Modern historical temperaments, was Re: If

[Michael Jorgensen]

Hi Carl,
    I agree with all that Ed Foote says and had a few thoughts to add if
you can bare them!  They are inserted below.

Carl Root wrote:

> A good temperament has been defined as as one that does not favor any
> key signatures or any intervals, ie there is a constant rate of increase
> of beat rates as you go up the scale.  So we have agreed on what a good
> temperament is.
> 
> Yes, this assumes that we are talking about equal temperament.

IMHO a good temperament is any historical or Equal which is accurately
tuned.  A good temperament system is one that does not have any harmonic
waste. (i.e all tempering of intervals result in atleast an equal total
benefit to other intervals affected).  

 I would be interested in knowing how tuners who tune historical
> temperaments deal with the the issue of determining how an oddly scaled
> piano will affect beat rates of all or just some intervals.

IMHO uneven scaling affects both equal and historical temperaments in a
simular way.  Both must be fudged or bent to work over uneven
inhormonicity terrain inorder to create the closest possible resemblance
to the theoretically correct versions of either.    


> I guess I am concerned that this interest in historical temperaments in
> the last few years could lead to newcomers to our profession deciding
> that the ability to set an equal temperament by aurally measuring each
> piano's inharmonicity is not really important.  Just invent your own
> modern historical temperament and off you go.  No one will notice.

EEK! Some will notice!  Historical temperaments are not guesswork but
require careful following of directions of a published or carefully
thought out temperament.  Trying to tune Just Intonation (which is not
really a temperament since no notes are altered) should work without
directions, but tempered systems require that one know what they are
doing otherwise alot of harmonic waste will occur.  All professionals
should know how to tune an equal temperament as IMHO it is about the
hardest to tune.
-Mike Jorgensen