back to list

27/26?

🔗genewardsmith <genewardsmith@juno.com>

2/11/2002 10:45:22 PM

Another thing it would be nice to agree on is what symbol we should use for 27/26. Any thoughts on that? Even for so simple a thing as
22-et it would be handy to have, and it lets us push on to 13.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/11/2002 11:50:38 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> Another thing it would be nice to agree on is what symbol we should
use for 27/26. Any thoughts on that? Even for so simple a thing as
> 22-et it would be handy to have, and it lets us push on to 13.

I don't even want to know why you'd want to use a tridecimal-comma to
notate 22-tET (when it isn't even 13-limit consistent).

What are the simplest ET and linear temperament for which you'd really
feel a _need_ for such a symbol, say to avoid having more than one
accidental (in addition to # or b) on any note?

I get 87-tET and 121-tET as the simplest 13-limit-consistent ETs where
the number of steps required for 26:27 is different from those
required for 80:81 (^v), 63:64 (<>), 32:33 ([]) and different from the
difference between any of these and the number of steps required for
2048:2187 (b#). But this could well be wrong. I'm not too confident of
the validity of some of my shortcuts.

I can't say I've heard anyone express any great interest in composing
in these ETs. Do they define a temperament we've ever heard of?

But it seems that the Sims notation could be extended to 13-limit by
adding another "flag" to the quarter-tone (undecimal diesis) symbols
in the way the quarter-tone symbols add flags to the sixth-tone
(septimal comma) symbols. I think this could be done in such a way as
not to introduce left-right or 2-3 confusability (or even 1-2
confusability).

🔗genewardsmith <genewardsmith@juno.com>

2/12/2002 12:16:09 AM

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

> > Another thing it would be nice to agree on is what symbol we should
> use for 27/26. Any thoughts on that? Even for so simple a thing as
> > 22-et it would be handy to have, and it lets us push on to 13.
>
> I don't even want to know why you'd want to use a tridecimal-comma to
> notate 22-tET (when it isn't even 13-limit consistent).

Because I think symbols for one and two 2-et steps would be nice, and the idea is to have the symbol set for a temperament be a reduced version of a symbol set for some p-limit. In the case of 22-et, we have 81/80 and 33/32 mapping to 1, and 64/63 to 0. Sharps and flats aren't doing us a lot of good, since 2187/2048 maps to 3 and using
16/15 or 15/14 gets us off into something not a subset of the general system. While 13 is not very well mapped by 22, if we had a symbol for 27/26 it would reasonably be mapped to 2 and thus serve us as our hoped-for 2 step symbol.

The idea is to get the symbolism used in various temperaments to correspond, rather than to fight each other. We *could* use # and b for two steps, but that would set up contradictions with other uses.

> What are the simplest ET and linear temperament for which you'd really
> feel a _need_ for such a symbol, say to avoid having more than one
> accidental (in addition to # or b) on any note?

By my way of thinking, 22 can already use it.

> But it seems that the Sims notation could be extended to 13-limit by
> adding another "flag" to the quarter-tone (undecimal diesis) symbols
> in the way the quarter-tone symbols add flags to the sixth-tone
> (septimal comma) symbols. I think this could be done in such a way as
> not to introduce left-right or 2-3 confusability (or even 1-2
> confusability).

Actually it can be extended farther than that.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/12/2002 1:12:26 AM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > I don't even want to know why you'd want to use a tridecimal-comma
to
> > notate 22-tET (when it isn't even 13-limit consistent).
>
> Because I think symbols for one and two 2-et steps would be nice,

Even coming from you, I have to assume you really mean 22-tET here,
not 2-tET. :-)

>and the idea is to have the symbol set for a temperament be a reduced
version of a symbol set for some p-limit.

Sure.

> In the case of 22-et, we
have 81/80 and 33/32 mapping to 1, and 64/63 to 0. Sharps and flats
aren't doing us a lot of good, since 2187/2048 maps to 3
>

I don'tr understand why you say "Sharps and flats aren't doing us a
lot of good"

> and using
> 16/15 or 15/14 gets us off into something not a subset of the
general system.

Yeah, forget that.

> While 13 is not very well mapped by 22, if we had a
symbol for 27/26 it would reasonably be mapped to 2 and thus serve us
as our hoped-for 2 step symbol.
>

What a kludge.

> The idea is to get the symbolism used in various temperaments to
correspond, rather than to fight each other. We *could* use # and b
for two steps, but that would set up contradictions with other uses.
>

No. 3 steps it must be.

> > What are the simplest ET and linear temperament for which you'd
really
> > feel a _need_ for such a symbol, say to avoid having more than one
> > accidental (in addition to # or b) on any note?
>
> By my way of thinking, 22 can already use it.

By my way of thinking 2 steps is adequately notated as #v and b^.

> > But it seems that the Sims notation could be extended to 13-limit
by
> > adding another "flag" to the quarter-tone (undecimal diesis)
symbols
> > in the way the quarter-tone symbols add flags to the sixth-tone
> > (septimal comma) symbols. I think this could be done in such a way
as
> > not to introduce left-right or 2-3 confusability (or even 1-2
> > confusability).
>
> Actually it can be extended farther than that.

Very likely, but why do we care?

🔗genewardsmith <genewardsmith@juno.com>

2/12/2002 1:41:21 AM

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

> Even coming from you, I have to assume you really mean 22-tET here,
> not 2-tET. :-)

Maybe you should say "especially coming from me" given my dubious
proof-reading skills and the fact that I should get a new keyboard, having spilled coffee on this one.

> I don'tr understand why you say "Sharps and flats aren't doing us a
> lot of good"

Do we really want to notate a C-major tonic triad as C-D#-G rather than C-Ev-G?

> > While 13 is not very well mapped by 22, if we had a
> symbol for 27/26 it would reasonably be mapped to 2 and thus serve us
> as our hoped-for 2 step symbol.
> >
>
> What a kludge.

It's not really so much of a kludge if a 13-limit symbol is already a part of the system.

🔗jpehrson2 <jpehrson@rcn.com>

2/12/2002 8:32:41 AM

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

/tuning/topicId_34071.html#34080

> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > > I don't even want to know why you'd want to use a tridecimal-
comma
> to
> > > notate 22-tET (when it isn't even 13-limit consistent).
> >
> > Because I think symbols for one and two 2-et steps would be nice,
>
> Even coming from you, I have to assume you really mean 22-tET here,
> not 2-tET. :-)
>

****Perhaps some of you will recall the *entire opera* written by Tom
Johnson of Village Voice repute, that used only *four* notes. (from
our 12-tET set, though...)

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/12/2002 10:52:36 AM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > I don't understand why you say "Sharps and flats aren't doing us
a
> > lot of good"
>
> Do we really want to notate a C-major tonic triad as C-D#-G rather
than C-Ev-G?
>

Certainly not. Try this notation for 22-tET. No need for a 13-limit
accidental.

D
D^
Eb^
Ev
E
F
F^
F#v
Gv
G
G^
G#v or Ab^
Av
A
A^
Bb^
Bv
B
C
C^
C#v
Dv
D

There certainly are ETs that require accidentals for other than 80:81,
63:64, 32:33 in order to notate them with monotonic letters and no
repeated accidentals and no more than 2 accidentals, but 22-tET isn't
one of them. How about 26,27,28,30,32,37.

See my attempts in
http://dkeenan.com/Music/NotatingETs.xls.zip

You will notice that I now agree with you about using <> instead of []
for 31-tET.

I don't think we should use a set of comma-accidentals for an ET
unless that set's primes (or maybe odds) (including 3) form a
Hahn-consistent set for that ET.

🔗paulerlich <paul@stretch-music.com>

2/12/2002 12:42:55 PM

i've never been able to evoke the 13th harmonic in 22-equal. what am
i missing?

🔗genewardsmith <genewardsmith@juno.com>

2/12/2002 12:53:27 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

> i've never been able to evoke the 13th harmonic in 22-equal. what am
> i missing?

Probably nothing. I think a naming scheme with a symbol for two 22-et
steps would be nice, but Dave has a workable version which uses # and
b instead. I think 22-et is basically an 11-limit system.

🔗genewardsmith <genewardsmith@juno.com>

2/12/2002 12:59:17 PM

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

> You will notice that I now agree with you about using <> instead of []
> for 31-tET.

Progress! Now can you explain why f and j for 33/32? I would have picked } and { myself, but perhaps you think that would be too similar to ] and [?

> I don't think we should use a set of comma-accidentals for an ET
> unless that set's primes (or maybe odds) (including 3) form a
> Hahn-consistent set for that ET.

Why wouldn't being in good enough tune that it actually sounds something like the JI version do?

🔗paulerlich <paul@stretch-music.com>

2/12/2002 1:06:23 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > i've never been able to evoke the 13th harmonic in 22-equal. what
am
> > i missing?
>
> Probably nothing. I think a naming scheme with a symbol for two 22-
et
> steps would be nice, but Dave has a workable version which uses #
and
> b instead. I think 22-et is basically an 11-limit system.

and what a simple one too! twenty-two! twenty-two! (my girlfriend is
twenty-two)

🔗genewardsmith <genewardsmith@juno.com>

2/12/2002 1:19:14 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

twenty-two! twenty-two! (my girlfriend is
> twenty-two)

Just don't give her a complex about turning 23--if you tell her that's half of 46, I'm sure she'll feel better about it.

🔗genewardsmith <genewardsmith@juno.com>

2/12/2002 1:31:37 PM

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

> I don't think we should use a set of comma-accidentals for an ET
> unless that set's primes (or maybe odds) (including 3) form a
> Hahn-consistent set for that ET.

I note that even though you have a symbol for 27/26, you are adverse to using it. For the 27-et, {3,5,13} fits your criterion, and notating it by D D^ Df Ej Ev E looks like a good solution to me.

🔗paulerlich <paul@stretch-music.com>

2/12/2002 1:37:16 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> twenty-two! twenty-two! (my girlfriend is
> > twenty-two)
>
> Just don't give her a complex about turning 23--if you tell her
>that's half of 46, I'm sure she'll feel better about it.

actually, one of the nice things about 46 is that it's got 23 in it,
and that's great for pelog!

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/12/2002 6:37:15 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > You will notice that I now agree with you about using <> instead
of []
> > for 31-tET.
>
> Progress! Now can you explain why f and j for 33/32? I would have
picked } and { myself, but perhaps you think that would be too similar
to ] and [?
>

These were for 26:27, not 32:33, as I expect you know. There was not a
great deal of thought behind them. I was imagining a pair of
extended-Sims-type accidentals where an extra slanted stroke is added
to each of the quarter-tone symbols. Then I looked for ASCII
characters to suggest this. {} may be better for ASCII, so long as we
are not also using (). However, I am yet to be convinced of the need
for a symbol for 26:27 in notating ETs less than 72, although it would
solve a problem with 20-tET.

There seem to be several requirements for accidentals other than
v^<>[] in ETs less than 72, which cannot be solved by adding symbols
for 26:27.

From 30-tET onwards we often want a symbol for a single step and none
of our commas, (or any pair of them) gives it to us.

Both Paul Rapoport and George Secor seem to have an unacceptably high
number of new symbols. Rapoport seems to have 10 pairs that are
considered essential. How many pairs George? We're trying to do it
with only 3 new pairs and now we're learning what some of the problems
are. Reinventing helps in understanding other people's wheels. But we
should certainly push the only-3-extra-pairs idea as far as it will
go. I figured out 26-tET. It's a similar solution to 22-tET, with G#>
= Ab<. 20, 25, 27, 28, 30-tET are still problematic. See the latest
version of
http://dkeenan.com/Music/NotatingETs.xls.zip

> > I don't think we should use a set of comma-accidentals for an ET
> > unless that set's primes (or maybe odds) (including 3) form a
> > Hahn-consistent set for that ET.
>
> Why wouldn't being in good enough tune that it actually sounds
something like the JI version do?

Because if it is inconsistent, then there are at least two equally
valid but different ways of notating the same ET with the same
symbols. Ambiguity is bad.

Ideally, any comma that disappears should have its prime included in
the consistent set too.

🔗genewardsmith <genewardsmith@juno.com>

2/12/2002 7:30:39 PM

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

> Both Paul Rapoport and George Secor seem to have an unacceptably high
> number of new symbols.

I propose one symbol pair per prime (counting octave numbers as a symbol pair). That is sufficient, and for JI also necessary.

> > Why wouldn't being in good enough tune that it actually sounds
> something like the JI version do?
>
> Because if it is inconsistent, then there are at least two equally
> valid but different ways of notating the same ET with the same
> symbols. Ambiguity is bad.

So pick one mapping and stick with it.

🔗genewardsmith <genewardsmith@juno.com>

2/12/2002 7:49:06 PM

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
I figured out 26-tET. It's a similar solution to 22-tET, with G#>
> = Ab<. 20, 25, 27, 28, 30-tET are still problematic. See the latest
> version of
> http://dkeenan.com/Music/NotatingETs.xls.zip

I think my proposal solves 27 nicely; I haven't looked at the rest.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/12/2002 8:29:58 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > I don't think we should use a set of comma-accidentals for an ET
> > unless that set's primes (or maybe odds) (including 3) form a
> > Hahn-consistent set for that ET.
>
> I note that even though you have a symbol for 27/26, you are adverse
to using it. For the 27-et, {3,5,13} fits your criterion, and notating
it by D D^ Df Ej Ev E looks like a good solution to me.

Let's use {} instead of jf.

Yes. This is where the additional criterion I mentioned makes me
uneasy about that solution. Namely that the 7-comma vanishes so it
should be included in the consistent set if it is less than some other
prime in the set. 27-tET is 3-5-7 consistent and 3-5-13 consistent but
not 3-5-7-13 consistent. Maybe this is just getting too picky?

Another reason is that I wanted the 3 chains of fifths to be spelled
correctly. And 5 is way more important than 13.

Dv Av Ev Bv F#v C#v G#v D#v A#v
Bb F C G D A E B F#
Gb^ Db^ Ab^ Eb^ Bb^ F^ C^ G^ D^

But this gives non-monotonic letters.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/12/2002 9:33:39 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > Both Paul Rapoport and George Secor seem to have an unacceptably
high
> > number of new symbols.
>
> I propose one symbol pair per prime (counting octave numbers as a
symbol pair). That is sufficient,

Since there is an infinite number of primes, I don't doubt it. ;-) The
question is how many primes do we need to notate all ETs less than say
96-tET? And will those primes always be meanigful or will they
sometimes just be a kludge to get us the number of steps we need? I
think that invoking 17 for anything less than 72-tET is out of the
question.

But if we're to be consistent in having our accidentals always
representing commas, we need a comma that will come out as fewer steps
than the ones we've got. What about using some other 3-5 commas like
Rapoport does, like the diesis 125:128 or diaschisma, 2025:2048?

> and for JI also necessary.

Yes.

> > > Why wouldn't being in good enough tune that it actually sounds
> > something like the JI version do?
> >
> > Because if it is inconsistent, then there are at least two equally
> > valid but different ways of notating the same ET with the same
> > symbols. Ambiguity is bad.
>
> So pick one mapping and stick with it.

Pick which one, and why? And how will the reader know? I say, do this
only as a last resort.

🔗genewardsmith <genewardsmith@juno.com>

2/13/2002 12:23:17 AM

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

> But if we're to be consistent in having our accidentals always
> representing commas, we need a comma that will come out as fewer steps
> than the ones we've got. What about using some other 3-5 commas like
> Rapoport does, like the diesis 125:128 or diaschisma, 2025:2048?

Now you're contradicting what I thought was one of the criteria, rather than the other way around. Isn't it desirable to have a unique spelling for JI?

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/13/2002 9:55:46 AM

Hi Dave,

----- Original Message -----
From: "David C Keenan" <d.keenan@uq.net.au>
To: "D.Stearns" <stearns@capecod.net>
Sent: Tuesday, February 12, 2002 10:16 PM
Subject: Re: [tuning] Re: 27/26?

> At 00:45 13/02/02 -0800, you wrote:
> >Hi Dave,
> >
> >Just a quick hello to say that you are, as usual, doing some nice
work
> >here.
>
> Thanks Dan,
>
> It's lovely to receive such a note from you.
>
> I'd prefer to say _we're_ doing some nice work here. I'm hoping that
what
> Gene and I are working on will come out giving the same results as
what you
> and Monz have been looking at, but possibly it won't. I don't have
time to
> follow up your line of thinking, but I encourage you to persue it or
to
> encourage Monz to persue it.

