Holder on the "Holdrian comma"

Holder discusses it, but attributes it to Nicolas Mercator.

First he says Mersenne computes the number of commas in an octave as a
little more than 58.5; how Mersenne came up with that I have no idea.
Then he says Mercator figured out that the number of commas in an
octave is a touch over 55, which is also kind of screwed up, as the
number of 81/80s to an octave is 55.7976. However, Mercator also
discussed what he called an "artificial comma", 1/53 of an octave exactly.

Holder then gives a table of 5-limit intervals and how many steps they
encompass in 53-et. Aside from the comma business, at least one other
thing looks interesting, which are names for intervals.

----- Original Message -----
From: "Gene Ward Smith" <gwsmith@svpal.org>
To: <tuning@yahoogroups.com>
Sent: 21 Aral�k 2005 �ar�amba 6:54
Subject: [tuning] Holder on the "Holdrian comma"

> Holder discusses it, but attributes it to Nicolas Mercator.
>
> First he says Mersenne computes the number of commas in an octave as a
> little more than 58.5; how Mersenne came up with that I have no idea.

20.5 cent commas? That's funny. Almost as if advocating 59-tET. Should have
been 51.151 if it is a question of the Pythagorean comma.

> Then he says Mercator figured out that the number of commas in an
> octave is a touch over 55, which is also kind of screwed up, as the
> number of 81/80s to an octave is 55.7976.

55.7976305 to be precise.

However, Mercator also
> discussed what he called an "artificial comma", 1/53 of an octave exactly.
>

So, it seems that we are correct when we Turks refer to it as the
Mercator/Holder comma.

> Holder then gives a table of 5-limit intervals and how many steps they
> encompass in 53-et. Aside from the comma business, at least one other
> thing looks interesting, which are names for intervals.
>
>

Thank you very much for the summary Gene.
Cordially,
Oz.

On Wed, 21 Dec 2005, Gene Ward Smith wrote:
>
> Holder discusses it, but attributes it to Nicolas Mercator.
>
> First he says Mersenne computes the number of commas in an octave as a
> little more than 58.5; how Mersenne came up with that I have no idea.
> Then he says Mercator figured out that the number of commas in an
> octave is a touch over 55, which is also kind of screwed up, as the
> number of 81/80s to an octave is 55.7976. However, Mercator also
> discussed what he called an "artificial comma", 1/53 of an octave exactly.
>
> Holder then gives a table of 5-limit intervals and how many steps they
> encompass in 53-et. Aside from the comma business, at least one other
> thing looks interesting, which are names for intervals.

Gene,

Thanks for giving us the facts, so we can settle
the issue: The 'Holder komasi' of the Turkish
musicians is, properly, a 'Mercator comma'.

With regards to the interval names, does Holder
have any names for intervals whose later names
conflict with? If so, perhaps his names should
take some kind of precedence.

Regards,
Yahya

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