Re: Tanaka and the Kleisma

[John Chalmers TD258.1]
>Tanaka defined the Kleisma (Greek for lid or lock) as 6 minor thirds
>(6/5) down and a further 4/3 down, the interval between c# and fb (with
>a bar over the f in his notation), the ratio 15625/15552 or 8.107+
>cents. See Tanaka,Shohe'. 1890. "Studien im Gebiet der reinen
>Stimmung." pp. 1-90, _in_ Vierteljahrsschrift fuer Musikwissenschaft,
>Friedrich Chrysander, Philipp Spita and Guido Adler, eds., Leipzig.
>Pages 8-18 of this work were excerpted and translated by Daniel J. Wolf
>and appeared in Xenharmonikon 16.

Thanks heaps for that John.

Can Dan Wolf, or someone with Xenharmonikon 16, please tell us briefly what
it's about, what Tanka used the kleisma for, and if and how it relates to
the current discussion on chain-of-minor-thirds scales.

Babel Fish translates the title as "Studies in the area of the pure
tendency" (not terribly enlightening) and the journal as 'Quarterly
Publication for Music Science'.

-- Dave Keenan
http://dkeenan.com

David!
BTW there is a diagram at the end of
http://www.anaphoria.com/hanson.html that shows the Kleisma. Sorry the page
takes a while to load!

David C Keenan wrote:

>
>
> Can Dan Wolf, or someone with Xenharmonikon 16, please tell us briefly what
> it's about, what Tanka used the kleisma for, and if and how it relates to
> the current discussion on chain-of-minor-thirds scales.
>
> Babel Fish translates the title as "Studies in the area of the pure
> tendency" (not terribly enlightening) and the journal as 'Quarterly
> Publication for Music Science'.
>
> -- Dave Keenan
> http://dkeenan.com
>
>

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

I would rather translate Tanaka's title as "Studies in the area of just
intonation".
Heinz Bohlen

[Dave Keenan, TD 259.2]
>
> [John Chalmers TD258.1]
>> See Tanaka,Shohe'. 1890. "Studien im Gebiet der reinen
>> Stimmung." pp. 1-90, _in_ Vierteljahrsschrift fuer
>> Musikwissenschaft, Friedrich Chrysander, Philipp Spita and
>> Guido Adler, eds., Leipzig.
>
> <snip>
>
> Babel Fish translates the title as "Studies in the area of the
> pure tendency" (not terribly enlightening) and the journal as
> 'Quarterly Publication for Music Science'.

'Reinen Stimmung', in this context, is the German idiomatic
expression which means 'just-intonation'. The title of the
article could be translated adequately into English as 'Studies
in the field of just-intonation'.

'Musikwissenschaft' likewise means something like 'the science
of music', referring to technical aspects of music, as opposed
to a publication which would focus on more poetic aspects.

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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Dave: Tanaka used the kleisma (along with the skhisma) to define a
53-tone scale in 3x5 JI and notate it by using kleismatic and skhismatic
equivalences.

He also built an instrument to play the tuning. See Ellis's appendices
to Helmholtz for details.

Reine Stimmung is German for "pure tuning," aka JI.

Siemen Terpstra seems to have independently discovered the kleisma when
he studied large arrays of 5-limit intervals and notation.

--John