The difference is that I'm not looking at lower consistent tunings
like 20 as consistent JI sets relative to commas, but rather as
subsets of larger consistent tunings where their generators are
considered commensurate--here's the 20 out of 31 example I've been
using in Fokker interval names:

4 1 5 6 11 17
--, --, --, --, --, --, ...
7 2 9 11 20 31

perfect prime
augmented prime
minor second
major second
supra second
minor third
mean third
supra third
infra fourth
supra fourth
augmented fourth-diminished fifth
infra fifth
supra fifth
infra sixth
mean sixth
major sixth
infra seventh
minor seventh
major seventh
diminished octave
perfect octave

At least this way we don't have the confusions of 750ï¿½ 3/2s and 450ï¿½
5/4s as we would with a vis a vis JI based consistency notation. Of
course they'll be other problems, but is there a problem free 20-tet
notation that shoehorns the whole deal into the standard seven
alphabetized note names?

I haven't thought out this subset idea very far, so it's really just
something that I'm throwing out there at the moment because it seems
to have some promise. Could you do me a favor and explain your 20-tet
notation for me?

BTW, here's my old 12 shoehorned 20-tet--all sharps and flats are 120ï¿½
and all double sharps and flats are 180ï¿½.

C 0
F 8 G 12
Bb 16 D 3
Eb 5 A 15
Ab 13 E 7
Db 1 B 18
Gb 10 F# 10
Cb 18 C# 2
Fb 6 G# 14
Bbb 15 D# 5
Ebb 4 A# 17
Abb 12 E# 9
Dbb 0 B# 20

thanks,

--Dan Stearns

>
> >I haven't been keeping track so much, but I think I'm going to
start
> >trying a little harder.
>
> If you have time, it would be good if you could look at some of the
> proposed notations for some of the more obscure ETs you are familiar
with, in
> http://uq.net.au//~zzdkeena/Music/NotatingETs.xls.zip
>
> It's a zipped Excel spreadsheet. If you can't read that and would
like some
> other format, let me know.
>
> Warm Regards,
> -- Dave Keenan

🔗paulerlich <paul@stretch-music.com>

2/13/2002 12:27:55 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

> > Because if it is inconsistent, then there are at least two
equally
> > valid but different ways of notating the same ET with the same
> > symbols. Ambiguity is bad.
>
> So pick one mapping and stick with it.

this sucks major eggs, if you pardon the expression. i'm interested
in 76-equal precisely because different mappings are capable of
different things. i would never want to stick with just one.

🔗genewardsmith <genewardsmith@juno.com>

2/13/2002 1:50:32 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
>
> > > Because if it is inconsistent, then there are at least two
> equally
> > > valid but different ways of notating the same ET with the same
> > > symbols. Ambiguity is bad.
> >
> > So pick one mapping and stick with it.
>
> this sucks major eggs, if you pardon the expression. i'm interested
> in 76-equal precisely because different mappings are capable of
> different things. i would never want to stick with just one.

In that case, you should welcome the ambiguity, and be happy with more than one spelling.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/13/2002 4:17:01 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > But if we're to be consistent in having our accidentals always
> > representing commas, we need a comma that will come out as fewer
steps
> > than the ones we've got. What about using some other 3-5 commas
like
> > Rapoport does, like the diesis 125:128 or diaschisma, 2025:2048?
>
> Now you're contradicting what I thought was one of the criteria,
rather than the other way around. Isn't it desirable to have a unique
spelling for JI?

Hmm. Yes it is desirable. But that means strictly one comma (and hence
one pair of accidentals) per prime. So this is pushing me to accept
that some low number ETs may use some high prime accidentals which are
really meaningless in terms of actual usable approximations, but
merely fill in the gaps left by the meaningful primes.

I'm starting to come around to this, since I don't like the
alternative chosen by Rapoport. He uses symbols to represent 1/n of
his commas where n can be different for different ETs (typically n = 2
or 3). So they essentially act as symbols representing a single step
of the ET, something which, it seems to me, we should avoid.

I'm curious as to what George Secor proposes to do about these. So far
George, you've been notating the easy ones. How does your notational
semantics handle 20,25,27,28,30,32,37,42,44-tET. In most of these the
septimal comma vanishes and the syntonic comma and undecimal diesis
are the same size (1 or 2 steps) and the apotome (size of sharp or
flat) is 4 to 7 steps and is equal to, or nearly equal to, the size of
the whole tone (8:9). And so e.g. C# is way higher than Db and
therefore sharps and flats are next to useless if we wish to have
letters monotonic with pitch.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/13/2002 6:19:03 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> The difference is that I'm not looking at lower consistent tunings
> like 20 as consistent JI sets relative to commas, but rather as
> subsets of larger consistent tunings where their generators are
> considered commensurate--here's the 20 out of 31 example I've been
> using in Fokker interval names:
>
> 4 1 5 6 11 17
> --, --, --, --, --, --, ...
> 7 2 9 11 20 31
>
> perfect prime
> augmented prime
> minor second
> major second
> supra second
> minor third
> mean third
> supra third
> infra fourth
> supra fourth
> augmented fourth-diminished fifth
> infra fifth
> supra fifth
> infra sixth
> mean sixth
> major sixth
> infra seventh
> minor seventh
> major seventh
> diminished octave
> perfect octave
>
>
> At least this way we don't have the confusions of 750¢ 3/2s and 450¢
> 5/4s as we would with a vis a vis JI based consistency notation. Of
> course they'll be other problems, but is there a problem free 20-tet
> notation that shoehorns the whole deal into the standard seven
> alphabetized note names?

There are no 750 or 450 cent intervals in 20-tET, but I'll take it you
are referring to the fact that 20-tET is not 3,5-consistent. It is
however 3,7,11-consistent and 3,11,13-consistent.

> I haven't thought out this subset idea very far, so it's really just
> something that I'm throwing out there at the moment because it seems
> to have some promise. Could you do me a favor and explain your
20-tet
> notation for me?

20-tET is treated as 4 independent cycles of 720 cent fifths. Each
one notated as BC G D A EF but with accidentals to distinguish the
four chains. If you don't like the double-letters BC and EF then I'd
suggest just using C and E and you have to remember that E:C is a
fifth and C:E is a fourth. Yes it's messy however you do it. And
although 20-tET is not 3,5-consistent. It is 3,7,11-consistent and
3,11,13-consistent. It happens that the 3,7-comma vanishes while the
3,11-comma is 1 step and the 3,13-comma is 2 steps. I've come around
to accepting Gene's proposal that we should use the 11 and 13
accidentals for 20-tET, mainly because its 8:13 approximation is such
a good one (within 0.5 cent). So it looks like this.

D
D]
D}
EF[
EF
EF]
EF}
G[
G
G]
G}
A[
A
A]
A}
BC[
BC
BC]
BC}
D[
D

[On the web you'll need to do Message Index, Expand Messages to see
the following properly]

Here's an ASCII-grafix rendering of the Sims accidentals and some
possible extensions.

.
| /|\
| | v^ 80:81 ratios of 5
\|/ |
'

.
| /|
\ | / | <> 63:64 ratios of 7
\| |
'

/
/ .
| /|
\| | [] 32:33 ratios of 11
' /
/

/
/ .
\| /|
\| /| {} 26:27 ratios of 13
' /
/

\ /
\ / .
\| /|
\| /| jf 16:17 ??? ratios of 17
' / \
/ \

Gene, should the 3,17 comma be 16:17 or 17:18, or is there a smaller
(in cents) superparticular comma? And why do they need to be
superparticular? There's 2^12:3^5*17 and 2^7*17:3^7.

By going to higher primes we seem to be getting only larger commas.
How are we ever going to get the single-step commas we need for
notating many ETS above 30-tET?

But for 20-tET you can just read [] as -+60 cents and {} as -+120
cents.

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/13/2002 10:36:32 PM

Hi Dave,

The 750 threes and 450 fives were a reference to 8-tet specifically,
but the point was that consistency would spell these C-G and C-Ev,
which to my mind is a sarcasm!

Rather than thinking of 20-tet as being 3-consistent, I sometimes
prefer to think of there as a being a hole where the perfect fifth
should be, and instead you have the two fifths on either side of it,
the infra and supra fifths.

I don't think I fully understand your 20-tet notation. For instance,
you have D, D] and D} corresponding with 0, 60 and 120 cents. However,
according to your accidentals, the ] symbol means you raise D by a
33/32, which seems fine enough so far, but then } would mean you raise
D by a 27/26--how does this relate to 120 cents? I mean there's only
12ï¿½ between the two of them! Again, this seems to me one of those
consistency sarcasm... also, how would you write EF and BC on the
staff? It's all certainly interesting though, the no sharps and flats,
I like that. I guess I'll have to think about it all some more.

BTW, in the past I've posted RI interpretations of the 9- and 11-tone
scales in 20-tet based on some Augusto Novarro
like identities such as 11:13:15, and 13:16:19 and 17:21:25--note that
20-tet is consistent through:

11:13:15:17:19:21
13:16:19:22:25:28:31:34:37
17:21:25:29:33:37:41:45

take care,

--Dan Stearns

----- Original Message -----
From: "dkeenanuqnetau" <d.keenan@uq.net.au>
To: <tuning@yahoogroups.com>
Sent: Wednesday, February 13, 2002 6:19 PM
Subject: [tuning] Re: 27/26?

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> The difference is that I'm not looking at lower consistent tunings
> like 20 as consistent JI sets relative to commas, but rather as
> subsets of larger consistent tunings where their generators are
> considered commensurate--here's the 20 out of 31 example I've been
> using in Fokker interval names:
>
> 4 1 5 6 11 17
> --, --, --, --, --, --, ...
> 7 2 9 11 20 31
>
> perfect prime
> augmented prime
> minor second
> major second
> supra second
> minor third
> mean third
> supra third
> infra fourth
> supra fourth
> augmented fourth-diminished fifth
> infra fifth
> supra fifth
> infra sixth
> mean sixth
> major sixth
> infra seventh
> minor seventh
> major seventh
> diminished octave
> perfect octave
>
>
> At least this way we don't have the confusions of 750ï¿½ 3/2s and 450ï¿½
> 5/4s as we would with a vis a vis JI based consistency notation. Of
> course they'll be other problems, but is there a problem free 20-tet
> notation that shoehorns the whole deal into the standard seven
> alphabetized note names?

There are no 750 or 450 cent intervals in 20-tET, but I'll take it you
are referring to the fact that 20-tET is not 3,5-consistent. It is
however 3,7,11-consistent and 3,11,13-consistent.

D
D]
D}
EF[
EF
EF]
EF}
G[
G
G]
G}
A[
A
A]
A}
BC[
BC
BC]
BC}
D[
D

[On the web you'll need to do Message Index, Expand Messages to see
the following properly]

Here's an ASCII-grafix rendering of the Sims accidentals and some
possible extensions.

.
| /|\
| | v^ 80:81 ratios of 5
\|/ |
'

.
| /|
\ | / | <> 63:64 ratios of 7
\| |
'

/
/ .
| /|
\| | [] 32:33 ratios of 11
' /
/

/
/ .
\| /|
\| /| {} 26:27 ratios of 13
' /
/

\ /
\ / .
\| /|
\| /| jf 16:17 ??? ratios of 17
' / \
/ \

Gene, should the 3,17 comma be 16:17 or 17:18, or is there a smaller
(in cents) superparticular comma? And why do they need to be
superparticular? There's 2^12:3^5*17 and 2^7*17:3^7.

By going to higher primes we seem to be getting only larger commas.
How are we ever going to get the single-step commas we need for
notating many ETS above 30-tET?

But for 20-tET you can just read [] as -+60 cents and {} as -+120
cents.

------------------------ Yahoo! Groups
Sponsor ---------------------~-->
Get your FREE credit report with a FREE CreditCheck
Monitoring Service trial
http://us.click.yahoo.com/ACHqaB/bQ8CAA/ySSFAA/RrLolB/TM
---------------------------------------------------------------------~
->

You do not need web access to participate. You may subscribe through
email. Send an empty email to one of these addresses:
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning
group.
tuning-nomail@yahoogroups.com - put your email message delivery on
hold for the tuning group.
tuning-digest@yahoogroups.com - change your subscription to daily
digest mode.
tuning-normal@yahoogroups.com - change your subscription to
individual emails.
tuning-help@yahoogroups.com - receive general help information.

Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/

🔗genewardsmith <genewardsmith@juno.com>

2/13/2002 8:05:13 PM

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

> Gene, should the 3,17 comma be 16:17 or 17:18, or is there a smaller
> (in cents) superparticular comma? And why do they need to be
> superparticular? There's 2^12:3^5*17 and 2^7*17:3^7.

Since we are already using 2187/2048, clearly they don't need to be superparticular, and my way of coming at this problem has nothing to do with superparticular rations. If h5 and h7 are the "standard" vals mapping to the nearest integer for the various primes, and v5,v7,v11,v13,v17 and v19 are p-adic valuations, mapping p to 1 and every other prime to 0, then we may form the matrix of column vectors
[h5,h7,v5,v7,v11,v13,v17,v19] and invert it, obtaining
<2187/2048,256/243,80/81,33/32,26/27,4131/4096,513/512>. If instead we invert [h5,h7-v17,v5,v7,v11,v13,v17,v19] we obtain instead
<2187/2048,256/243,80/81,63/64,33/32,26/27,17/16,513/512>. Hence it seems it would be reasonable to pick either 4131/4096 (giving us another comma symbol) or 17/16 (giving us a new semitone symbol). Either way, we pick up 513/512 if we push on to the 19-limit, giving us a nice small interval.

> By going to higher primes we seem to be getting only larger commas.
> How are we ever going to get the single-step commas we need for
> notating many ETS above 30-tET?

I would guess 4131/4096 and 513/512 between them would do the trick.

🔗jpehrson2 <jpehrson@rcn.com>

2/13/2002 8:10:48 PM

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

/tuning/topicId_34086.html#34149

I'm happy to see extensions to the Sims system!

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/13/2002 9:55:12 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Hi Dave,
>
> The 750 threes and 450 fives were a reference to 8-tet specifically,
> but the point was that consistency would spell these C-G and C-Ev,
> which to my mind is a sarcasm!

I know what you mean and I agree.

The rule for when the "fifth" is unacceptable, is to notate N-tET as
every second note of 2N-tET, or every third note of 3N-tET if
necessary to get an acceptable fifth.

8-tET is notated as every 3rd note of 24-tET as

D
E[
F
G[
G# or Ab
A]
B
C]
D

Notating 20-tET as every second note of 40-tET we get

D
D>
E<
E
E>
Fb
F#
F#>
Gb
G#
G#> or Ab<
Ab
A#
Bb<
Bb
B#
C<
C
C>
D<
D

The # and b can also be read as your 11-comma (32:33) or your 13-comma
(26:27). You may prefer to use [] instead of b#.

Obviously 5-tET and 10-tET could be notated as every nth note of the
above too.

> Rather than thinking of 20-tet as being 3-consistent, I sometimes
> prefer to think of there as a being a hole where the perfect fifth
> should be, and instead you have the two fifths on either side of it,
> the infra and supra fifths.

Yes. The above gives you that doesn't it?

> I don't think I fully understand your 20-tet notation. For instance,
> you have D, D] and D} corresponding with 0, 60 and 120 cents.
However,
> according to your accidentals, the ] symbol means you raise D by a
> 33/32, which seems fine enough so far, but then } would mean you
raise
> D by a 27/26--how does this relate to 120 cents? I mean there's only
> 12¢ between the two of them!

Ok. Well it doesn't actually mean raise the D by 26:27 what it means
is that C:A{ is an approximate 8:13 because 3/2 * 3/2 * 3/2 * 26/27 =
13/8 (ignoring octaves). In this particular case, most of the actual
26:27 occurs in the 3 fifths, you might say.

> Again, this seems to me one of those
> consistency sarcasm... also, how would you write EF and BC on the
> staff?

Good question. Fortunately we don't have to answer it given the above
notation.

>It's all certainly interesting though, the no sharps and
flats,
> I like that.

Ok. Then you'll definitely substitute [] for b# above.

