Historical temperamentals

[Richard Moody]

----------
> From: A440A@AOL.COM
> To: pianotech@ptg.org
> Subject: Re: Historical temperamentals
> Date: Sunday, August 08, 1999 7:00 AM
> 
>  Greetings, 
>     Richard Moody writes,
> > As research continues  historical evidence is mounting that ET has been
> >around a lot longer than the proponents of  "other than ET" have been 
> proposing..
> >Aristoxenes of the ancient Greeks mentions the concept of  it.  
> 
>       I would like to offer a possible alternative view of this, as applied 
> today. 
>  The last 50 years of research, from Murry Barbour on, have actually pointed 
> out that the documented use of equal temperament on keyboards is a rather 
> late development.  

Regarding historical research and conclusions based thereon. One generally chooses
what best supports his hypothesis. From what I remember Barbour did not believe even
in 1934 that many tuners acheived ET. 

>My understanding of the Aristoxeneans argument with the 
> Pythagoreans was that it centered not so much on temperament, 

Ellis (translator of Helmholtz) states, "When once the Pythagorean division of the
Octgave had been settled, and it had been observed that 12 Fifths exceeded 7 Octaves
by the small interval of a Pythagorean comma... the idea of distributing this error
among the 12 Fifths was obvious.  Aristoxenus, a pupil of Aristotle.... is said to
have advocated this."  (p 548)
 
 
> >Mersenne in 1637 gives lute and monochord. 
> >distances accurate from .00 to .04 cents. 


>      And mentioned, (according to Owen J.) that these would be of little 
> value to the strung keyboards, as they had to be tuned by ear.

But the point is that lutes and fretted instruments being tuned in ET means that
people were hearing ET in music in 1637. Actually  a case can be made that the
best sounding lutes, guitars, etc can only have their frets arranged in equal
proportions.    The concept of ET or if you will mathematical predictions of ET have
existed at least since Mersenne. As to when ET was heard on strung keyboards, well
Barbour was still skeptical of tuners in 1934. Mersenne tries to give instructions
for tuning ET but in the end says it is the "secret of the masters"  It is not even
possible to draw conclusions from Mersenne that keyboards were actually tuned in ET,
but he sure gives indications that it was a goal, that it was something music could
look forward to. (Marin Mersenne _Harmonie Universelle_  trans Roger E. Chapman,
pub. Martinus Nijhoff / The Hague, 1957.) 
>  
> >The problem it seems is that ET was a goal, but no one knew how to tune
> >it. 
> 
>    Ah,  this is were I must repectfully disagree, and would like to offer a 
> few points why. 

I am not sure what you are disagreeing with.  That ET was a goal, or that no one
knew how to tune it. 

OK  In every historical era you will find some opposed to ET, or the concept of ET
in music esp the concept that ET "distroys the 'variety' of the keys". There is no
denying that. 
But certainly the vast bulk of documentation points to the desire "tune so that all
the keys can be played in, without making some keys sweet and other keys sour" From
this desire we have ET. 

>      The vast bulk of the documentation points to something else as a goal.  
> August DeMorgan was a mathematical genius, 
   > In addition to the "Ivory Tower" advocacy of unequal tuning , I must 
> mention "The "Tuner's Guide",  an instruction manual of 1840 which 
> purportedly supports the use of "equal temperament".  .  It 
> goes through a variety of temperaments as training ground for equal 
> temperament, and then gives instructions for a crude ET,
>...  Montal's booklet of 1832 
> certainly didn't take the world by storm, but if followed, will yield a fine 
> ET.  How come it didn't see any widespread popularity?

How do you know it didn't?  Or what was popular then? Or perhaps ET old hat by then.
According to Ellis in 1811 John Farey showed the tempering of the fifth to be 1/50
of a semitone or two cents. This was correcting James Broadwood who said 1/40 of a
semitone. (this is oneargument not to get caught up in, there are at least three
kinds of semitones) 

>      To assume that the tuners of the early 1800's were  working their way 
> through the various temperaments until they finally were tuning the most 
> difficult, newest, and least documented style of tuning in 1850 is, in my 
> opinion,  a mistake.  Reinforcing this is the documentation done at the 
> Broadwood factory in 1850, where Hipkins states the tuners weren't tuning 
> anything like equal temperament.  

This is according to, I am guessing a secondary source.  According to Ellis (p 548)
Mr James Broadwood in 1811 in the New Monthly Magazine, gave "a practical method of
producing equal temperament".  Regarding Mr. Hipkins, "from him I learn", Ellis
states, that the son of Broadwood's concert tuner  "writes to Mr.
Hipkins that his father (Mr. Peppercorn) 'always tuned so that all keys can be
played in, and never held with making some keys sweet and others sour' . "  That
Hipkins tries to show
that Broadwood pianos were not tuned in ET because a piano in Broadwood's country
home was tuned in meantone, "To Mr Hipkin's knowledge and no other", is flimsey
evidence in the face of James Broadwood's claim in 1811 that his pianos were tuned
in ET. It turns out that it seems Mr.Hipkins was trying to claim that he introduced
ET to the Broadwood factory in 1846, "at about which time it was introduced into
Broadwoods' under the superintendence of Mr. Hipkins himself." Ellis seems to go
along with Hipkins, "It is one thing to propose equal temperament, to calculate its
ratios, and to have trial instruments aproximately tuned in accordance with it, and
another thing to use it commercially in all instruments sold.  For pianos in England
it did not become a trade usage till 1846..."

>     The strongest evidence for temperament variety is the analysis Jorgensen 
> presents of Ellis's findings in 1885,  35 years after Hipkins had 
> "instructed" the tuners at Broadwood's to tune in ET.   Scientific 
> measurement at the time was advanced enough for credibility, I think, and 
> these results clearly show a strong bias for the same style of inequality 
> that had been recognized for over 150 years.  

Are you referring to Ellis data on page 485 of Helmholtz? "Specimens of Tuning in
Equal Temperament"  Of which Ellis states "the above figures in lines 2, 3,4, 5,
show how very close an approximation is now possible in pianofortes."  Of which one
was "My own piano, tuned by one of Broadwood's usual tuners and let stand unused for
a fortnight."  The scientific measurement was an advanced set of tuning forks.  
	

I>is it just coincidence that the 
> factory tuners of 1885 were still tuning temperments that followed the intent 
> of Werckmiesters rules?  

And the data shows that?  
The intent of Werckmeister is.......?    not ET?   Or anything but ET? 

Suppose the method of tuning the "Specimens of Tuning.."  was given. Would that make
a differnce in how the data is interpreted?    
	"These were all tuned by the modern way of Fifths up and Fourths down, and the
object is to make the Fifth up 2 cents too close and the Fourth down too open.  As
this interval of 2 cents lies on the very boundary of perception by ear, the
difficulty of tuning thus without attending to the beats is enormous.  The above
figures show how very close an approximation is now possible in pianofortes." Ellis
(p485). 

In this I am in more agreement with Ellis than Jorgensen. I doubt if tuning by only
fourths and fifths I could come that close. If this is closer to Werkmiester than ET
I would be interested to know why.        ric