[tuning] BASIC: What was temperament again? (was: True nature of the blackjack scale (in 7-limit) . . . and more epimores)

Paul Erlich schrieb:
>

> Confused? Maybe it would help to add that the good old diatonic scale
> in 5-limit is the result of forming a periodicity block with the
> unison vectors 81:80 and 25:24; treating 81:80 as a commatic unison
> vector and tempering it out; and treating 25:24 as a chromatic unison
> vector and not tempering it out.
>

Whereas I think I can follow the rest in a (vague enough) way, this
seems puzzling. How is the 5-limit diatonic scale tempered? By
_pretending_ there is no difference between 9/8 and 10/9 (of 4/3 and
27/20)?

Klaus

--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:
> Paul Erlich schrieb:
> >
>
> > Confused? Maybe it would help to add that the good old diatonic
scale
> > in 5-limit is the result of forming a periodicity block with the
> > unison vectors 81:80 and 25:24; treating 81:80 as a commatic
unison
> > vector and tempering it out; and treating 25:24 as a chromatic
unison
> > vector and not tempering it out.
> >
>
> Whereas I think I can follow the rest in a (vague enough) way, this
> seems puzzling. How is the 5-limit diatonic scale tempered? By
> _pretending_ there is no difference between 9/8 and 10/9 (of 4/3 and
> 27/20)?
>
> Klaus

Hi Klaus. I meant the diatonic scale of Western musical practice,
since the advent of 5-limit harmony in the late 15th century. All
_practical_ tuning systems for this music have tempered out the
81:80. There is no difference between 9/8 and 10/9, not only
physically in these tunings, but also conceptually in the music
itself, that is, 99% of the common-practice and Renaissance
repertoire. This point has been made exceptionally well by Daniel
Wolf here in the past.

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, June 06, 2001 11:15 AM
> Subject: [tuning] Re: BASIC: What was temperament again?
> (was: True nature of the blackjack scale (in 7-limit) . . . and more
epimores)
>

>
> Hi Klaus. I meant the diatonic scale of Western musical practice,
> since the advent of 5-limit harmony in the late 15th century

Hi Paul. I think it would be preferable to say
"... since the predominance of 5-limit harmony...".

There's absolutely no doubt that the Babylonians (c. 1500 BC)
and probably the Sumerians (as far back as 3000 BC) used 5-limit
tuning systems, and most likely 5-limit remained a part of
popular or folk musical practice all over Europe and Asia
from such remote times.

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
> There's absolutely no doubt that the Babylonians (c. 1500 BC)
> and probably the Sumerians (as far back as 3000 BC) used 5-limit
> tuning systems, and most likely 5-limit remained a part of
> popular or folk musical practice all over Europe and Asia
> from such remote times.
>
>
>
> -monz
> http://www.monz.org
> "All roads lead to n^0"
>

Isn't there a lot of doubt about these numbers? I know that one
tablet has been controversly interpreted as being in pythagorean, but
thats an interpretation (based on tuning fifths) without any ratios
in the source.

Xavier

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> There's absolutely no doubt that the Babylonians (c. 1500 BC)
> and probably the Sumerians (as far back as 3000 BC) used 5-limit
> tuning systems,

Absolutely no doubt? Care to back that up?