> I guess I'll have to think about it all some more.
>
> BTW, in the past I've posted RI interpretations of the 9- and
11-tone
> scales in 20-tet based on some Augusto Novarro
> like identities such as 11:13:15, and 13:16:19 and 17:21:25--note
that
> 20-tet is consistent through:
>
> 11:13:15:17:19:21
> 13:16:19:22:25:28:31:34:37
> 17:21:25:29:33:37:41:45

That's amazing!

Maybe we shouldn't assume cycles of fifths for a tuning unless it is
at least 3,9 consistent. That means we can't use 40-tET to get 20-tET,
but must go to 60-tET which is also of course 5*12-tET. In that case
we get the following notation for 20-tET, in which A-G,b,# are as for
12-tET, and v^ are -+20 cents, <> are -+40 cents.

D
Eb<
Eb^
Ev
E>
F
F#<
F#^
Gv
G>
G#
A<
A^
Bbv
Bb>
B
C<
C^
C#v
C#>
D

🔗paulerlich <paul@stretch-music.com>

2/13/2002 9:56:27 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

i don't think this is consistency sarcasm at all. i think the only
meaning ratios such as 33:32 and 27:26 have (at least, the only
meaning they have in this context) is in terms of chains of consonant
intervals, but when the consonant intervals are so far from ji, as in
20-equal, there's no reason to expect a 12¢ difference to remain
anything like a 12¢ difference.

for example, 2400:2401 is less than a cent, but it represents a
semitone difference in 12-equal -- when 2400:2401 is understood as it
would be in any context in which it is put forward as a comma.

🔗monz <joemonz@yahoo.com>

2/13/2002 10:49:01 PM

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, February 13, 2002 8:10 PM
> Subject: [tuning] Re: 27/26?
>
>
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> /tuning/topicId_34086.html#34149
>
> I'm happy to see extensions to the Sims system!
>
> JP

yuck.

(no disrepect intended towards Dave's labor or ideas
... it's the original premise i don't like) ;-b

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

🔗genewardsmith <genewardsmith@juno.com>

2/13/2002 11:00:26 PM

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

> (no disrepect intended towards Dave's labor or ideas
> ... it's the original premise i don't like) ;-b

I still don't see any semantic difference, so how do the premises differ?

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/14/2002 3:24:00 PM

Hi Dave,

Thanks, this is exactly what I was trying to get at with the subsets
of 31--using a temperament with a high consistency, reasonable errors
and a good notation to spell a temperament with a low consistency,
questionable errors and no notation, like 20:

Is there a good ascii Fokker--my feeling was to spell 31 as a subset
of 72? Does Fokker's 31 line up with your 72 note naming scheme?

I like your idea about not assuming cycles of fifths for a tuning
unless it's at least 1:3:9 consistent--though I'd say cycles of
perfect fifths or some such thing to avoid confusion as a tuning like
20-tet can be seen as a cycle of infra fifths. This seems like a step
in the right direction.

take care,

--Dan Stearns

----- Original Message -----
From: "dkeenanuqnetau" <d.keenan@uq.net.au>
To: <tuning@yahoogroups.com>
Sent: Wednesday, February 13, 2002 9:55 PM
Subject: [tuning] Re: 27/26?

I know what you mean and I agree.

The rule for when the "fifth" is unacceptable, is to notate N-tET as
every second note of 2N-tET, or every third note of 3N-tET if
necessary to get an acceptable fifth.

8-tET is notated as every 3rd note of 24-tET as

D
E[
F
G[
G# or Ab
A]
B
C]
D

Notating 20-tET as every second note of 40-tET we get

D
D>
E<
E
E>
Fb
F#
F#>
Gb
G#
G#> or Ab<
Ab
A#
Bb<
Bb
B#
C<
C
C>
D<
D

The # and b can also be read as your 11-comma (32:33) or your 13-comma
(26:27). You may prefer to use [] instead of b#.

Obviously 5-tET and 10-tET could be notated as every nth note of the
above too.

Yes. The above gives you that doesn't it?

> Again, this seems to me one of those
> consistency sarcasm... also, how would you write EF and BC on the
> staff?

Good question. Fortunately we don't have to answer it given the above
notation.

>It's all certainly interesting though, the no sharps and
flats,
> I like that.

Ok. Then you'll definitely substitute [] for b# above.

That's amazing!

D
Eb<
Eb^
Ev
E>
F
F#<
F#^
Gv
G>
G#
A<
A^
Bbv
Bb>
B
C<
C^
C#v
C#>
D

Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/

🔗gdsecor <gdsecor@yahoo.com>

2/14/2002 12:23:06 PM

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> >
> > > But if we're to be consistent in having our accidentals always
> > > representing commas, we need a comma that will come out as
fewer
> steps
> > > than the ones we've got. What about using some other 3-5 commas
> like
> > > Rapoport does, like the diesis 125:128 or diaschisma, 2025:2048?
> >
> > Now you're contradicting what I thought was one of the criteria,
> rather than the other way around. Isn't it desirable to have a
unique
> spelling for JI?
>
> Hmm. Yes it is desirable. But that means strictly one comma (and
hence
> one pair of accidentals) per prime. So this is pushing me to accept
> that some low number ETs may use some high prime accidentals which
are
> really meaningless in terms of actual usable approximations, but
> merely fill in the gaps left by the meaningful primes.
>
> I'm starting to come around to this, since I don't like the
> alternative chosen by Rapoport. He uses symbols to represent 1/n of
> his commas where n can be different for different ETs (typically n
= 2
> or 3). So they essentially act as symbols representing a single
step
> of the ET, something which, it seems to me, we should avoid.
>
> I'm curious as to what George Secor proposes to do about these. So
far
> George, you've been notating the easy ones. How does your
notational
> semantics handle 20,25,27,28,30,32,37,42,44-tET. In most of these
the
> septimal comma vanishes and the syntonic comma and undecimal diesis
> are the same size (1 or 2 steps) and the apotome (size of sharp or
> flat) is 4 to 7 steps and is equal to, or nearly equal to, the size
of
> the whole tone (8:9). And so e.g. C# is way higher than Db and
> therefore sharps and flats are next to useless if we wish to have
> letters monotonic with pitch.

So I'm notating the *easy* ones, huh? I thought I was notating the
*good* ones. I threw systems like these into my microtonal garbage
can during the first week or so that I spent investigating
microtonality (yes, rejected without a hearing, late in 1963), and
since that time I have never even entertained the thought of making a
trip to the microtonal junkyard to reclaim them. And I can't imagine
that the rest of the world might beat a path to anyone's door because
of any music made in them, either.

If I seem a bit narrow-minded by your standards, please understand
that I would rather invest my time and effort in those directions
that are most likely to have an impact on the non-microtonal world.

So in answer to your question: absolutely nothing!

--George

(Gee, answering that one was fun! Depending on how you look at it,
this place can be either a firing squad or a shooting gallery. Given
a choice between the two, I prefer the latter.)

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/14/2002 3:48:39 PM

Hi Paul,

Well that's why consistency as a notational device is of questionable
utility to my mind--when the consonant intervals are so far from JI,
as you said.

I think an idea like a set of symbols as -+ n-cents relative to
traditional spellings is going to be a lot easier for most reading
folks to get their mind around than a maze of JI
references--especially if deviations and relevant accumulated errors
make a mockery of what the ratios are understood to imply.

take care,

--Dan Stearns

----- Original Message -----
From: "paulerlich" <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, February 13, 2002 9:56 PM
Subject: [tuning] Re: 27/26?

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

i don't think this is consistency sarcasm at all. i think the only
meaning ratios such as 33:32 and 27:26 have (at least, the only
meaning they have in this context) is in terms of chains of consonant
intervals, but when the consonant intervals are so far from ji, as in
20-equal, there's no reason to expect a 12ï¿½ difference to remain
anything like a 12ï¿½ difference.

for example, 2400:2401 is less than a cent, but it represents a
semitone difference in 12-equal -- when 2400:2401 is understood as it
would be in any context in which it is put forward as a comma.

Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/

🔗genewardsmith <genewardsmith@juno.com>

2/14/2002 1:12:18 PM

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

> So I'm notating the *easy* ones, huh? I thought I was notating the
> *good* ones. I threw systems like these into my microtonal garbage
> can during the first week or so that I spent investigating
> microtonality (yes, rejected without a hearing, late in 1963), and
> since that time I have never even entertained the thought of making a
> trip to the microtonal junkyard to reclaim them.

If you really threw 27 into the garbage heap as well as 58, I think you'd better take a trip to the junkyard and reclaim them. :)

🔗jpehrson2 <jpehrson@rcn.com>

2/14/2002 8:03:34 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_34071.html#34207

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > (no disrepect intended towards Dave's labor or ideas
> > ... it's the original premise i don't like) ;-b
>
> I still don't see any semantic difference, so how do the premises
differ?

***The answer, with all respect to Monz... There are none.

He just likes arrows for 1/4 tones and *we* (or some of us) like
arrows for 1/12 tones.

I certainly think you were right, Gene (or maybe it was Dave) that
the *arrow* is such an obvious and readable symbol that it's bound to
come up as *some* kind of indicator.

Although arrows *do* have a history in the notation of quarter-tones,
the fact of the matter is that the little plusses and minuses for the
syntonic comma don't work, at least not on a score.

The "minuses" are particularly bad, since they could easily be
mistaken for an "accent" or "tenuto" mark. They also tend to "get
lost" above or below ledger lines.

Similarly, the "plusses" look like "left-handed pizzicato" for the
strings. And, those indications are excessively small.

Otherwise, *theoretically* they might be good, but from strictly
a "legibility" perspective I believe Sims are superior...

J. Pehrson

🔗gdsecor <gdsecor@yahoo.com>

2/15/2002 11:31:06 AM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > So I'm notating the *easy* ones, huh? I thought I was notating
the
> > *good* ones. I threw systems like these into my microtonal
garbage
> > can during the first week or so that I spent investigating
> > microtonality (yes, rejected without a hearing, late in 1963),
and
> > since that time I have never even entertained the thought of
making a
> > trip to the microtonal junkyard to reclaim them.
>
> If you really threw 27 into the garbage heap as well as 58, I think
you'd better take a trip to the junkyard and reclaim them. :)

And I think not. As I observed in my very first posting, life is
short, and, we must establish our priorities for ourselves.
Considering all of the music that has come out of the resources of a
12-tone octave, I believe that those tonal systems that I have judged
to be excellent would occupy me for many lifetimes, so that I have no
need to concern myself with others that I perceive as less worthy of
my time and effort.

You and your fellow "Scavengers" (which warm appellation I intend not
to be taken in any derogatory sense) are more than welcome to
these "treasures" that have been thoughtlessly discarded by myself
and others of like mind, even as Margo Schulter offered some very
beautiful words (re: microtonal "recycling"):

/tuning/topicId_34255.html#34255

And so the very essence of discovery, innovation, and creativity is
to see beauty or utility in those places where the rest of us pass
by, unaware of the possibilities.

--George

Love / joy / peace / patience / kindness / goodness ...

🔗genewardsmith <genewardsmith@juno.com>

2/15/2002 6:00:03 PM

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

> > If you really threw 27 into the garbage heap as well as 58, I think
> you'd better take a trip to the junkyard and reclaim them. :)

> And I think not. As I observed in my very first posting, life is
> short, and, we must establish our priorities for ourselves.
> Considering all of the music that has come out of the resources of a
> 12-tone octave, I believe that those tonal systems that I have judged
> to be excellent would occupy me for many lifetimes, so that I have no
> need to concern myself with others that I perceive as less worthy of
> my time and effort.

If you adopt that point of view, you need to be careful to do your discarding carefully. Given that 27 is one of the better 7-limit systems and 58 one of the relatively best systems for the 11, 13, 15 and 17 limits (making it comparable to 31, 41, 46 or 72 and in some respects better) it is not clear you have. It could be you are confining yourself to the 11-limit, but I don't see why that should be, or it could be you are systematically underestimating the value of systems with a strong tendency for primes to map either to the flat or sharp side.

> You and your fellow "Scavengers"

That appellation hardly applies to me, I don't know what others would think of it.

> And so the very essence of discovery, innovation, and creativity is
> to see beauty or utility in those places where the rest of us pass
> by, unaware of the possibilities.

I'm simply doing the mundane math here.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/16/2002 5:12:19 PM

This is an attempt to give a meaninful title to one strand of what
started as "notation mess" and has appeared under "27/26?" and
"Notation individualists".

I'm sorry I don't have time now to summarise where we've got to, but
here (in a zipped excel spreadsheet) is the latest version of my
attempt to apply the proposals of Gene Ward-Smith and Dan Stearns and
others to all the ETs from 5 to 41-tET, and selected ones up to
171-tET.

http://dkeenan.com/Music/NotatingETs.xls.zip

Please, anyone, let me know what you _don't_ like about any of these.
If you are interested, but can't read Excel files, email and I'll see
what I can do.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/16/2002 5:19:36 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Hi Dave,
>
> Thanks, this is exactly what I was trying to get at with the subsets
> of 31--using a temperament with a high consistency, reasonable
errors
> and a good notation to spell a temperament with a low consistency,
> questionable errors and no notation, like 20:
>
> perfect prime
> augmented prime
> minor second
> major second
> supra second
> minor third
> mean third
> supra third
> infra fourth
> supra fourth
> augmented fourth-diminished fifth
> infra fifth
> supra fifth
> infra sixth
> mean sixth
> major sixth
> infra seventh
> minor seventh
> major seventh
> diminished octave
> perfect octave
>
> Is there a good ascii Fokker--my feeling was to spell 31 as a subset
> of 72?

I think of the above as only a system for naming intervals, not
pitches. As such it is abbreviated as things like
P1 A1 m2 M2 SM2 m3 M3 SM3 s4 S4 A4/d5 etc.

> Does Fokker's 31 line up with your 72 note naming scheme?

Yes.

> I like your idea about not assuming cycles of fifths for a tuning
> unless it's at least 1:3:9 consistent--though I'd say cycles of
> perfect fifths or some such thing to avoid confusion as a tuning
like
> 20-tet can be seen as a cycle of infra fifths.

Good point.

> This seems like a step
> in the right direction.

OK. Great.

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

2/16/2002 5:26:49 PM

On 2/16/02 8:12 PM, "dkeenanuqnetau" <d.keenan@uq.net.au> wrote:

> Please, anyone, let me know what you _don't_ like about any of these.
> If you are interested, but can't read Excel files, email and I'll see
> what I can do.
>

I really have to get back on this list fulltime. I was doing this exact
thing a couple months ago, running through all the ET's I use and trying to
work out a notation for them. In Excel.

I'll have to dig mine up. This should be interesting, comparing. A LOT of
the things I came up with look similar at first glance.

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/16/2002 9:19:18 PM

Hi Dave,

I see that your 20-tet notation is identical to the miracle one I
posted yesterday. Just at a quick glance I thought 11-tet looked
funky, so I thought I'd pass this 11 out of 72 one by you:

9 2 11 13
--, --, --, --, ...
50 11 61 72

C Db^ D^ Eb> E> F[ G] Ab< A< Bbv Bv

72-tet seems a good bet to me to base these smaller, ornery
temperaments on, but I'll have to take a good look at your results to
see if the differences are for the better or not. How about we start
with 11-tet--is this 72 derived notation better than the 22 derived
one or not?

take care,

--Dan Stearns

----- Original Message -----
From: "dkeenanuqnetau" <d.keenan@uq.net.au>
To: <tuning@yahoogroups.com>
Sent: Saturday, February 16, 2002 5:12 PM
Subject: [tuning] Notating ETs with one comma per prime

> This is an attempt to give a meaninful title to one strand of what
> started as "notation mess" and has appeared under "27/26?" and
> "Notation individualists".
>
> I'm sorry I don't have time now to summarise where we've got to, but
> here (in a zipped excel spreadsheet) is the latest version of my
> attempt to apply the proposals of Gene Ward-Smith and Dan Stearns
and
> others to all the ETs from 5 to 41-tET, and selected ones up to
> 171-tET.
>
> http://dkeenan.com/Music/NotatingETs.xls.zip
>
> Please, anyone, let me know what you _don't_ like about any of
these.
> If you are interested, but can't read Excel files, email and I'll
see
> what I can do.
>
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
> Get your FREE credit report with a FREE CreditCheck
> Monitoring Service trial
> http://us.click.yahoo.com/ACHqaB/bQ8CAA/ySSFAA/RrLolB/TM
> --------------------------------------------------------------------
-~->
>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning
group.
> tuning-nomail@yahoogroups.com - put your email message delivery on
hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily
digest mode.
> tuning-normal@yahoogroups.com - change your subscription to
individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

🔗genewardsmith <genewardsmith@juno.com>

2/16/2002 7:09:56 PM

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

> Please, anyone, let me know what you _don't_ like about any of these.

