reversed text/score accidentals (was: Notation individualists)

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 6:13 PM
> Subject: [tuning] Re: Notation individualists
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_33858.html#33973
>
> >
> > oddly enough, Dave's exactly right about this too.
> > even tho my theory and notation is all based on
> > prime-factorization, looking back on my scores and
> > theoretical writings now i can see that i've always
> > done it the way he says too: by decreasing size in cents
> > (text) and increasing size (score).
> >
> > i wonder why we like the positions reversed like that?
> > it would be interesting to investigate that.
> >
> >
>
> ***Monz, this is interesting, but I want to know a little bit more
> about it. You're saying modifiers of a note start with the largest
> cent value modifiers and then put the smaller ones next, yes?
>
> But, what's the bit about the *size* again? I'd like to follow this.

i mean "cents values" when i say "size".

in other words:

a typical 72edo note might be Eb< in both of our notations.
this is a "sixth-low minor 3rd", or "slm3" i believe is the
current term.

well here's the breakdown of all the different symbols:

assuming that we're reading from left to right:

1)
the letter-name indicates the generator number. in
72edo, the generator could be several different intervals,
most likely either 700 cents (the "5th"), 100 cents
(the "semitone") or 116&2/3 cents (the "secor").

just for the sake of simplicity, let's assume that
the "5th" generation is implied. so this is like
counting "5ths" in 12edo, which lots of musicians
do all the time.

so if C=1/1 is our reference, and this is a closed
cyclic system modulo 72 (and cents is closed modulo 1200),
then the "E" part of Eb< indicates a movement from the
reference C either upward by 4 * 700 mod 1200 = 400 cents
= 4 * 6 mod 72 = 24 degrees of 72edo; or downward by
8 * 700 mod 1200 = 800 cents = 8 * 6 mod 72 = 48 degrees
of 72edo.

so "E" = "+" 2^(24/72) = "-" 2^(48/72)
= + 400 cents = - 800 cents .

and mod 1200, -800 = +400 anyway.

2)
the next symbol to the right is b. this indicates
a "chromatic" alteration by a semitone = 100 cents.

so you see so far, the letter-name indicates either
+400 or -800 cents, the b symbol indicates -100 cents,
a much smaller value.

3)
the last symbol on the right is the < symbol, which
indicates an intonational inflection downward by 1/6-tone
from the unaltered note.

this interval is 2 degrees of 72edo = 2^(2/72) =
33&1/3 cents.

so:

E b <
+ 400 - 100 - 33&1/3 cents = 267&2/3 cents

you can see how the "size" or "cent value" of each
symbol decreases as you read to the left.

in writing a score, it's exactly the opposite, for
some reason i don't know. the example would be
written < b E, but with a notehead for the E instead
of the letter.

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
> a typical 72edo note might be Eb< in both of our notations.
> this is a "sixth-low minor 3rd", or "slm3" i believe is the
> current term.

Err. An Eb< is a note, not an interval, so it can't be a sixth-low
minor anything!

> well here's the breakdown of all the different symbols:
>
> assuming that we're reading from left to right:
>
> 1)
> the letter-name indicates the generator number. in
> 72edo, the generator could be several different intervals,
> most likely either 700 cents (the "5th"), 100 cents
> (the "semitone") or 116&2/3 cents (the "secor").

What are you smokin' Monz? :-)

The letter name has nothing to do with generators and everything to do
with fifths (or their octave inversions and equivalents).

> From: dkeenanuqnetau <d.keenan@uq.net.au>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 10:31 PM
> Subject: [tuning] Re: reversed text/score accidentals (was: Notation
individualists)
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > a typical 72edo note might be Eb< in both of our notations.
> > this is a "sixth-low minor 3rd", or "slm3" i believe is the
> > current term.
>
> Err. An Eb< is a note, not an interval, so it can't be a sixth-low
> minor anything!

ok, so i put the "so if C=1/1 is our reference" bit later
instead of here where it should be.

so, i f C=1/1 is our reference, Eb< is a "sixth-low minor 3rd"
from that. is that better?

>
> > well here's the breakdown of all the different symbols:
> >
> > assuming that we're reading from left to right:
> >
> > 1)
> > the letter-name indicates the generator number. in
> > 72edo, the generator could be several different intervals,
> > most likely either 700 cents (the "5th"), 100 cents
> > (the "semitone") or 116&2/3 cents (the "secor").
>
> What are you smokin' Monz? :-)

hey, can't afford the good stuff! :)

> The letter name has nothing to do with generators and everything
> to do with fifths (or their octave inversions and equivalents).

ok, i didn't express that as clearly as i should have.

but in 72edo, the "5th" can also be a generator, which creates
a closed 12-tone subset (= 12edo) with enharmonic equivalents,
which is only 1 of the 6 bicycle chains of 72edo.

but with that enharmonic equivalence, 1 of those chains still
provides all 21 of the Pythagorean-based notes of 7 letters,
7 sharps, and 7 flats. in the HEWM and Sims/Maneri notations,
the other 60 degrees of 72edo must employ the other accidentals.

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_34067.html#34067

>
> in writing a score, it's exactly the opposite, for
> some reason i don't know. the example would be
> written < b E, but with a notehead for the E instead
> of the letter.
>

****Thanks, Monz, for clarifying this... Well, that was simple
enough. My guess is that, since there are *rhythmic* qualifiers,
like dots and double dots after notes, traditionally, the accidentals
couldn't go there...

It would be interesting to trace the notational history of all this,
since there obviously *is* one. That would also be a cool Monz web
page...starting with the 4-line staff, neumes, etc., etc., etc. with,
of course, the *tuning* implications...

Well, just a thought...

best,

Joe

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_34067.html#34070

> The letter name has nothing to do with generators and everything to
do with fifths (or their octave inversions and equivalents).

***So, if I'm understanding this correctly, Dave, what you're saying
is that the "letter names" we are using in our 72-tET system, being
Pythagorean-based, are only *coincidental* to the Miracle system and
the generator. But since they *do* coincide, it enables us to use
this "historically established" letter-naming practice... with
some "alterations..."

??

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> /tuning/topicId_34067.html#34070
>
>
> > The letter name has nothing to do with generators and everything
to
> do with fifths (or their octave inversions and equivalents).
>
> ***So, if I'm understanding this correctly, Dave, what you're saying
> is that the "letter names" we are using in our 72-tET system, being
> Pythagorean-based, are only *coincidental* to the Miracle system and
> the generator. But since they *do* coincide, it enables us to use
> this "historically established" letter-naming practice... with
> some "alterations..."
>
> ??
>
> JP

I don't see that there is any particular coincidence. It has been
forced because that's what you wanted. The coincidence is that 12-tET
is a subset of 72-tET which is an excellent Miracle ET.