Wendy Galovich wrote:
This is obvious if you're going to break the tempered scale down to that
degree.
Comment:
1. What is obvious?
2. I didn't break anything down. The ratio 1.059 is by definition the
interval of a semitone in the equal tempered scale. More about this
later.
Anselm Lingnau wrote:
This is also to do with the fact that the twelfth-root-of-two (or 1.059)
ratio applies to' physically ideal' strings that have no diameter. If
you look at a piano with the various lids and covers off you will find
that this is obviously not true, especially for the bass notes. It turns
out that a piano tuning must be `stretched' somewhat for the piano to
sound in tune with itself on account of these deviations, and good piano
tuners are supposed to cater for this.
Comment:
'Physically ideal' strings requires definition and all strings have a
diameter. See below also.
The following are two quotes taken from firstly "Intervals, Scales and
Temperment by Lewelyn Lloyd. Lloyd was an advisor to "Groves Dictionary
of Music", a twenty volume publication considered by many the "bible" of
music. In a foreword to the book a Mr. Kenneth Van Barthold, who was a
professional pianist, a teacher of the pianoforte at Trinity College of
Music and head of the music department at the City Literary Institute.
On the subject of 'pitch' or intonation he writes:
"What has happened is that the keyboard has come to be the arbiter of
intonation. Many a singer is brought up suddenly by a bang on the piano.
But piano intonation equivocates; the sounds are impure, many of the
overtones lost or damped on purpose, and every interval except the
octave out of tune [and many octaves are 'stretched' for added
brilliance]. This then is the arbiter we use; more, it is for many
students their first contact with the quality and classification of
tonal intervals and harmonics. The dangers to the sensitivity of the ear
are obvious.
" We cannot put the clock back. Equal temperment provides the most
effective compromise so far discovered. It is ignorance of the nature of
this compromise which is inexcusable, as is the assumption that it
should dictate to our ears where it has no right [e.g.in string playing
and singing].This means, Wendy, that if the Connecticut and
Massachusetts fiddlers were doing what you have said they are doing,
i.e., playing in the tempered scale, they would be playing every note
except the octave out of tune.
My second quote is on the same subject and is taken from the book "My
Viola and I" written by Liomel Turtis. Turtis was one of the greatest
violists of this century and a noted string teacher. He writes:
"Perfect intonation is the rock-foundation of the string player's
equipment........Faulty intonation in most cases is the result of utter
carelessness,.........Most of us who profess to play a string instrument
have 'good ears', that is sensitive to true intonation, and what is
more, most of us are capable of discerning and attaining this. But how
many do not...... A 'good ear' can become permanently perverted by
negligent, superficial, non-penetrative listening on the part of the
performer. This inattention to one's faculty of hearing is a vice of
such rapid growth that in a very short time the player accepts faulty
intonation with equanimity, eventually becoming quite unconscious that
he is playing out of tune".......A note infinitesimally flat or sharp
lacks the rich, round, penetrative, lucious sound that only a note
perfectly in tune will give you".
Alexander
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