I'm not wild about the double notes, such as EF. Do you start on D because of its central location? Also, I notice you've opted for
1053/1024, which goes with h5-v13, rather than 27/26, which pairs with h5. Is this because it's smaller, or does it simply work better?

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/16/2002 9:36:33 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > Please, anyone, let me know what you _don't_ like about any of
these.
>
> I'm not wild about the double notes, such as EF. Do you start on D
because of its central location? Also, I notice you've opted for
> 1053/1024, which goes with h5-v13, rather than 27/26, which pairs
with h5. Is this because it's smaller, or does it simply work better?

Smaller is nice, but also, as I said in another message (somewhere?),
I have an intuition that we will get a more acceptable notation if we
only use 1,3,p-commas that vanish in 12-tET, except when 12-tET is
1,3,p-inconsistent, like when p=11.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/16/2002 9:42:09 PM

Nor am I. Let's lose 'em. What would you prefer?

> Do you start on D because of its central location?

Absolutely. Because it is central in the chain of fifths, FCGDAEB.
Starting and ending on D gives us symmetrical notations. When there is
a middle note that could equally well be a modified A as a modified G,
the convention is to use the G.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/16/2002 9:50:21 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Hi Dave,
>
> I see that your 20-tet notation is identical to the miracle one I
> posted yesterday. Just at a quick glance I thought 11-tet looked
> funky, so I thought I'd pass this 11 out of 72 one by you:
>
> 9 2 11 13
> --, --, --, --, ...
> 50 11 61 72
>
> C Db^ D^ Eb> E> F[ G] Ab< A< Bbv Bv
>
> 72-tet seems a good bet to me to base these smaller, ornery
> temperaments on, but I'll have to take a good look at your results
to
> see if the differences are for the better or not. How about we start
> with 11-tet--is this 72 derived notation better than the 22 derived
> one or not?

It's hard for me to know what someone would want in an 11-tET notation
, since I don't know why anyone would want to use 11-tET, except to
maximise dissonance, or to use with a special inharmonic timbre.

How does 22-tET come out in your scheme.

I think your scheme is aimed at making the accidentals represent, as
close as possible, a constant deviation from 12-tET across all ETs,
whereas Gene's and mine and George Secor's and Manuel's and
Rappoport's etc. are aimed at telling you where the approximate JI
intervals are, in a consistent way across all ETs.

Now if we could come close to achieving both these aims at the same
time ...

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

2/16/2002 10:48:40 PM

On 2/17/02 12:42 AM, "dkeenanuqnetau" <d.keenan@uq.net.au> wrote:

>> Do you start on D because of its central location?
>
> Absolutely. Because it is central in the chain of fifths, FCGDAEB.

Kudos. I've been a "D" believer for quite many moons now. Notes get hairy
and symmetry gets far away from intuitive if you use C, I recall.

> Starting and ending on D gives us symmetrical notations. When there is
> a middle note that could equally well be a modified A as a modified G,
> the convention is to use the G.

Convention? I'm curious. Whose.

🔗genewardsmith <genewardsmith@juno.com>

2/16/2002 11:44:22 PM

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

> > I'm not wild about the double notes, such as EF.
>
> Nor am I. Let's lose 'em. What would you prefer?

If one is closer to D, why not pick that one?

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

2/16/2002 11:55:22 PM

On 2/17/02 2:44 AM, "genewardsmith" <genewardsmith@juno.com> wrote:

> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
>>> I'm not wild about the double notes, such as EF.
>>
>> Nor am I. Let's lose 'em. What would you prefer?
>
> If one is closer to D, why not pick that one?
>

D E G A C D?

🔗genewardsmith <genewardsmith@juno.com>

2/17/2002 12:59:28 AM

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> D E G A C D?

That doesn't look much like a circle of fifths to me. Why not
C G D A E?

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

2/17/2002 1:11:19 AM

On 2/17/02 3:59 AM, "genewardsmith" <genewardsmith@juno.com> wrote:

>> D E G A C D?
>
> That doesn't look much like a circle of fifths to me. Why not
> C G D A E?

Ehh I was just typing that, don't know why I sent it. I was thinking that
as opposed to D EF G A BC D, in 5 equal.

It's frightening to be able to type while asleep, or sleep while having eyes
open.

Nice to start and finish sentences. Mumble through the middle.

Yeah ... I was noticing for 5 equal I think, if you're looking to pick one
from the EF and BC, I'd go with E and C. Didn't mean to give a partial
answer out of turn or context.

Coffee.

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/17/2002 8:44:22 AM

Hi Dave,

Way back when I first started posting here I coined the EDO acronym
because I was tired of always having to look at tunings like 11, 13
and 20-EDO as temperaments relative to JI. The solution I was using
then was to notate everything in 144-EDO--why? Because I felt that if
performers could handle the Sims-Maneri 72 glyphs, then they could
probably handle the same glyphs with the simple addition of a
crosshatch as well. To my mind, 144-EDO would accurately approximate
every equal tuning that I was interested in as I felt 72-EDO was too
coarse. So 144-EDO was a notational tuning, and not so much a tuning
of special interest because of any acoustic property relative to JI,
such as 72-tet. To these ends, I still think this works very
effectively--I think the route you and George and Gene and Manuel (et
al) are taking is a more sophisticated shoehorn, but a shoehorn it
still is!

Here's the 22 out of 72 notation (where P = 600ï¿½):

5 4 9 13
--, --, --, --, ...
14 11 25 36

C Db] Db^ D< D^ Eb< Eb> EV E> Fv F[

BTW, 11-tet has a sweet and useful side without having to resort to
using it with a special inharmonic timbre or maximizing dissonance.
I've got one piece which I'm extremely happy with in 11-tet that I
will get somebody to convert to mp3 for me one of these days. It's
melodic and pretty but with just enough spice to sound fresh. To my
mind that's really the beauty of tunings like 11, 13 and 20-tet--the
alien spicing of consonances, and not the maximizing of dissonances!
Tunings like these made simple consonances not so simple and even
interesting again (for these ears anyway).

take care,

--Dan Stearns

----- Original Message -----
From: "dkeenanuqnetau" <d.keenan@uq.net.au>
To: <tuning@yahoogroups.com>
Sent: Saturday, February 16, 2002 9:50 PM
Subject: [tuning] Re: Notating ETs with one comma per prime

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> > Hi Dave,
> >
> > I see that your 20-tet notation is identical to the miracle one I
> > posted yesterday. Just at a quick glance I thought 11-tet looked
> > funky, so I thought I'd pass this 11 out of 72 one by you:
> >
> > 9 2 11 13
> > --, --, --, --, ...
> > 50 11 61 72
> >
> > C Db^ D^ Eb> E> F[ G] Ab< A< Bbv Bv
> >
> > 72-tet seems a good bet to me to base these smaller, ornery
> > temperaments on, but I'll have to take a good look at your results
> to
> > see if the differences are for the better or not. How about we
start
> > with 11-tet--is this 72 derived notation better than the 22
derived
> > one or not?
>
> It's hard for me to know what someone would want in an 11-tET
notation
> , since I don't know why anyone would want to use 11-tET, except to
> maximise dissonance, or to use with a special inharmonic timbre.
>
> How does 22-tET come out in your scheme.
>
> I think your scheme is aimed at making the accidentals represent, as
> close as possible, a constant deviation from 12-tET across all ETs,
> whereas Gene's and mine and George Secor's and Manuel's and
> Rappoport's etc. are aimed at telling you where the approximate JI
> intervals are, in a consistent way across all ETs.
>
> Now if we could come close to achieving both these aims at the same
> time ...
>
>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning
group.
> tuning-nomail@yahoogroups.com - put your email message delivery on
hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily
digest mode.
> tuning-normal@yahoogroups.com - change your subscription to
individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

🔗paulerlich <paul@stretch-music.com>

2/17/2002 2:00:22 PM

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...>
wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> >
> > > Please, anyone, let me know what you _don't_ like about
any of
> these.
> >
> > I'm not wild about the double notes, such as EF. Do you start
on D
> because of its central location? Also, I notice you've opted for
> > 1053/1024, which goes with h5-v13, rather than 27/26, which
pairs
> with h5. Is this because it's smaller, or does it simply work
better?
>
> Smaller is nice, but also, as I said in another message
(somewhere?),
> I have an intuition that we will get a more acceptable notation if
we
> only use 1,3,p-commas that vanish in 12-tET, except when
12-tET is
> 1,3,p-inconsistent, like when p=11.

but dave, i don't think a 1:3:13 chord exists in 12-equal at all,
consistency notwithstanding. and if 1:3:5:7:9:11:13 chords exist
in 12-equal, it is with a _different_ approximation of 13.

🔗paulerlich <paul@stretch-music.com>

2/17/2002 2:04:37 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> I've got one piece which I'm extremely happy with in 11-tet that I
> will get somebody to convert to mp3 for me one of these days.
It's
> melodic and pretty but with just enough spice to sound fresh.
To my
> mind that's really the beauty of tunings like 11, 13 and
20-tet--the
> alien spicing of consonances, and not the maximizing of
dissonances!
> Tunings like these made simple consonances not so simple
and even
> interesting again (for these ears anyway).
>
>
> take care,
>
> --Dan Stearns

as any 22-equal user will know, 11 gets you those great
4:7:8:9:11 chords.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/17/2002 2:25:19 PM

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> > Starting and ending on D gives us symmetrical notations. When
there is
> > a middle note that could equally well be a modified A as a
modified G,
> > the convention is to use the G.
>
> Convention? I'm curious. Whose.

In the meantone era, Eb to G# was more common than Ab to C#.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/17/2002 3:01:10 PM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
>
> > D E G A C D?
>
> That doesn't look much like a circle of fifths to me. Why not
> C G D A E?

Marc gave them in pitch order, as expected. But as Dan Stearns points
out, there aren't any perfect fifths in 5-tET, or in 10,20,25,30-tET,
so why pretend? 5,10 and 15-tET are all 1,3,9-consistent but their
1:3s and 1:9s are no better than 20-tET's. All of these, except
25-tET, can be notated as every nth note of 60-tET (5*12-tET), which
is 9-limit consistent. 5-tET then becomes

D E> Gv A^ C< D

So maybe we need to specify cutoffs on perfect-fifth size. I have
elsewhere attempted to define a wolf fifth as one for which a chain of
12 notes or less will generate a better fifth than those making the
chain. From 714.9 cents up to 720 cents (5-tET), a chain of 6 fifths
produces a better 2:3 than the fifths making up the chain. Similarly
from 689.3 cents down to 685.7 cents (7-tET), a chain of 8 fifths
produces a better 2:3 than the fifths making up the chain.

For example 47-tET just barely scrapes in with its 689.4 c fifth but
it fails the 1,3,9-consistency test and so should still be notated as
every second note of 94-tET.

What do you think of these proposed rules?

🔗paulerlich <paul@stretch-music.com>

2/17/2002 3:23:05 PM

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...>
wrote:
> > --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> >
> > > D E G A C D?
> >
> > That doesn't look much like a circle of fifths to me. Why not
> > C G D A E?
>
> Marc gave them in pitch order, as expected. But as Dan
Stearns points
> out, there aren't any perfect fifths in 5-tET, or in 10,20,25,30-tET,
> so why pretend? 5,10 and 15-tET are all 1,3,9-consistent but
their
> 1:3s and 1:9s are no better than 20-tET's. All of these, except
> 25-tET, can be notated as every nth note of 60-tET (5*12-tET),
which
> is 9-limit consistent. 5-tET then becomes
>
> D E> Gv A^ C< D
>
> So maybe we need to specify cutoffs on perfect-fifth size. I have
> elsewhere attempted to define a wolf fifth as one for which a
chain of
> 12 notes or less will generate a better fifth than those making
the
> chain. From 714.9 cents up to 720 cents (5-tET), a chain of 6
fifths
> produces a better 2:3 than the fifths making up the chain.
Similarly
> from 689.3 cents down to 685.7 cents (7-tET), a chain of 8 fifths
> produces a better 2:3 than the fifths making up the chain.
>
> For example 47-tET just barely scrapes in with its 689.4 c fifth
but
> it fails the 1,3,9-consistency test and so should still be notated
as
> every second note of 94-tET.
>
> What do you think of these proposed rules?

blackwood and other composers have shown that the 15-equal
perfect fifth is highly acceptable and consonant in triads with
'pastelized' timbres such as the classical guitar. i also like
678-cent fifths but generally need inharmonic timbres to pull
them off.

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

2/17/2002 5:03:48 PM

On 2/17/02 5:25 PM, "dkeenanuqnetau" <d.keenan@uq.net.au> wrote:

> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote: Starting and
> ending on D gives us symmetrical notations. When there is a middle note that
> could equally well be a modified A as a modified G, the convention is to use
> the G.
>
>> Convention? I'm curious. Whose.
>>
> In the meantone era, Eb to G# was more common than Ab to C#.
>

Oh thanks, that's so cool. I never knew that.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/17/2002 5:08:16 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Hi Dave,
>
> Way back when I first started posting here I coined the EDO acronym
> because I was tired of always having to look at tunings like 11, 13
> and 20-EDO as temperaments relative to JI. The solution I was using
> then was to notate everything in 144-EDO--why? Because I felt that
if
> performers could handle the Sims-Maneri 72 glyphs, then they could
> probably handle the same glyphs with the simple addition of a
> crosshatch as well.

A crosshatch? I thought it was a tilde "~". I'd call the standard
sharp symbol a crosshatch, or hash.

> To my mind, 144-EDO would accurately approximate
> every equal tuning that I was interested in as I felt 72-EDO was too
> coarse. So 144-EDO was a notational tuning, and not so much a tuning
> of special interest because of any acoustic property relative to JI,
> such as 72-tet. To these ends, I still think this works very
> effectively--I think the route you and George and Gene and Manuel
(et
> al) are taking is a more sophisticated shoehorn, but a shoehorn it
> still is!

This does seem like the best approach when knowing the deviations from
12-tET is more important than knowing what ratios are approximated,
and maybe that's all the time, when you're a performer.

And if the aim of a notation is to aid in JI-based composition or
harmonic analysis, then I guess Graham and Paul are right that the
best notation is one specific to the temperament, such as their
10-nominal notations for miracle and paultone/pajara respectively.

> Here's the 22 out of 72 notation (where P = 600¢):
>
> 5 4 9 13
> --, --, --, --, ...
> 14 11 25 36
>
> C Db] Db^ D< D^ Eb< Eb> EV E> Fv F[

Here's mine followed by how I assume yours would continue (correcting
what I assume are some typos and changing Db to C#). [Use Message
Index, Expand Messages to see them lined up on Yahoo's dopey web
interface].

C C^ C#v Dv D D^ Eb^ Ev E F F^ F#v Gv G G^ G#v Av A A^ Bb^ Bv
B C
C C] C#^ D< D^ Eb< Eb> Ev E> Fv F[ F# G[ G^ G#< G#^ A< A> Bbv Bb> Bv
C[ C
-3--4---3--3--3---4---3--3--3--4--3--3---4--3---3---3--4--3---3---3--4
--3-

Correct me if I'm wrong. Is your algorithm here: Find which interval
of the n-EDO under consideration falls closest to an interval of
144-EDO and then treat the n-EDO as a chain (or chains?) of those
intervals and notate it accordingly, starting from C?

How do you decide when to use sharps vs flats?

Why not simply align the C (or D) of both scales and then name each
note the same as the nearest 144-EDO (or 72-EDO) note. Wouldn't it
give the same results? How do you decide when to use 144-EDO vs
72-EDO?

> BTW, 11-tet has a sweet and useful side without having to resort to
> using it with a special inharmonic timbre or maximizing dissonance.
> I've got one piece which I'm extremely happy with in 11-tet that I
> will get somebody to convert to mp3 for me one of these days.

I look foward to hearing it.

