing to play
blind fold on a piano you tuned and a piano I tuned for an audience who
would "judge"? 
I am not gung ho on 3rds.  Below F3 they can be ambiguous esp in and
around the break. Maybe your temperament might test out as ET to me, but
yet a machine might show "deviations".  

  Are you 
> saying that for 
> the last 200 years, pianos have been tuned to within a cent 
> of ET?  Using 
> what methods? 

Within a cent, yes probably among the most skilled and those attempting
ET the best they could of the times. 
You have to realize ET is an evolutionary process that went hand in hand
with the evolution of the piano. There are too many unknowns to say ET
200 years ago was within one cent.  Cents weren't even known until 1870.
How do we know there were not scaling problems that prevented the tuning
of any temperament with in one cent? 
You asked what methods, I have the words of James Broadwood himself how
to tune ET in 1811.  Of course there will be those who argue, "well it
could not be within one cent"   Well so what?  What tuning today is
within one cent?  I am sure you can take any machine and test any tuning
and find one or two  or three notes more than "one cent off". 

>You 
> may KNOW the 
> truth of ET being the norm for the last 2 centuries, but I'm 
> afraid reality 
> shows us otherwise. 

Well that is nothing to fear.  Go and do the research and share it.
Especially if you are literate in French, German and Italian.  There are
many works on ET from the mid 1700's to 1850 that need to be dug up.
>From 1850 there are many texts available in university libraries and
microfilm of magazines of the 19th century.  
For what I have come up with check out www.pnotec.com under "articles".





 How many people taking the PTG test miss a 
> note by more than 
> a cent? 

We all miss in every tuning one or two or three or more notes by more
than a cent.  Does this mean we don't tune ET?  That is not the point.
The point is we get as close as we can, just like the performer wants to
get as close to the perfect performance.  That we piano tuners can be
measured to "one cent" is part of the turf of 21st century tuning.
----ric moody