Temperament nomenclature

[Jason Kanter]

Once upon a time...

First there was "Pythagorean" or "just" tuning, favoring perfect fifths and
consequently with very noisy major thirds. Music didn't use major thirds
much. If you tune perfect fifths (and fourths) CGDAE, you wind up with a CE
major third that is 21.5 cents expanded, as opposed to the 13.7 cents
expanded that we are so accustomed to in our equal temperament. These major
thirds are called "Pythagorean".

Then, early Renaissance, musical sensibility in Europe flip-flopped and
composers started experimenting with "sweet" major thirds (just/pure or at
least a lot slower-beating than the Pythagorean third). Note - to tune a
perfect 5:4, beatless major third, where CE is pure, you therefore have to
narrow all four of the fifths CGDAE substantially (averaging about 5 cents
narrow, as compared to the 1.96 cents narrow that we are now accustomed to).
There developed a number of variations called "meantone" tuning. Generally,
eight of the 12 major thirds in meantone were tuned to be pretty clean, --
but the remaining four thirds (usually BD#, F#A#, C#F, and AbC) were
unplayably harsh (some expanded by 40 cents or more), and one of the fifths
(usually AbEb) was very wide (actually a diminished sixth) and such a
horrible sound that it was called the "wolf".

Then as keyboard instruments evolved, composers wanted to be able to play in
more than 8 major and 8 minor keys, so they started experimenting first with
what is now called "modified meantone" (nine playable keys) and then "well
temperament" (12 playable keys). Basically, still keeping the CE third
cleaner and sweeter than the other thirds, tuners of "well temperament" took
meantone's four harsh thirds down to a maximum of 21.5 cents expanded (e.g.
adopted the "Pythagorean third" as the limit of tolerability) and
distributed the remaining harshness among the remaining thirds, keeping the
"white" keys sweeter at the expense of the black keys. This kind of tuning
produced a distinctive "key color" that was also used consciously by
composers in the 18th-19th centuries. Over time, from Bach's era to the
early 20th century (when the math for tuning Equal Temperament was first
solidified and a reliable ET bearing plan was first developed), the
differences between the sweetest third and the harshest third were gradually
reduced, but the key color remained, even though it got fainter as we
advanced into the Victorian era.

This whole story is told in Jorgensen's "big red" book called TUNING, and
many of the historic temperaments are also graphed (with short explanatory
excerpts from Jorgensen) in my website, www.rollingball.com. The graphs make
it easier to see at a glance what is going on in a given temperament.

"Broadwood's Best" is the legacy of a scientific experiment conducted in
1885 by Ellis, who invited seven tuners to tune various instruments (pianos,
a harmonium and an organ), analyzed their tunings with a complex set of
scientific instruments, and concluded that although there was much talk
throughout the 19th century of "equal temperament", no one was able to
actually tune it in 1885. Two of the tuners he used for this were sent by
the Broadwood factory, one referred to as a "usual" tuner and the other as
"Broadwood's best" tuner. (This tuner may have been Chopin's personal tuner
as well.) A third tuner was from Moore & Moore, and his tuning is now
referred to as the "Moore" or the "representative Victorian" temperament.
Ellis recorded this experiment in the appendix to Helmholtz' book, "On the
Sensation of Tone" -- and Jorgensen "corrected" Ellis's figures based on
assumptions/deductions about loose tuning pins, etc. The offsets that are
noted on my website and also included in the sets of historic temperaments
that are included with all the ETDs are taken primarily from Jorgensen.

Hope this helps. I write from memory and may have some of the minor details
wrong -- Ed Foote or others, please correct me -- but I believe this is
pretty accurate.

Jason Kanter

-----Original Message-----
From: pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org] On Behalf
Of Michael Gamble
Sent: Saturday, May 14, 2005 12:48 PM
To: Jon Page; pianotech@ptg.org
Subject: Re: Temperament nomenclature

Hello Jon and List
>From the land that built Broadwoods I've never heard of "Broadwood Best" . 
Is this a recognised temperament? I recognise "Young" but "Young 
WTemperament" .... "Young Temperament" is similar to "Vallotti Temperament".

If you say "Young Well Temperament" would you also say "Vallotti Well 
Temperament". So what is "Well" ?? All this is making me feel 
(un)well....:-(    - Then how about Equwell Temperament? :-)
Regards from a darkening Sussex Village
Michael G.(UK)
----- Original Message ----- 
From: "Jon Page" <jonpage@comcast.net>
To: "Michael Gamble" <michael@gambles.fsnet.co.uk>
Sent: Saturday, May 14, 2005 6:26 PM
Subject: Re: Tuner Recommendation


> >Jon - What IS WT and Broadwood Best?? These wretched acronyms...I guess 
> >ET = =temperament.. Non?
>>Michael G.(UK)
>
>
> Michael.
> ET is Equal Temperament.  WT is Well Temperament.
> Broadwood Best is a WT (Broadwood Factory, c.1885).
> Milder than Young WT but stronger than Thos. Moore WT.
>
> Best Regards,
>
> Jon Page
>
> 


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