> It's
> melodic and pretty but with just enough spice to sound fresh. To my
> mind that's really the beauty of tunings like 11, 13 and 20-tet--the
> alien spicing of consonances, and not the maximizing of dissonances!
> Tunings like these made simple consonances not so simple and even
> interesting again (for these ears anyway).

I think the results of our algorithm would be essentially identical to
yours if we restricted the range of sizes we allow for our perfect
fifths to a small range around 700 cents. I think we'd have to limit
them to plus or minus half a step of 144-EDO (+-4&1/6 cents), or if
you use 72-EDO then the allowable would be appprox +-8&1/3. I've
proposed a range of approx -12.7 to +12.9 cents from 702.0 cents
(2:3).

So, Paul Erlich, what problems do you see with Dan's, and my, proposed
22-EDO notations?

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/17/2002 8:29:46 PM

Hi Paul,

Musically, I see no problems whatsoever with wild fifths. Roughly
anything within the 650-750 cent range I could call a workable fifth
in a piece of music written to accommodate it--they work just fine for
me with normal timbres as well.

What I'm interested in notation wise is a kind of master note naming
grid, most likely based on 72-tet but 144-tet seems a better candidate
to me, where there are families of fifths, but only certain ones
falling within a given range would be "perfect fifths". The only
question I really have is whether to base the basic unadorned
intervals on a just or a 12-tet scheme...

take care,

--Dan Stearns

----- Original Message -----
From: "paulerlich" <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Sunday, February 17, 2002 3:23 PM
Subject: [tuning] Re: Notating ETs with one comma per prime

> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > --- In tuning@y..., "genewardsmith" <genewardsmith@j...>
> wrote:
> > > --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> > >
> > > > D E G A C D?
> > >
> > > That doesn't look much like a circle of fifths to me. Why not
> > > C G D A E?
> >
> > Marc gave them in pitch order, as expected. But as Dan
> Stearns points
> > out, there aren't any perfect fifths in 5-tET, or in
10,20,25,30-tET,
> > so why pretend? 5,10 and 15-tET are all 1,3,9-consistent but
> their
> > 1:3s and 1:9s are no better than 20-tET's. All of these, except
> > 25-tET, can be notated as every nth note of 60-tET (5*12-tET),
> which
> > is 9-limit consistent. 5-tET then becomes
> >
> > D E> Gv A^ C< D
> >
> > So maybe we need to specify cutoffs on perfect-fifth size. I have
> > elsewhere attempted to define a wolf fifth as one for which a
> chain of
> > 12 notes or less will generate a better fifth than those making
> the
> > chain. From 714.9 cents up to 720 cents (5-tET), a chain of 6
> fifths
> > produces a better 2:3 than the fifths making up the chain.
> Similarly
> > from 689.3 cents down to 685.7 cents (7-tET), a chain of 8 fifths
> > produces a better 2:3 than the fifths making up the chain.
> >
> > For example 47-tET just barely scrapes in with its 689.4 c fifth
> but
> > it fails the 1,3,9-consistency test and so should still be notated
> as
> > every second note of 94-tET.
> >
> > What do you think of these proposed rules?
>
> blackwood and other composers have shown that the 15-equal
> perfect fifth is highly acceptable and consonant in triads with
> 'pastelized' timbres such as the classical guitar. i also like
> 678-cent fifths but generally need inharmonic timbres to pull
> them off.
>
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
> Get your FREE credit report with a FREE CreditCheck
> Monitoring Service trial
> http://us.click.yahoo.com/ACHqaB/bQ8CAA/ySSFAA/RrLolB/TM
> --------------------------------------------------------------------
-~->
>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning
group.
> tuning-nomail@yahoogroups.com - put your email message delivery on
hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily
digest mode.
> tuning-normal@yahoogroups.com - change your subscription to
individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/17/2002 5:33:14 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > Smaller is nice, but also, as I said in another message
> (somewhere?),
> > I have an intuition that we will get a more acceptable notation if
> we
> > only use 1,3,p-commas that vanish in 12-tET, except when
> 12-tET is
> > 1,3,p-inconsistent, like when p=11.
>
> but dave, i don't think a 1:3:13 chord exists in 12-equal at all,
> consistency notwithstanding.

Nor do I. But this seems like a good reason to want the 1,3,13-comma
and its accidentals to vanish in 12-tET.

> and if 1:3:5:7:9:11:13 chords exist
> in 12-equal, it is with a _different_ approximation of 13.

Anyone who believes that 1:3:5:7:9:11:13 chords exist in 12-tET
probably also believes in Santa Claus, the Tooth Fairy and the War on
Terrorism. ;-)

What I'm saying is, I want all the prime accidental commas to vanish
in 12-tET. But if 12-tET is 1,3,p-inconsistent for some prime p, then
it means that all 1,3,p commas can have two values (in steps), clearly
only one of these can be zero. And I guess I should add that one of
them _should_ be zero.

But remember I said this was only an intuition. I can't really justify
it yet. But as long as it doesn't cost anything I'll go with it. Do
you see some cost I've missed? Would you prefer other commas for some
reason?

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/17/2002 5:44:54 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> as any 22-equal user will know, 11 gets you those great
> 4:7:8:9:11 chords.

Yes. Thanks. You could also throw a 15 on the end of that.

This looks like an argument for notating it based on the 22-tET fifth,
not the 72-tET = the 12-tET.

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/17/2002 9:12:07 PM

Hi Dave,

I guess the question of what notation's best for performers is still
open, but when it comes to a general, all ET type notation I doubt it
will be a complex and morphing one based on a host of phantom commas!

What's the hash mark some people put through a seven called? That's
what I'm referring to when I say a crosshatch, though a tilde might
work even better as there'd be less chance of it being confused with a
partial ledger line.

The method I use finds the commensurate generator in whatever the
theoretical note template is, I prefer either 72 or 144-tet, and then
takes the resulting chain of generators and truncates it at whatever
the equal tuning you're trying to notate is.

Here's a simple example, first in 72, then 144, using 5-tet:

25 2 27 29
--, --, --, --, ...
62 5 67 72

0
717 483
233 967
950 250
467 733
1183 17

27 1 28 29
---, ---, ---, ---, ...
134 5 139 144

0
958 242
717 483
475 725
233 967
1192 8

The symbols or glyphs are exist, Joe Monzo came up with an ascii
adaptation of my Sims-Maneri 144-tet notation, so all that's left is
the correct letter spellings and a note naming scheme--at least for
144, I believe you yourself already devised one for 72-tet, right?

Let me know what you think of these ideas, and especially point me in
the direction of your 72-tet note naming scheme (a la Fokker's 31),
thanks.

take care,

--Dan Stearns

----- Original Message -----
From: "dkeenanuqnetau" <d.keenan@uq.net.au>
To: <tuning@yahoogroups.com>
Sent: Sunday, February 17, 2002 5:08 PM
Subject: [tuning] Re: Notating ETs with one comma per prime

A crosshatch? I thought it was a tilde "~". I'd call the standard
sharp symbol a crosshatch, or hash.

This does seem like the best approach when knowing the deviations from
12-tET is more important than knowing what ratios are approximated,
and maybe that's all the time, when you're a performer.

> Here's the 22 out of 72 notation (where P = 600ï¿½):
>
> 5 4 9 13
> --, --, --, --, ...
> 14 11 25 36
>
> C Db] Db^ D< D^ Eb< Eb> EV E> Fv F[

How do you decide when to use sharps vs flats?

I look foward to hearing it.

So, Paul Erlich, what problems do you see with Dan's, and my, proposed
22-EDO notations?

Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/17/2002 6:36:57 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Hi Dave,
>
> I guess the question of what notation's best for performers is still
> open, but when it comes to a general, all ET type notation I doubt
it
> will be a complex and morphing one based on a host of phantom
commas!
>

What about a simple and only slightly-morphing one based on a few
commas. Not sure what you mean by "phantom".

Notice that your 22-EDO notation uses 3 new pairs of accidentals while
mine only uses one new pair.

> The method I use finds the commensurate generator in whatever the
> theoretical note template is, I prefer either 72 or 144-tet,

You say "the" commensurate generator. How do you find it? Most ETs
have more than one generator. And what about when they have a
1/n-octave period in association with some generator?

> and
then
> takes the resulting chain of generators and truncates it at whatever
> the equal tuning you're trying to notate is.
>
> Here's a simple example, first in 72, then 144, using 5-tet:
>
>
> 25 2 27 29
> --, --, --, --, ...
> 62 5 67 72
>
> 0
> 717 483
> 233 967
> 950 250
> 467 733
> 1183 17
>
>
> 27 1 28 29
> ---, ---, ---, ---, ...
> 134 5 139 144
>
> 0
> 958 242
> 717 483
> 475 725
> 233 967
> 1192 8

Can you give me an example where this gives you a different result
from simply rounding to the nearest 72 or 144 EDO note?

> The symbols or glyphs are exist, Joe Monzo came up with an ascii
> adaptation of my Sims-Maneri 144-tet notation,

I think that's where I saw the tilde.

> so all that's left is
> the correct letter spellings and a note naming scheme--at least for
> 144, I believe you yourself already devised one for 72-tet, right?

Here's where I've already taken Paul Erlich and Joseph Pehrson to
task previously. It's an interval naming scheme, not a note naming
scheme. Note names are things like "C sharp twelfth down". The two may
be confused without too much pain in ETs, but not in MOS or other
non-ET tunings.

> Let me know what you think of these ideas, and especially point me
in
> the direction of your 72-tet note naming scheme (a la Fokker's 31),
> thanks.

http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt

You may prefer Paul Erlich's/Boston scheme where a (unqualified) major
third is 400c rather than the best 4:5 approximation.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/17/2002 6:55:53 PM

By the way Gene,
It seems that our scheme can't give us a notation for 144-tET without
going beyond prime 19, unless we use one of the two possible values of
the 17-comma (4096:4131) (1 step) as corresponding to Dan's tilde, and
use an occasional triple accidental. I can accept that.

D
Df
D^
D^f
D>
D>f
D]
D]f
Eb<
Ebvj
Ebv
Ebj
Eb
Ebf
Eb^
Eb^f
Eb>
E[j
E[
E<j
E<
Evj
Ev
Ej
E

So the f corresponds to Dan's tilde and the j is its inverse. These
are of course merely intended as ASCII stand-ins for some yet to be
designed/decided glyphs.

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/17/2002 10:03:11 PM

Hi Paul,

My favorite scale in that piece is this 6-tone scale--0 2 4 5 7 9 11.
As you can see this scale has that identity as part of it, but I
wasn't using it that way at all.

It was simply one of those scales that was magic in that it managed to
easily support melodic ideas, and these melodic ideas combined in free
counterpoint result in wonderfully sweet but spicy incidental
harmonies. These are some of my favorite kinds of scales, and when
they exist in exotic and often tunings like 11, 13 and 20-tet they add
a truly magical X-factor... it's like all the expected dissonance is
doubly reborn as new consonance, and it's been my experience that this
more often than not seems to have very little to do with approximate
identities.

take care,

--Dan Stearns

----- Original Message -----
From: "paulerlich" <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Sunday, February 17, 2002 2:04 PM
Subject: [tuning] Re: Notating ETs with one comma per prime

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
>
> > I've got one piece which I'm extremely happy with in 11-tet that I
> > will get somebody to convert to mp3 for me one of these days.
> It's
> > melodic and pretty but with just enough spice to sound fresh.
> To my
> > mind that's really the beauty of tunings like 11, 13 and
> 20-tet--the
> > alien spicing of consonances, and not the maximizing of
> dissonances!
> > Tunings like these made simple consonances not so simple
> and even
> > interesting again (for these ears anyway).
> >
> >
> > take care,
> >
> > --Dan Stearns
>
> as any 22-equal user will know, 11 gets you those great
> 4:7:8:9:11 chords.
>
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
> Get your FREE credit report with a FREE CreditCheck
> Monitoring Service trial
> http://us.click.yahoo.com/ACHqaB/bQ8CAA/ySSFAA/RrLolB/TM
> --------------------------------------------------------------------
-~->
>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning
group.
> tuning-nomail@yahoogroups.com - put your email message delivery on
hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily
digest mode.
> tuning-normal@yahoogroups.com - change your subscription to
individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/17/2002 7:23:36 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> These are some of my favorite kinds of scales, and when
> they exist in exotic and often tunings like 11, 13 and 20-tet they
add
> a truly magical X-factor... it's like all the expected dissonance is
> doubly reborn as new consonance, and it's been my experience that
this
> more often than not seems to have very little to do with approximate
> identities.

Nevertheless we are astoundingly ignorant of the rational identities
available in ETs that don't include 3's or 5's.

Who can generate a list for all the ETs up to 2000, giving for each ET
the maximal sets of mutually-consistently-approximated odd numbers up
to 35? And then give the reverse-lookup version of that list, where
each maximal set has the corresponding list of ETs after it.

So for example, if it were limited to odds up to 13,
20-tET would show 1:3:11:13 and 1:3:7:11, but not 1:3:7 (because it's
included in 1:3:7:11) and not 1:3:7:11:13 (because they are not all
mutually consistent). 11-tET would show 1:3:11 and 1:7:9:11.

Likewise, in the reverse list, 20-tET would not appear next to 1:3:7
because it has a larger consistent set containing that.

🔗genewardsmith <genewardsmith@juno.com>

2/17/2002 9:09:03 PM

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> By the way Gene,
> It seems that our scheme can't give us a notation for 144-tET without
> going beyond prime 19, unless we use one of the two possible values of
> the 17-comma (4096:4131) (1 step) as corresponding to Dan's tilde, and
> use an occasional triple accidental. I can accept that.

Would 736/729 help?

🔗paulerlich <paul@stretch-music.com>

2/17/2002 9:52:25 PM

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

> So, Paul Erlich, what problems do you see with Dan's, and my,
proposed
> 22-EDO notations?

i'm going to stay out of this, as i'm not that interested in notation.
maybe there should be a separate list for it?

🔗paulerlich <paul@stretch-music.com>

2/17/2002 9:59:43 PM

> > but dave, i don't think a 1:3:13 chord exists in 12-equal at all,
> > consistency notwithstanding.
>
> Nor do I. But this seems like a good reason to want the
1,3,13-comma
> and its accidentals to vanish in 12-tET.

this makes no sense to me. am i dense?
>
> > and if 1:3:5:7:9:11:13 chords exist
> > in 12-equal, it is with a _different_ approximation of 13.
>
> Anyone who believes that 1:3:5:7:9:11:13 chords exist in 12-tET
> probably also believes in Santa Claus, the Tooth Fairy and the
War on
> Terrorism. ;-)

since 11:7 and 13:11 are pretty close to 12-equal, i can see
where monz among others are coming from in hearing
'dominant 13th' chords as having something to do with the
harmonic series. though in terms of roughness a different tuning
might be optimal, in terms of tonalness the harmonic series
rules.

> What I'm saying is, I want all the prime accidental commas to
vanish
> in 12-tET. But if 12-tET is 1,3,p-inconsistent for some prime p,
then
> it means that all 1,3,p commas can have two values (in steps),
clearly
> only one of these can be zero. And I guess I should add that
one of
> them _should_ be zero.

i'm lost.

🔗paulerlich <paul@stretch-music.com>

2/17/2002 10:06:02 PM

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

>
> Nevertheless we are astoundingly ignorant of the rational
identities
> available in ETs that don't include 3's or 5's.
>
> Who can generate a list for all the ETs up to 2000, giving for
each ET
> the maximal sets of mutually-consistently-approximated odd
numbers up
> to 35?

i though carl lumma wrote a program to do something like this.

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/18/2002 1:17:11 AM

Hi Dave,

Thanks for the link, that's just the sort of thing I was looking for.
I think my first inclination for a similar situation in 144-tet would
be to use 12-tet rather than JI as the reference, but I'm still
undecided.

