43 EDO

I've been looking at Merides/43EDO, and taken a peek at Monz' pages. Is
it me or can 43EDO be reasonable to the 15-limit? I know 7/4 is a bit
off, but I just wondered if there were any tolerances on 7/4 to
indicate if 973.9¢ was 'close enough'? To me it's sufficiently close to
be 'acceptable', in the way that temperament represent ji 'acceptably'

Anyone used 43EDO at all - not just as a meantone?

Mark

hi Mark,

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:

> I've been looking at Merides/43EDO, and taken a peek
> at Monz' pages. Is it me or can 43EDO be reasonable to
> the 15-limit? I know 7/4 is a bit off, but I just wondered
> if there were any tolerances on 7/4 to indicate if 973.9¢
> was 'close enough'? To me it's sufficiently close to
> be 'acceptable', in the way that temperament represent
> ji 'acceptably'.

well ... thanks to your questions, i've added a nice fat
juicy graphic to the bottom of my "meride" page showing
the cents and %-edo-step errors of 43edo from the 11-limit
tonality-diamond ratios:

http://sonic-arts.org/dict/meride.htm

haven't looked at 13- or 15-limit, but there you have
it for 11.

> Anyone used 43EDO at all - not just as a meantone?

i'm pretty sure that Marc Jones has used it, especially
"not as a meantone", and probably Brian McLaren as well.

sorry i don't have more details, but those two have
explored a large number of EDOs in their compositions.

-monz

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:

> I've been looking at Merides/43EDO, and taken a peek at Monz'
pages. Is
> it me or can 43EDO be reasonable to the 15-limit?

i would answer yes, but with a very important caveat: it's only
consistent through the 7-limit. So for 9-limit or higher consonant
chords, you will find that the best approximations of the just
consonances don't always fit together into semblances of the just
chords you expect them to.

> I know 7/4 is a bit
> off, but I just wondered if there were any tolerances on 7/4 to
> indicate if 973.9¢ was 'close enough'?

it's of course a function of context, duration, timbre, loudness,
etc., but yes, absolutely. it's with ratios of 9 that you begin to
get into ambiguities in 43-equal.

> Anyone used 43EDO at all - not just as a meantone?

yes, i've used it as an 'escapade' tuning -- actually what i was
using was every other note of 43-equal, so it repeats every 2
octaves . . .

Hi guys for the bits and pieces. I did think that 9-limit (as a meantone 43 confounds 9/8 10/9 so there would be problems there), but I'll post a list of the 8ve repeating scales for 43 soon, as part of my studies into scale patterns. Being a prime EDO, every difference between pitch-classes is a generator, so there's quite an interesting selection out there.

Mark

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
> Hi guys for the bits and pieces. I did think that 9-limit (as a
> meantone 43 confounds 9/8 10/9 so there would be problems there),

That's not the problem -- i see nothing wrong with confounding ratios
as long as other notes in the chord can clarify the context --
rather, the difficulty is that, while there appear to be acceptable
approximations to 4:7, 7:9, and 4:9 (35, 16, and 50 steps of 43-
equal, respectively), they don't combine as they would in just
intonation to produce a 4:7:9 triad (since 35 + 16 does not equal
50). This is the 'consistency' issue i've been harping on for over
six years now.

> but
> I'll post a list of the 8ve repeating scales for 43 soon, as part
of my
> studies into scale patterns. Being a prime EDO, every difference
> between pitch-classes is a generator, so there's quite an
interesting
> selection out there.

non-prime EDO suffer no paucity in this regard -- many temperaments
such ETs belong to simply turn out to have a period which is 1/2 or
1/3 or 1/4 . . . octave instead of 1 octave. For example meantone
derives from 81:80 (the syntonic comma) vanishing, but if you have
2048:2025 (the diaschisma) vanish instead, you end up with a period
of 1/2 octave and the diaschismic family of scales that includes 10,
12, 22, 34, etc. Then if you dislike the 'atonal' or 'polytonal' feel
of the most obvious scales derived in this way, simply make some
chromatic alterations and you end up with something less ambiguous-
sounding -- and sometimes even omnitetrachordal!