"David Webber" <dave@[EMAIL PROTECTED]
> a écrit dans le message
de
news: ftnt9n$bgk$1$8300dec7@[EMAIL PROTECTED]
>
> "Alain Naigeon" <anaigeon@[EMAIL PROTECTED]
> wrote in message
> news:47feae51$0$2694$426a74cc@[EMAIL PROTECTED]
>> "David Webber" <dave@[EMAIL PROTECTED]
> a écrit dans le
message
>> de
>> news: ftkfs7$8iq$1$830fa79d@[EMAIL PROTECTED]
>
>>> Sorry if I missed this is in another answer. Apart from
mathematical
>>> reasons, the strongest musical reason is the V-I cadence. For
example
>>> chord-of-G -> chord-of-C. If you're in the key of C this sounds like
a
>>> particularly good "finish" (so good that it is known as a "perfect
>>> cadence") and has been around for hundreds of years.
>>
>> Well, it was, IMHO, not as frequent as it became later, and
nevertheless
>> the
>> "circle" of fifths was used to build the Pythagorean scale used in
these
>> times.
>
> Except that Pythagoras found it was a spiral of 5ths <g>
That's what I meant with my quotes ;-)
- it was only with
> tempered scales that it became a circle
I think "tempered" is done for several different reasons.
Changing the spiral into a circle is one of them (Pythagore's comma).
But then you have still to make a decision, for instance, about which
kind of major third you wish : syntonic and enharmonic commas.
Their names may vary from one author to another, but the former one
is, of course, the discrepancy between the 5/4 third and the 4th fifth,
(81/80), and the latter one is the difference between three 5/4 thirds
and the octave (125/128).
What I mean is that the size of the fifth results from all these choices,
not only from forcing the closure of the spiral.
> But building a scale from frequency ratios 3^m/2^n is what I regard as a
> "mathematical" exercise.
Well, they've been writing mathematical music for hundred years :-)
--
Français *==> "Musique renaissance" <==* English
midi - facsimiles - ligatures - mensuration
http://anaigeon.free.fr
| http://www.medieval.org/emfaq/anaigeon/
Alain Naigeon - anaigeon@[EMAIL PROTECTED]
- Oberhoffen/Moder, France
|