What I'm doing is trying to create an analogous situation to the
circle of fifths, and if you look at the 5 out of 72, I suppose you
could spell it

C
Fv G^
Bb< D>
Eb[ A]
Abb< E#<
Dbb^ B#v

where

C = Dbb^,B#v
D> = Eb[ and Eb[ = D]
Fv = E#<
G^ = Abb<
Bb< = A] and A#[ = A]

You couldn't get this sort of a thing from just rounding to the
nearest interval of a given ET.

take care,

--Dan Stearns

----- Original Message -----
From: "dkeenanuqnetau" <d.keenan@uq.net.au>
To: <tuning@yahoogroups.com>
Sent: Sunday, February 17, 2002 6:36 PM
Subject: [tuning] Re: Notating ETs with one comma per prime

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> > Hi Dave,
> >
> > I guess the question of what notation's best for performers is
still
> > open, but when it comes to a general, all ET type notation I doubt
> it
> > will be a complex and morphing one based on a host of phantom
> commas!
> >
>
> What about a simple and only slightly-morphing one based on a few
> commas. Not sure what you mean by "phantom".
>
> Notice that your 22-EDO notation uses 3 new pairs of accidentals
while
> mine only uses one new pair.
>
> > The method I use finds the commensurate generator in whatever the
> > theoretical note template is, I prefer either 72 or 144-tet,
>
> You say "the" commensurate generator. How do you find it? Most ETs
> have more than one generator. And what about when they have a
> 1/n-octave period in association with some generator?
>
> > and
> then
> > takes the resulting chain of generators and truncates it at
whatever
> > the equal tuning you're trying to notate is.
> >
> > Here's a simple example, first in 72, then 144, using 5-tet:
> >
> >
> > 25 2 27 29
> > --, --, --, --, ...
> > 62 5 67 72
> >
> > 0
> > 717 483
> > 233 967
> > 950 250
> > 467 733
> > 1183 17
> >
> >
> > 27 1 28 29
> > ---, ---, ---, ---, ...
> > 134 5 139 144
> >
> > 0
> > 958 242
> > 717 483
> > 475 725
> > 233 967
> > 1192 8
>
> Can you give me an example where this gives you a different result
> from simply rounding to the nearest 72 or 144 EDO note?
>
> > The symbols or glyphs are exist, Joe Monzo came up with an ascii
> > adaptation of my Sims-Maneri 144-tet notation,
>
> I think that's where I saw the tilde.
>
> > so all that's left is
> > the correct letter spellings and a note naming scheme--at least
for
> > 144, I believe you yourself already devised one for 72-tet, right?
>
> Here's where I've already taken Paul Erlich and Joseph Pehrson to
> task previously. It's an interval naming scheme, not a note naming
> scheme. Note names are things like "C sharp twelfth down". The two
may
> be confused without too much pain in ETs, but not in MOS or other
> non-ET tunings.
>
> > Let me know what you think of these ideas, and especially point me
> in
> > the direction of your 72-tet note naming scheme (a la Fokker's
31),
> > thanks.
>
> http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt
>
> You may prefer Paul Erlich's/Boston scheme where a (unqualified)
major
> third is 400c rather than the best 4:5 approximation.
>
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
> Get your FREE credit report with a FREE CreditCheck
> Monitoring Service trial
> http://us.click.yahoo.com/ACHqaB/bQ8CAA/ySSFAA/RrLolB/TM
> --------------------------------------------------------------------
-~->
>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning
group.
> tuning-nomail@yahoogroups.com - put your email message delivery on
hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily
digest mode.
> tuning-normal@yahoogroups.com - change your subscription to
individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

2/17/2002 10:58:41 PM

On 2/18/02 12:52 AM, "paulerlich" <paul@stretch-music.com> wrote:

> i'm going to stay out of this, as i'm not that interested in notation.
> maybe there should be a separate list for it?

Tuning-notation ? I second

🔗genewardsmith <genewardsmith@juno.com>

2/17/2002 11:54:07 PM

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> On 2/18/02 12:52 AM, "paulerlich" <paul@s...> wrote:
>
> > i'm going to stay out of this, as i'm not that interested in notation.
> > maybe there should be a separate list for it?
>
> Tuning-notation ? I second

I vote nay. There are too many lists as it is, and it makes people (or at least me) miss things.

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

2/18/2002 12:02:58 AM

On 2/18/02 2:54 AM, "genewardsmith" <genewardsmith@juno.com> wrote:

> I vote nay. There are too many lists as it is, and it makes people (or at
> least me) miss things.

Oh? Sorry - all it takes for me is a minute to set up a new folder and new
mailing rule in Microsoft Entourage. If you're doing it linear mail or on
the web, yeah it might be difficult to keep up with.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/18/2002 12:36:25 AM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > By the way Gene,
> > It seems that our scheme can't give us a notation for 144-tET
without
> > going beyond prime 19, unless we use one of the two possible
values of
> > the 17-comma (4096:4131) (1 step) as corresponding to Dan's tilde,
and
> > use an occasional triple accidental. I can accept that.
>
> Would 736/729 help?

So this is a 1,3,23-comma that vanishes in 12-tET. 144-tET _is_
1,3,23-consistent, but this comma is 3 steps, not 1, so it's messy,
and I don't really want to have that many accidentals. And I'm not
sure I believe in the 23rd harmonic. :-) I think I'd rather call it an
inconsistent 1-step 17-comma.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/18/2002 12:41:44 AM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > So, Paul Erlich, what problems do you see with Dan's, and my,
> proposed
> > 22-EDO notations?
>
> i'm going to stay out of this, as i'm not that interested in
notation.

Really!

> maybe there should be a separate list for it?

Gimme a break. There are so many separate tuning lists for everything,
and half of 'em are all but dead. But it could go to tuning-math if
people think it should.

🔗genewardsmith <genewardsmith@juno.com>

2/18/2002 12:45:01 AM

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> Oh? Sorry - all it takes for me is a minute to set up a new folder and new
> mailing rule in Microsoft Entourage. If you're doing it linear mail or on
> the web, yeah it might be difficult to keep up with.

I've got enough junk arriving in my mailbox, so I try to keep up on the web.

🔗jpehrson2 <jpehrson@rcn.com>

2/18/2002 8:01:49 AM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_34071.html#34379

> Hi Paul,
>
> Musically, I see no problems whatsoever with wild fifths. Roughly
> anything within the 650-750 cent range I could call a workable fifth
> in a piece of music written to accommodate it--they work just fine
for
> me with normal timbres as well.
>
> What I'm interested in notation wise is a kind of master note naming
> grid, most likely based on 72-tet but 144-tet seems a better
candidate
> to me, where there are families of fifths, but only certain ones
> falling within a given range would be "perfect fifths". The only
> question I really have is whether to base the basic unadorned
> intervals on a just or a 12-tet scheme...
>
>
> take care,
>
> --Dan Stearns
>

****Personally, I think this "elaboration" of 72-tET into 144-tET is
a *wonderful* idea!

I'm hoping, though, just for "consistency" if the notation is to be
performed with our past traditions, the basis is 12-tET...

J. Pehrosn

🔗jpehrson2 <jpehrson@rcn.com>

2/18/2002 11:33:32 AM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_34071.html#34386

>
> It was simply one of those scales that was magic in that it managed
to
> easily support melodic ideas, and these melodic ideas combined in
free
> counterpoint result in wonderfully sweet but spicy incidental
> harmonies. These are some of my favorite kinds of scales, and when
> they exist in exotic and often tunings like 11, 13 and 20-tet they
add
> a truly magical X-factor... it's like all the expected dissonance is
> doubly reborn as new consonance, and it's been my experience that
this
> more often than not seems to have very little to do with approximate
> identities.
>
>
> take care,
>
> --Dan Stearns
>

***This is very much along the lines of the experiences of the "nutty
professor..." [OK, OK, I know, he's *no* professor, but he *is*
nutty!...]

🔗manuel.op.de.coul@eon-benelux.com

2/19/2002 6:00:22 AM

Dave wrote:

>So why not admit that what we're both really wanting is a symbol that
>represents a single step of the ET? At least then you wouldn't need
>symbol pairs for the variable fraction of every comma.

But on the other hand, then you can't have the symbols for 1+1/n
comma/semitone.

>The way I see it, calling it a _variable_ fraction of some particular
>5-limit comma (there is sometimes more than one to choose from) is no
>less specious than calling it a whole comma involving some higher
>prime.

It's not specious since it's always clear what fraction it is.

>Presumably you would use the diesis (3 steps) and 1/n-diesis (in this
>case 1/3-diesis = 1 step) symbols.

Yes.

>I'll use the septimal comma symbols <> to mean 3 steps and the
>syntonic comma symbols v^ to mean 1 step.

The syntonic comma vanishes in 105-tET.

Manuel

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/19/2002 1:54:14 PM

--- In tuning@y..., manuel.op.de.coul@e... wrote:
> Dave wrote:
>
> >So why not admit that what we're both really wanting is a symbol
that
> >represents a single step of the ET? At least then you wouldn't need
> >symbol pairs for the variable fraction of every comma.
>
> But on the other hand, then you can't have the symbols for 1+1/n
> comma/semitone.

I don't feel the need for them. I'd just use the symbol for the comma
alongside the symbol for one step.

> >The way I see it, calling it a _variable_ fraction of some
particular
> >5-limit comma (there is sometimes more than one to choose from) is
no
> >less specious than calling it a whole comma involving some higher
> >prime.
>
> It's not specious since it's always clear what fraction it is.

Is it? How? By the fact that it is a single step of the ET?

> >Presumably you would use the diesis (3 steps) and 1/n-diesis (in
this
> >case 1/3-diesis = 1 step) symbols.
>
> Yes.
>
> >I'll use the septimal comma symbols <> to mean 3 steps and the
> >syntonic comma symbols v^ to mean 1 step.
>
> The syntonic comma vanishes in 105-tET.

I must correct this misconception. 105-tET is 1,3,5-inconsistent. This
means that there are _two_ possible values (in steps) for the syntonic
comma. You get one value when you use the best 1:5 and therefore get
the second-best 3:5 (in this case the syntonic comma vanishes), and
you get the other when you assume the best 3:5 and therefore get the
second-best 1:5 (in this case the syntonic comma is 1 step).

I try to avoid notating based on inconsistent comma, but having been
more-or-less forced into it, I choose the value that is most useful
for notation.

🔗paulerlich <paul@stretch-music.com>

2/19/2002 4:03:41 PM

--- In tuning@y..., manuel.op.de.coul@e... wrote:

> The syntonic comma vanishes in 105-tET.

i'm afraid i can't agree, manuel. the syntonic comma is usually the
difference between three 4:3s (minus an octave) and a 6:5.

i hope scala doesn't give out misinformation such as this.

🔗manuel.op.de.coul@eon-benelux.com

2/20/2002 2:02:49 AM

Paul wrote:

>i'm afraid i can't agree, manuel. the syntonic comma is usually the
>difference between three 4:3s (minus an octave) and a 6:5.

The definition used for "the syntonic comma" or "best syntonic comma"
is based on the best (approximation of) 3/2 and best 5/4,
four (best 3/2) minus two octaves minus (best 5/4).
Scala also gives the "2nd best syntonic comma" based on the
second best 5/4 when appropriate. This is the comma you and Dave
are referring to, which is one step in 105-tET.
I'm not arguing against using this definition for a notation system
however.

>i hope scala doesn't give out misinformation such as this.

The difference is clear, you can check it yourself.

Manuel

🔗manuel.op.de.coul@eon-benelux.com

2/20/2002 2:07:49 AM

Dave wrote:

>Is it? How? By the fact that it is a single step of the ET?

By the legend provided which gives the intervals corresponding to
each symbol, how are people otherwise going to know what they
mean?

>> The syntonic comma vanishes in 105-tET.
>I must correct this misconception. 105-tET is 1,3,5-inconsistent.

Answered in the previous post.

Manuel

🔗paulerlich <paul@stretch-music.com>

2/20/2002 11:05:25 AM

--- In tuning@y..., manuel.op.de.coul@e... wrote:
> Paul wrote:
>
> >i'm afraid i can't agree, manuel. the syntonic comma is usually the
> >difference between three 4:3s (minus an octave) and a 6:5.
>
> The definition used for "the syntonic comma" or "best syntonic
comma"
> is based on the best (approximation of) 3/2 and best 5/4,
> four (best 3/2) minus two octaves minus (best 5/4).

that's too bad.

> Scala also gives the "2nd best syntonic comma" based on the
> second best 5/4 when appropriate.

hmm . . . there might be some tunings (64-equal, perhaps) where the
difference between three 4:3s (minus an octave) and a 6:5 is neither
your best syntonic comma or the second-best. :( :( :(

🔗manuel.op.de.coul@eon-benelux.com

2/21/2002 3:06:28 AM

Paul wrote:

>that's too bad.

I think not. All the commas are derived in the same consistent
way. Should one make an exception for the syntonic comma and
adopt your definition, then you get problems like the syntonic
comma and the schisma not adding up to the Pythagorean comma
anymore.

>hmm . . . there might be some tunings (64-equal, perhaps) where the
>difference between three 4:3s (minus an octave) and a 6:5 is neither
>your best syntonic comma or the second-best.

Yes, those cases are indicated too and called "best major triad
syntonic comma".

> :( :( :(

Cheers,

Manuel

🔗paulerlich <paul@stretch-music.com>

2/21/2002 3:58:31 AM

--- In tuning@y..., manuel.op.de.coul@e... wrote:
> Paul wrote:
>
> >that's too bad.
>
> I think not. All the commas are derived in the same consistent
> way. Should one make an exception for the syntonic comma and
> adopt your definition, then you get problems like the syntonic
> comma and the schisma not adding up to the Pythagorean comma
> anymore.

i didn't propose a definition, just observed the usual music meaning due to triangular lattice considerations.

> >hmm . . . there might be some tunings (64-equal, perhaps) where the
> >difference between three 4:3s (minus an octave) and a 6:5 is neither
> >your best syntonic comma or the second-best.
>
> Yes, those cases are indicated too and called "best major triad
> syntonic comma".

if you used a "best major triad" definition for *all* the 5-limit commas, they're sure to add up the way they're supposed to, nein? this sort of thing is what "best syntonic comma" *should* mean, in my opinion . . .

🔗manuel.op.de.coul@eon-benelux.com

2/21/2002 5:28:31 AM

Paul wrote:

>if you used a "best major triad" definition for *all* the 5-limit commas,

>they're sure to add up the. way they're supposed to, nein?

That's not the point. The "best Pythagorean comma" is based on the best
fifth.
The best syntonic comma is based on the best fifth and the best major
third.
If I'd change it the way you say, the best syntonic comma is not based on
the
best fifth anymore but on the best major triad, and the best Pythagorean
comma
could become different too, not anymore based on the best fifth. I'd say
that
would become very confusing.
So it's important to remember that "best" in "best syntonic comma" only
refers
to the approximation, not to the sound of triads or function in music or
size
in cents or whatever.

Manuel

🔗genewardsmith <genewardsmith@juno.com>

2/21/2002 11:16:11 AM

--- In tuning@y..., manuel.op.de.coul@e... wrote:

> I think not. All the commas are derived in the same consistent
> way.

Your standard way of defining commas is related to my "standard" ets, which Paul also objects to--it's really the same argument.

🔗paulerlich <paul@stretch-music.com>

2/21/2002 11:18:47 AM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., manuel.op.de.coul@e... wrote:
>
> > I think not. All the commas are derived in the same consistent
> > way.
>
> Your standard way of defining commas is related to my "standard"
>ets, which Paul also objects to--it's really the same argument.

i noticed that. oh well, you guys should at least be more explicit
that you're basing everything on the best approximations to the
primes and not the other consonant intervals -- 'prime basis' might
be a good qualifier for you guys to use.

🔗gdsecor <gdsecor@yahoo.com>

2/21/2002 11:55:14 AM

Gene,

I'm sorry I've taken so long to reply to this one. After coming back
to the List since the weekend, I've been swamped trying to read
everything and managed to reply to only one other before this.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > > If you really threw 27 into the garbage heap as well as 58, I
think
> > you'd better take a trip to the junkyard and reclaim them. :)
>
> > And I think not. As I observed in my very first posting, life is
> > short, and, we must establish our priorities for ourselves.
> > Considering all of the music that has come out of the resources
of a
> > 12-tone octave, I believe that those tonal systems that I have
judged
> > to be excellent would occupy me for many lifetimes, so that I
have no
> > need to concern myself with others that I perceive as less worthy
of
> > my time and effort.
>
> If you adopt that point of view, you need to be careful to do your
discarding carefully. Given that 27 is one of the better 7-limit
systems and 58 one of the relatively best systems for the 11, 13, 15
and 17 limits (making it comparable to 31, 41, 46 or 72 and in some
respects better) it is not clear you have. It could be you are
confining yourself to the 11-limit, but I don't see why that should
be, or it could be you are systematically underestimating the value
of systems with a strong tendency for primes to map either to the
flat or sharp side.
>
> > You and your fellow "Scavengers"
>
> That appellation hardly applies to me, I don't know what others
would think of it.
>
> > And so the very essence of discovery, innovation, and creativity
is
> > to see beauty or utility in those places where the rest of us
pass
> > by, unaware of the possibilities.
>
> I'm simply doing the mundane math here.

