Macintosh temperament

Macintosh, it seems uses 3072-edo for music. This therefore joins 768,
49152 (pitch bend) and 196608 (MIDI tuning standard) as a tuning
system chosen for technical reasons.

By the sheer luck of the draw, it is a better-than-average 3 and 5
limit system. In the 5-limit, it can be completely characterized as
the temperament tempering out both the atom of Kirnberger, |161 -84
-12>, and the whoosh comma, |37 25 -33>. It's actually a poptimal
tuning for whoosh temperament, and in fact the smallest such tuning,
but unfortunately that does not extend nicely to the 7-limit. The most
interesting of the 7-limit commas is the landscape comma, 250047/250000.

Maybe whoosh would be better named macintosh?

On 2/2/06, Gene Ward Smith <genewardsmith@coolgoose.com> wrote:
> Macintosh, it seems uses 3072-edo for music. This therefore joins 768,
> 49152 (pitch bend) and 196608 (MIDI tuning standard) as a tuning
> system chosen for technical reasons.
>
> By the sheer luck of the draw, it is a better-than-average 3 and 5
> limit system. In the 5-limit, it can be completely characterized as
> the temperament tempering out both the atom of Kirnberger, |161 -84
> -12>, and the whoosh comma, |37 25 -33>. It's actually a poptimal
> tuning for whoosh temperament, and in fact the smallest such tuning,
> but unfortunately that does not extend nicely to the 7-limit. The most
> interesting of the 7-limit commas is the landscape comma, 250047/250000.
>
> Maybe whoosh would be better named macintosh?

That's so ridiculous. I love it. I can't believe there are names for
all these things.

BTW my Yamaha SY77 uses 1024-edo, which has very good fifths but
that's about it.

Keenan

--- In tuning-math@yahoogroups.com, Keenan Pepper <keenanpepper@...>
wrote:

> BTW my Yamaha SY77 uses 1024-edo, which has very good fifths but
> that's about it.

That's getting into the slightly cheesy range, I think. The most
salient tuning fact seems to be that the parakleismic comma, |8 -14
13>, gets tempered out. The corresponding temperament has a low enough
complexity that it could be used in live music. 19 notes would be one
choice, but a 23 note MOS is a more exotic idea and besides has more
triads.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In tuning-math@yahoogroups.com, Keenan Pepper <keenanpepper@>
> wrote:
>
> > BTW my Yamaha SY77 uses 1024-edo, which has very good fifths but
> > that's about it.
>
> That's getting into the slightly cheesy range, I think. The most
> salient tuning fact seems to be that the parakleismic comma, |8 -14
> 13>, gets tempered out. The corresponding temperament has a low enough
> complexity that it could be used in live music. 19 notes would be one
> choice, but a 23 note MOS is a more exotic idea and besides has more
> triads.
>

As per your original statement:

>> Macintosh, it seems uses 3072-edo for music.
>> This therefore joins 768, 49152 (pitch bend) and
>> 196608 (MIDI tuning standard) as a tuning system
>> chosen for technical reasons.

1024-edo should join those as well. It was used not
only on the SY-77, but on a whole slew of other Yamaha
instrumnets as well. I have an entry for it in the
Encyclopedia, where i call it the "yamaha unit".

BTW, we also have those pseudo-Greek names for the
other four, altho i prefer to abbreviate the Greek
numerical prefix with regular numerals:

6mu = hexamu = 768-edo
8mu = oktamu = 3072-edo
12mu = dodekamu = 49152-edo
14mu = tetradekamu = 196608-edo

-monz
http://tonalsoft.com
Tonescape microtonal music software