Re: Moving on [to Cameron and others]
- --- In firstname.lastname@example.org, Mike Battaglia <battaglia01@...> wrote:
>Basically, the way something is used, not just the stuff from which it is made. Using the ditone of 41-edo would be a different modality, for example, and it would not effect "magic temperament". Even using the Just approximations of 41-edo, there is an enormous amount of music which would not implement "magic" in a tangible way.
> On Thu, Mar 1, 2012 at 2:50 AM, lobawad <lobawad@...> wrote:
> > --- In email@example.com, "Keenan Pepper" <keenanpepper@> wrote:
> > >
> > > --- In firstname.lastname@example.org, "lobawad" <lobawad@> wrote:
> > >
> > > Uh... a far cry from what? I don't understand the question.
> > > It seems like you're saying that once somebody uses an equal
> > > >temperament, we should also give them credit for every higher-rank
> > > >temperament consistent with it. For example if somebody uses 31tet >to
> > > approximate the 7 limit, then we should give them credit for >cynder, for
> > > valentine, for miracle... simply because they used a >temperament in which
> > > the appropriate commas vanish. Is this not what >you're saying?
> > >
> > > Keenan
> > A far cry "from 3125/3072 or "five major thirds make a perfect twelfth"",
> > your own words.
> > Were 41-edo not wielded with the appropriate modalities, "3125/3072 or
> > "five major thirds make a perfect twelfth"" would indeed be a far cry away,
> > or, better said, these things would be deeply buried.
> Can you define "modality?"
>Not that I know of. As far as I know, that is a happy accident. One thing he did say, between the lines, was that tempering out the syntonic comma was not a concern for him.
> Did Janko ever say specifically that he wanted to use 41-EDO because
> 3125/3072 vanishes in it?
>Nowhere did I say that. I said "the earliest implementation", nothing about discovery or even intent (I even added "by happy accident, it seems" to make that clear).
> > As far as questions of "credit", the most appropriate response to that is
> > "WTF?". Effecting a temperament, probably by accident, doesn't constitute
> > having created one of the systems which are called "temperaments" here.
> I agree, but you seemed above to be saying the opposite; that Janko
> gets credit for discovering magic because he used 41-EDO.
It is appropriate modalities (music of Janko's time provides plenty of these) applied to 41-edo that bring the temperament tempering-out-the-difference-between-P12-and-five-M3's to life.
>I don't know. Whether or not he did consider doing so, he chose not to temper it out.
> > If we want to give "credit" for first thinking of "magic", we'd have to give it
> > Helmholtz, as he seems to be the first to describe 3072:3125 as the fifth
> > less 5 major thirds.
> Yeah, but did he ever consider tempering that comma out?
Once again I suggest that you read older literature for yourself. It is dripping with interesting things.
- kraiggrady <kraiggrady@...> wrote:
> I have uploadedThe link shows that Wilson was still looking at the
> this document which is not yet cataloged in the archives
> [i will probably add to the treasure section at some
> point] http://anaphoria.com/PartchMappedTo41.pdf if you
> look especially on page 6 even though the document was
> done in 2001 he references Secor. So in this case i think
> George might be giving more credit elsewhere than maybe
> he should.
Cassandra/Schismatic (29&41) mapping. There's something to
be said for that because it maps the 43 notes of the Genesis
scale to 41 distinctly tempered notes with the only
ambiguity being the unavoidable one from 11/10 and 10/9
mapping to the same pitch. This means we have to ignore
100:99. (Two notes disappear because each pitch occurs
with its octave complement.)
You may recall that each of the 43 pitches is distinct in
Miracle (31&41) temperament. For the earlier Exposition on
Monophony scale, these 43 distinct pitches are included in
the first 45 Miracle generated pitches.
I've been looking at the ambiguous 41 note temperings
again. The coincidence of 43 just pitches mapping to a 41
note MOS doesn't hold with Cassandra and the Exposition
scale. 49/48 maps to 29 fifths.
To get exactly 41 tempered pitches, a rank 2 mapping has to
be consistent with 41-equal and temper out 100:99. It must
have an 11-limit complexity of no more than 20. The
highest complexity for an 11-limit pitch will then be 20
generators from the 1/1. Each pitch occurs with its octave
complement in the diamond, and the 11-limit diamond is a
subset of either Partch scale, so there will be 40
generators between these two worst-case pitches. 40
generators means 41 pitches.
The only mappings that comply with these conditions are
those for Cassandra, Octacot (31&27e), and Magic (19&22).
It turns out that Octacot needs 57 generated notes to
approximate either 43 note scale. But Magic needs exactly
41 for either scale. So both scales correspond to
periodicity blocks that detemper the 41 note Magic MOS with
two ambiguous pairs of pitches. Only Magic works like this
for both scales. Only Magic and Cassandra work like this
for either scale.
The discrepancy between the Genesis and Exposition scales
amounts to an interval of 245:243. Tempering out 245:243
is the same as ignoring the difference between the two
scales. Combining this with the 100:99 that allows us to
fit the 11-limit diamond into 41 pitches is consistent with
The most accurate are Bohpier (41&8d), Magic, Octacot, and
Varan (41&5e). This is another way of producing a shortlist
that includes Magic.