Just so there are no hard feelings about this, I want to point out
that sometimes a political, religious, or otherwise controversial
movement will adopt a label given to it by its critics as a badge of
honor, which is what I had in mind here. And I do find myself in a
rather inconsistent position on this one, since I had earlier stated
that I believed that diversity is one of the strengths of our
movement -- I just hadn't anticipated this much diversity.

Paul, Dave, & Gene: I have sought to include 27 & 58-EDO in the
sagittal notation by using the auxiliary symbols that I discarded
earlier from the native 41-EDO notation. See Figure 5 of:

/tuning/files/secor/notation/Figures.bmp

For 58-EDO, at first I tried deleting 64:63 as a defining comma for
the notation, which would then make the right-flag symbols (such as
|\ and |/) alter by 55:54 (i.e., 33:32 less 81:80), so that EDO's in
which 385:384 is maintained (such as 58) could be included (see line:
Native 58-tone, version a).

But with the auxiliary symbols defined as in the lower right corner
of the figure, 58 could be notated as in version b. This would also
make it possible to do 27-EDO, while providing another (and
possibly "cleaner") way to do 46 and 53 (for which I show versions a
and b), while maintaining compatibility with the way I have used them
for 96. And this would probably open the door to notating some other
EDO's as well.

--George

🔗gdsecor <gdsecor@yahoo.com>

2/21/2002 1:37:03 PM

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> It's hard for me to know what someone would want in an 11-tET
notation
> , since I don't know why anyone would want to use 11-tET, except to
> maximise dissonance, or to use with a special inharmonic timbre.

Just for the record (Monz, take note!), I may possibly be the very
first both to advocate and use 11-ET:

1) In an unpublished paper (April 1964) I advocated using it for
atonal music: Since it contains nothing that approximates a perfect
fifth or major third, you have to go to extraordinary lengths to try
to establish a key center. However, I didn't try it for several
years, because it's not an easy one to tune by ear.

2) In 1970 I recorded an improvisation on a retuned electronic organ:
4 voices overdubbed one at a time.

3) Around 1976 I did an improvisation in 11-ET as the main piece for
the Motorola Scalatron demo tape (also documented in my letter to the
editor in the first issue of _Interval_). This took both Erv Wilson
and Ivor Darreg by surprise -- neither one had imagined that 11 could
be of any use for anything.

Why use 11-ET? It's so "bad" that it's "good!" It's the
expressionist's dream! You can play whatever you want and not be
concerned about hitting any "wrong" notes, which makes using it a lot
of fun, just as long as you don't act timid, but play everything like
you mean it. Since the sonance range is minimized, nothing tends to
resolve to anything else. And you can get all of the tones on a
conventional keyboard (I tuned my electronic organ so that two
adjacent keys in each octave were alike).

Notating 11? If you must, do it as a subset of 22. But what's the
point? A precise score takes all of the fun out of it and turns a
performance into a lot of unnecessary work.

> How does 22-tET come out in your scheme.
>
> I think your scheme is aimed at making the accidentals represent,
as
> close as possible, a constant deviation from 12-tET across all ETs,
> whereas Gene's and mine and George Secor's and Manuel's and
> Rappoport's etc. are aimed at telling you where the approximate JI
> intervals are, in a consistent way across all ETs.
>
> Now if we could come close to achieving both these aims at the same
> time ...

Something such as this may be possible if you're willing to forego
Pythagorean relationships between the naturals, sharps, and flats,
i.e., B to F-sharp and B-flat to F will not be the interval nearest a
2:3 in some EDO's. I toyed with this idea back in the 1970's (see my
Xenharmonikon 3 articles, including the one in which you found my
description for the Miracle tuning -- if you take a good look at the
41-ET notation that I used, you'll see that I did something along
this line; Erv Wilson and a number of others didn't like the idea,
and I eventually abandoned it.)

--George

🔗paulerlich <paul@stretch-music.com>

2/21/2002 1:51:31 PM

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

> 11-ET:
>
> 1) In an unpublished paper (April 1964) I advocated using it for
> atonal music: Since it contains nothing that approximates a
perfect
> fifth or major third, you have to go to extraordinary lengths to
try
> to establish a key center.

this is exactly the same point i made in advocating 11-equal in my
paper on 22-equal (you know, the one in xenharmonikon 17). have you
looked at it yet?

but i later realized that certain voicings of the approximate
4:7:8:9:11 *can* work as a sort of 'tonic'.

🔗D.Stearns <STEARNS@CAPECOD.NET>

2/21/2002 5:52:03 PM

Hi George,

While I wouldn't want to sound disrespectful to anyone who was
discussing 11-tet before I was born!, I must take umbrage with some of
what you've written here.

I think the "it's so bad that it's good" argument for atonality that
you make for 11-tet, the very same one that is often made for 13-tet,
is, simply put, wrong and overly simplistic. It seems to me to be one
based entirely on the numbers.

I say this from working with both these tunings quite a bit. Simply
put, if one finds the right scale, or subset of these tunings and
sticks to it, it's hard to avoid a sense of a tonic!

With 11, try rotations of this 6-tone scale: 222122

With 13, try rotations of this 7-tone scale: 3121222

Here's a brief example in another 7-tone, 13-tet scale that I like,
2141221:

C D D# F# G A B C = 0 2 3 7 8 10 12 13

playfully,
mf - f
/ = 65
*

/(1)..................................\
| |
| CLARINET (sounds as written) |
| __ |
| / \ |
| /"/"/' / /' /' /' /' |
4/4 *`*`*```*```````*```*```*```*``` |
6 C |
5 B A F# G F# C |
c' B |
|.....................................|
| |
| GUITAR |
| ______ _ |
| / \ / \ |
| / /' /' /' /"/ |
4/4 *```````*```*```*.````*`*``````` |
| o``````````````````````````````` |
5 D F# D# |
c' B B A |
3 B |
|.....................................|
\ /

/(2).................................. \
| ||
| CLARINET ||
| ___ ||
| / \ ||
| {-----9:8------} ||
| {--3--} ||
| / /' /"/"/"/' /'/' /' ||
4/4 *```````*.````*`*`*`*.```*`*``*` ||
5 G D C D B A ||
c' A B ||
3 B ||
|.....................................||
| ||
| GUITAR ||
| ||
| ____ {-----5:4------} ||
| / \ {-3--} ||
| /' /"/"/"/' / /'/'/' ||
4/4 *```*`*`*`*.````*.````````*`*`*` ||
| * *. \_/ ||
| * *. ||
| * ||
5 D-- ||
' G ||
' F# D ||
c' D# B A G C D# D ||
3 G G A ||
|.....................................||
\ /

I should point out that all of these scales I found by ear. Yes, it's
easier to make music with tunings like 11 and 13-tet that is
dissonant, but it's also not impossible to do exactly the opposite.
Not by a long shot if one is so inclined and doesn't get hysterical
and run screaming at the first signs of resistance--that's been my
experience at least, your mileage may of course vary.

take care,

--Dan Stearns

----- Original Message -----
From: "gdsecor" <gdsecor@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: Thursday, February 21, 2002 1:37 PM
Subject: [tuning] 11-ET & Notating other ET's

> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> >
> > It's hard for me to know what someone would want in an 11-tET
> notation
> > , since I don't know why anyone would want to use 11-tET, except
to
> > maximise dissonance, or to use with a special inharmonic timbre.
>
> Just for the record (Monz, take note!), I may possibly be the very
> first both to advocate and use 11-ET:
>
> 1) In an unpublished paper (April 1964) I advocated using it for
> atonal music: Since it contains nothing that approximates a perfect
> fifth or major third, you have to go to extraordinary lengths to try
> to establish a key center. However, I didn't try it for several
> years, because it's not an easy one to tune by ear.
>
> 2) In 1970 I recorded an improvisation on a retuned electronic
organ:
> 4 voices overdubbed one at a time.
>
> 3) Around 1976 I did an improvisation in 11-ET as the main piece for
> the Motorola Scalatron demo tape (also documented in my letter to
the
> editor in the first issue of _Interval_). This took both Erv Wilson
> and Ivor Darreg by surprise -- neither one had imagined that 11
could
> be of any use for anything.
>
> Why use 11-ET? It's so "bad" that it's "good!" It's the
> expressionist's dream! You can play whatever you want and not be
> concerned about hitting any "wrong" notes, which makes using it a
lot
> of fun, just as long as you don't act timid, but play everything
like
> you mean it. Since the sonance range is minimized, nothing tends to
> resolve to anything else. And you can get all of the tones on a
> conventional keyboard (I tuned my electronic organ so that two
> adjacent keys in each octave were alike).
>
> Notating 11? If you must, do it as a subset of 22. But what's the
> point? A precise score takes all of the fun out of it and turns a
> performance into a lot of unnecessary work.
>
> > How does 22-tET come out in your scheme.
> >
> > I think your scheme is aimed at making the accidentals represent,
> as
> > close as possible, a constant deviation from 12-tET across all
ETs,
> > whereas Gene's and mine and George Secor's and Manuel's and
> > Rappoport's etc. are aimed at telling you where the approximate JI
> > intervals are, in a consistent way across all ETs.
> >
> > Now if we could come close to achieving both these aims at the
same
> > time ...
>
> Something such as this may be possible if you're willing to forego
> Pythagorean relationships between the naturals, sharps, and flats,
> i.e., B to F-sharp and B-flat to F will not be the interval nearest
a
> 2:3 in some EDO's. I toyed with this idea back in the 1970's (see
my
> Xenharmonikon 3 articles, including the one in which you found my
> description for the Miracle tuning -- if you take a good look at the
> 41-ET notation that I used, you'll see that I did something along
> this line; Erv Wilson and a number of others didn't like the idea,
> and I eventually abandoned it.)
>
> --George
>
>
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
> FREE COLLEGE MONEY
> CLICK HERE to search
> 600,000 scholarships!
> http://us.click.yahoo.com/iZp8OC/4m7CAA/ySSFAA/RrLolB/TM
> --------------------------------------------------------------------
-~->
>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning
group.
> tuning-nomail@yahoogroups.com - put your email message delivery on
hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily
digest mode.
> tuning-normal@yahoogroups.com - change your subscription to
individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

🔗paulerlich <paul@stretch-music.com>

2/21/2002 2:55:38 PM

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

> Something such as this may be possible if you're willing to forego
> Pythagorean relationships between the naturals, sharps, and flats,
> i.e., B to F-sharp and B-flat to F will not be the interval nearest
a
> 2:3 in some EDO's.

this was a feature of fokker's approach, by the way.

but the consensus on this list appears to be that both this approach
and the ben johnston approach (where D to A is not 3:2) are less
appealing than one that preserves the pythagorean note-names.

> I toyed with this idea back in the 1970's (see my
> Xenharmonikon 3 articles, including the one in which you found my
> description for the Miracle tuning -- if you take a good look at
the
> 41-ET notation that I used, you'll see that I did something along
> this line; Erv Wilson and a number of others didn't like the idea,
> and I eventually abandoned it.)

interesting -- i remember being impressed that you managed to use the
seven letter names and the accidentals in such a neat way -- but
ultimately it's too 'special-casey', you might say . . .

🔗jpehrson2 <jpehrson@rcn.com>

2/21/2002 5:37:54 PM

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

/tuning/topicId_34071.html#34624

>
> Notating 11? If you must, do it as a subset of 22. But what's the
> point? A precise score takes all of the fun out of it and turns a
> performance into a lot of unnecessary work.
>

***Hello George... and others,

This brings about an interesting point and I'm rather of *two* minds
about it (well, it's said *two* heads are better than *one*...)

Dave Keenan was interested in a "score" to my _Blect_ electronic
piece in Blackjack, since he wanted to follow along and wanted to
know what he was listening to.

Generally speaking, I only produce a *score* if there is some
*performance* point in it. In my older "traditional" music with
acoustic instruments this problem never came up since I *always* had
to have a score for *all* the instruments.

However, with electronic things that are not going to be *performed*
I haven't produced one, thinking that the *audible* result is really
where "all the action is" or "should be" anyway.

Anybody have any opinions at all on this topic?

Even in cases where I now have electronics *plus* a live instrument,
frankly, a *favorite* activity of late, I tend just to score out
certain melodic lines in the electronic part so that the acoustic
instrument can follow as a kind of "cue." Of course, the solo
*acoustic* part has to be written out... :)

I guess if there is some kind of "demand" for a written out score for
an electronic piece I could maybe be "talked into" working one out...
it might, in fact, help me remember what I did...

Chances are, though, I will be more interested in going on to the
next piece... and rather letting the analytic theory be dam*ed...

J. Pehrson

🔗paulerlich <paul@stretch-music.com>

2/21/2002 5:43:49 PM

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> However, with electronic things that are not going to be
*performed*
> I haven't produced one, thinking that the *audible* result is
really
> where "all the action is" or "should be" anyway.
>
> Anybody have any opinions at all on this topic?

i'm with you 100%.

🔗jpehrson2 <jpehrson@rcn.com>

2/21/2002 6:04:44 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_34071.html#34649

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> > However, with electronic things that are not going to be
> *performed*
> > I haven't produced one, thinking that the *audible* result is
> really
> > where "all the action is" or "should be" anyway.
> >
> > Anybody have any opinions at all on this topic?
>
> i'm with you 100%.

***Thanks, Paul, for the response...

🔗jonszanto <JSZANTO@ADNC.COM>

2/21/2002 6:45:45 PM

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> Anybody have any opinions at all on this topic?
> Chances are, though, I will be more interested in going on to the
> next piece... and rather letting the analytic theory be dam*ed...

I'm with Paul: you *must* have better things to do, JP! If anyone is
just totally killer interested in studying a score, send them the
midi sequencer file (saved as a plain midi), any mappings you need
them to have, and let them put it all together.

Go, you composer, you.

Cheers,
Jon

🔗Herman Miller <hmiller@IO.COM>

2/21/2002 7:35:11 PM

On Thu, 21 Feb 2002 17:52:03 -0800, "D.Stearns" <STEARNS@CAPECOD.NET>
wrote:

>I should point out that all of these scales I found by ear. Yes, it's
>easier to make music with tunings like 11 and 13-tet that is
>dissonant, but it's also not impossible to do exactly the opposite.
>Not by a long shot if one is so inclined and doesn't get hysterical
>and run screaming at the first signs of resistance--that's been my
>experience at least, your mileage may of course vary.

A few years ago, while listening to Wendy Carlos' example on _Secrets of
Synthesis_ of how bad 13-et could sound, I had the idea to try that scale
and see how _good_ I could make it sound. Here's the result:

http://www.io.com/~hmiller/midi/triskaidekaphobia.mid

But I've had a much harder time getting anything at all good to come out of
11-et. Until just recently. Here's a brief excerpt, still unfinished (and
it might remain unfinished for a long time), but enough to illustrate the
idea:

http://www.io.com/~hmiller/mp3/Unfinished-11et.mp3

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

🔗jpehrson2 <jpehrson@rcn.com>

2/21/2002 7:48:15 PM

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:

/tuning/topicId_34071.html#34665

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > Anybody have any opinions at all on this topic?
> > Chances are, though, I will be more interested in going on to the
> > next piece... and rather letting the analytic theory be dam*ed...
>
> I'm with Paul: you *must* have better things to do, JP! If anyone
is
> just totally killer interested in studying a score, send them the
> midi sequencer file (saved as a plain midi), any mappings you need
> them to have, and let them put it all together.
>
> Go, you composer, you.
>
> Cheers,
> Jon

***Hi Jon.

That's a really good suggestion. If anybody asks, I'll just send it
in "plain MIDI" and they can look it up on their *own* "piano roll..."

Thanks for the tip!

Joe

🔗genewardsmith <genewardsmith@juno.com>

2/21/2002 8:13:01 PM

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

> Just so there are no hard feelings about this, I want to point out
> that sometimes a political, religious, or otherwise controversial
> movement will adopt a label given to it by its critics as a badge of
> honor, which is what I had in mind here.

No problem; it's just that I don't think I am a member of a controversial movement of scale scavangers. You might say I'm a member of a fanatical cult called "mathematicians".

> Paul, Dave, & Gene: I have sought to include 27 & 58-EDO in the
> sagittal notation by using the auxiliary symbols that I discarded
> earlier from the native 41-EDO notation.

Good show! I'll check it out.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/23/2002 12:16:20 AM

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> Paul, Dave, & Gene: I have sought to include 27 & 58-EDO in the
> sagittal notation by using the auxiliary symbols that I discarded
> earlier from the native 41-EDO notation. See Figure 5 of:
>
>
/tuning/files/secor/notation/Figures.bmp
>
> For 58-EDO, at first I tried deleting 64:63 as a defining comma for
> the notation, which would then make the right-flag symbols (such as
> |\ and |/) alter by 55:54 (i.e., 33:32 less 81:80), so that EDO's in
> which 385:384 is maintained (such as 58) could be included (see
line:
> Native 58-tone, version a).
>
> But with the auxiliary symbols defined as in the lower right corner
> of the figure, 58 could be notated as in version b. This would also
> make it possible to do 27-EDO, while providing another (and
> possibly "cleaner") way to do 46 and 53 (for which I show versions a
> and b), while maintaining compatibility with the way I have used
them
> for 96. And this would probably open the door to notating some
other
> EDO's as well.

It's just too many symbols for my liking. I'd be happy to see your
symbols for the 5, 7 and 11 commas used (with a convex half-head on
the septimal-comma arrow). They are more logical than the Sims
symbols.

But when you start combining them into single symbols in a
less-than-obvious way, I get very lost.

Here (following Gene) is how I'd notate 27-tET:

D D^ D} E{ Ev E F

And here's 58-tET

D D^ D]v D] Eb Eb^ E[v E[ E[^ Ev E E^ E]v Fv F

Where
v^ syntonic comma (80:81)
<> septimal comma (63:64)
[] undecimal diesis (32:33)
{} 13-comma (1024:1053)
jf 17-comma (2176:2187)
yh 19-comma (512:513)

I'm not particularly attached to these specific ASCII symbols, but the
choice of commas is _v_e_r_y_ important.

We can have one consistent set of symbols for notating both JI and
ETs. The previous sentence should probably be in flashing lights.
I'll say it again.

* WE CAN HAVE ONE SMALL SET OF SYMBOLS FOR NOTATING BOTH JI AND ETS *

This seems like something we should have had a long time ago. Many
thanks to Gene for pushing the idea.

The beauty is, that with this choice of commas, there is no need to go
past 19-limit for notating all the ETs of interest, well into the
hundreds. 19-limit means we only need 6 new pairs of symbols. This is
far fewer than Rapoport's 5-limit system as used in Scala. This is
because Rapoport needs all those 1/n-comma symbols. Because the 17 and
19 commas are so small, we don't need these 1-step symbols.

These 17 and 19 commas just happen to step down in size from the
syntonic and septimal comma in an almost perfect trinary system!: 27c,
9c, 3c. To get the idea, notice how you can make up all the numbers
from -13 to +13 just using combinations of 0,-1,+1,-3,+3,-9,+9 without
using more than 3 of them and never using any of them more than once.

13 = +9 +3 +1
12 = +9 +3
11 = +9 +3 -1
10 = +9 +1
9 = +9
8 = +9 -1
7 = +9 -3 +1
6 = +9 -3
5 = +9 -3 -1
4 = +3 +1
3 = +3
2 = +3 -1
1 = +1
0
and so on.

The commas are also chosen so they vanish in 12-tET. In JI a complete
19-limit otonality on G would be spelled
G:D:Bv:F<:A:C]:Eb}:F#v:G#j:Bbh
1:3:5 :7 :9:11:13 :15 :17 :19

Notice that, sans commas, the above all fall within a chain of fifths
from Eb to G# and no note is repeated.

To get the best approximation of that chord in _any_ ET you would just
omit the symbols for any commas that vanish in that ET, and replace
any symbols for higher primes with those of lower primes that
correspond to the same number of steps. And sometimes we may use
_pairs_ of symbols for lower primes in place of those for a higher
prime.

For example, in 12-tET the best approximation (athough not a usable or
recognisable approximation) of that complete 19-limit otonality is
notated as.
G:D:B:F:A:C:Eb:F#:G#:Bb
We simply dropped all the comma symbols.

Is not such a system very much worth having????????????

-- Dave Keenan

🔗genewardsmith <genewardsmith@juno.com>

2/23/2002 1:38:44 PM

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

> Is not such a system very much worth having????????????

I'm in favor. :)

🔗gdsecor <gdsecor@yahoo.com>

2/26/2002 9:03:13 AM

Dave,

I'm sorry I have been so slow to reply, but I'm still working my way
through the volume of postings from the weekend. But this one (which
I printed & took home yesterday to ponder) is so important that I
needed to respond quickly (before reading any further).

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> It's just too many symbols for my liking. I'd be happy to see your
> symbols for the 5, 7 and 11 commas used (with a convex half-head on
> the septimal-comma arrow). They are more logical than the Sims
> symbols.

Yes, there are too many symbols, and in light of what you have to say
below, I'm almost 100 percent certain that I'm dumping the auxiliary
symbols!

> But when you start combining them into single symbols in a
> less-than-obvious way, I get very lost.

Regarding the issue of single vs. double symbols, I have been working
on a figure that illustrates some real problems with the Sims
notation, and I'm hoping that, by reworking the sagittal symbols in
light of what you have to say below, I will be able to make them more
obvious and intuitive, i.e., more to your liking. Your input has
been very helpful!

> Here (following Gene) is how I'd notate 27-tET:
>
> D D^ D} E{ Ev E F
>
> And here's 58-tET
>
> D D^ D]v D] Eb Eb^ E[v E[ E[^ Ev E E^ E]v Fv F
>
> Where
> v^ syntonic comma (80:81)
> <> septimal comma (63:64)
> [] undecimal diesis (32:33)
> {} 13-comma (1024:1053)
> jf 17-comma (2176:2187)
> yh 19-comma (512:513)
>
> I'm not particularly attached to these specific ASCII symbols, but
the
> choice of commas is _v_e_r_y_ important.

Yes, the choice of symbols is a completely separate issue from the
semantics.

I haven't had sufficient time to digest the handling of 27 & 58 yet,
so I will defer comment on that.

I am very impressed by the semantics you have shown above, and it has
caused me to completely rethink my sagittal notation, which I want to
conform to this as closely as possible (leaving aside the issue of
single vs. double symbols for the moment).

One question: Is the choice for the 13-comma graven in stone? Why
was 1024:1053 chosen instead of 26:27? I have a specific reason for
asking this: I have an idea for the sagittal symbols that would
notate primes 7 and 13 in combination (with curved flags). Only
primes 5 and 11 (and NOT 7) would be notated by the straight flags (/
and \). The curved flags would not show up in the native notations
for the simpler EDO's, such as 17, 22, 24, 31, and 41. A FULL ARROW
with CURVED lines would indicate alteration by 26:27, while a RIGHT
CURVED flag would indicate alteration by 63:64. Left-right
confusibility for the 72-EDO native notation could still be avoided
by a carefully chosen selection from both the curved and straight-
flag symbols. (While it would also be possible to mix straight and
curved flags in the same symbol, I would think very long and hard
about this before doing it, even though it would present an
additional alternative for theoretical or analytical purposes.)

> We can have one consistent set of symbols for notating both JI and
> ETs. The previous sentence should probably be in flashing lights.
> I'll say it again.
>
> * WE CAN HAVE ONE SMALL SET OF SYMBOLS FOR NOTATING BOTH JI AND ETS
*

YES, YES, YES!!!

> This seems like something we should have had a long time ago. Many
> thanks to Gene for pushing the idea.

Yes. Thank you, Gene!

> The beauty is, that with this choice of commas, there is no need to
go
> past 19-limit for notating all the ETs of interest, well into the
> hundreds. 19-limit means we only need 6 new pairs of symbols. This
is
> far fewer than Rapoport's 5-limit system as used in Scala. This is
> because Rapoport needs all those 1/n-comma symbols. Because the 17
and
> 19 commas are so small, we don't need these 1-step symbols.
>
> These 17 and 19 commas just happen to step down in size from the
> syntonic and septimal comma in an almost perfect trinary system!:
27c,
> 9c, 3c. To get the idea, notice how you can make up all the numbers
> from -13 to +13 just using combinations of 0,-1,+1,-3,+3,-9,+9
without
> using more than 3 of them and never using any of them more than
once.
>
> 13 = +9 +3 +1
> 12 = +9 +3
> 11 = +9 +3 -1
> 10 = +9 +1
> 9 = +9
> 8 = +9 -1
> 7 = +9 -3 +1
> 6 = +9 -3
> 5 = +9 -3 -1
> 4 = +3 +1
> 3 = +3
> 2 = +3 -1
> 1 = +1
> 0
> and so on.

Very impressive!

> The commas are also chosen so they vanish in 12-tET. In JI a
complete
> 19-limit otonality on G would be spelled
> G:D:Bv:F<:A:C]:Eb}:F#v:G#j:Bbh
> 1:3:5 :7 :9:11:13 :15 :17 :19
>
> Notice that, sans commas, the above all fall within a chain of
fifths
> from Eb to G# and no note is repeated.
>
> To get the best approximation of that chord in _any_ ET you would
just
> omit the symbols for any commas that vanish in that ET, and replace
> any symbols for higher primes with those of lower primes that
> correspond to the same number of steps. And sometimes we may use
> _pairs_ of symbols for lower primes in place of those for a higher
> prime.
>
> For example, in 12-tET the best approximation (athough not a usable
or
> recognisable approximation) of that complete 19-limit otonality is
> notated as.
> G:D:B:F:A:C:Eb:F#:G#:Bb
> We simply dropped all the comma symbols.
>
> Is not such a system very much worth having????????????
>
> -- Dave Keenan

YES!!!!!!!!!!!!

--George

🔗gdsecor <gdsecor@yahoo.com>

2/26/2002 1:56:40 PM

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Hi George,
>
> While I wouldn't want to sound disrespectful to anyone who was
> discussing 11-tet before I was born!, I must take umbrage with some
of
> what you've written here.
>
> I think the "it's so bad that it's good" argument for atonality that
> you make for 11-tet, the very same one that is often made for 13-
tet,
> is, simply put, wrong and overly simplistic. It seems to me to be
one
> based entirely on the numbers.
>
> I say this from working with both these tunings quite a bit. Simply
> put, if one finds the right scale, or subset of these tunings and
> sticks to it, it's hard to avoid a sense of a tonic! ...
>
> I should point out that all of these scales I found by ear. Yes,
it's
> easier to make music with tunings like 11 and 13-tet that is
> dissonant, but it's also not impossible to do exactly the opposite.
> Not by a long shot if one is so inclined and doesn't get hysterical
> and run screaming at the first signs of resistance--that's been my
> experience at least, your mileage may of course vary.
>
> take care,
>
> --Dan Stearns

Hi, Dan!

As you can see, I'm just starting to catch up on a backlog of
messages.

As you (and others) have demonstrated, there are all sorts of hidden
resources in tonal systems that are all too easy to overlook, and the
lesson is that we shouldn't be simplistic about any of these, which
makes it a non-issue to ask who got there first. As with any travel
destination, it all depends on what you saw and did once you got
there. And that depends, to some extent, on what you were (or
weren't) looking for at the time.

Even a system as "ordinary" as 31-EDO has meant different things to
different people. J. Murray Barbour (and many others before him)
looked at it without considering any primes above 5. Bosanquet used
some ratios of 7, but only to "improve" dominant 7th chords. Fokker,
on the other hand, found new harmonies in the prime numbers above 5
and did more with the system than anyone who came before him.

And I am one of those who visited 11-ET a couple of times but never
stayed more than a day or so -- a trifler at best.

--George

🔗gdsecor <gdsecor@yahoo.com>

2/26/2002 2:04:42 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > 11-ET:
> >
> > 1) In an unpublished paper (April 1964) I advocated using it for
> > atonal music: Since it contains nothing that approximates a
> perfect
> > fifth or major third, you have to go to extraordinary lengths to
> try
> > to establish a key center.
>
> this is exactly the same point i made in advocating 11-equal in my
> paper on 22-equal (you know, the one in xenharmonikon 17). have you
> looked at it yet?

Once I have more time -- I have two major projects going on now, plus
barely managing to keep up with the tuning list. (Anyway, thanks for
the reminder.)

--George

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/26/2002 10:01:24 PM

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> I am very impressed by the semantics you have shown above, and it
has
> caused me to completely rethink my sagittal notation, which I want
to
> conform to this as closely as possible (leaving aside the issue of
> single vs. double symbols for the moment).

Great.

> One question: Is the choice for the 13-comma graven in stone?

Nothing is graven in stone yet.

> Why was 1024:1053 chosen instead of 26:27?

Because 26:27 is 65 cents where 1024:1053 is 48 cents. And so 26:27
does not disappear in either 12-tET or a true Pythagorean chain. It
maps to a sharp or flat in both these systems. You could notate 26:27
as pairs like "b}" and "#{", but this could lead to ugly things like
F#b}. I consider 8:13 to be a narrow neutral sixth (11:18 being the
ordinary one). Ask yourself, is it more like a kind of C:Ab or a kind
of C:A; more like a kind of A:F or a kind of A:F#. Based purely on
distance in cents the answer in both 12-tET and Pythagorean is C:Eb}
and A:F{.

We have enough large commas already in the 11-limit. To notate as many
ETs as possible without going too far up the primes, we need smaller
commas, not larger. With the choice I've given, I've noticed that 11
and 13 commas are rarely needed together, in case that's relevant.

> I have a specific reason for
> asking this: I have an idea for the sagittal symbols that would
> notate primes 7 and 13 in combination (with curved flags). Only
> primes 5 and 11 (and NOT 7) would be notated by the straight flags
(/
> and \). The curved flags would not show up in the native notations
> for the simpler EDO's, such as 17, 22, 24, 31, and 41. A FULL ARROW
> with CURVED lines would indicate alteration by 26:27, while a RIGHT
> CURVED flag would indicate alteration by 63:64. Left-right
> confusibility for the 72-EDO native notation could still be avoided
> by a carefully chosen selection from both the curved and straight-
> flag symbols. (While it would also be possible to mix straight and
> curved flags in the same symbol, I would think very long and hard
> about this before doing it, even though it would present an
> additional alternative for theoretical or analytical purposes.)

I'm hoping you can come up with an alternative that can use the
1024:1053.

> > * WE CAN HAVE ONE SMALL SET OF SYMBOLS FOR NOTATING BOTH JI AND
ETS
> *
>
> YES, YES, YES!!!

If you're still planning to assume that certain very small commas
vanish (so certain combinations of the prime-commas never occur) then
they had better be very small (like 1 cent or less) to keep the JI
folks happy.

> > These 17 and 19 commas just happen to step down in size from the
> > syntonic and septimal comma in an almost perfect trinary system!:
> 27c,
> > 9c, 3c. To get the idea, notice how you can make up all the
numbers
> > from -13 to +13 just using combinations of 0,-1,+1,-3,+3,-9,+9
> without
> > using more than 3 of them and never using any of them more than
> once.
> >
> > 13 = +9 +3 +1
> > 12 = +9 +3
> > 11 = +9 +3 -1
> > 10 = +9 +1
> > 9 = +9
> > 8 = +9 -1
> > 7 = +9 -3 +1
> > 6 = +9 -3
> > 5 = +9 -3 -1
> > 4 = +3 +1
> > 3 = +3
> > 2 = +3 -1
> > 1 = +1
> > 0
> > and so on.
>
> Very impressive!

Except that as Manuel pointed out, it's considered bad form to combine
an up accidental with a down. In that case you'd need a binary
sequence like 1, 2, 4, 8. At least we do have that with the larger
commas (and hence lower numbered ETs).

🔗paulerlich <paul@stretch-music.com>

2/27/2002 8:58:25 AM

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

> > Why was 1024:1053 chosen instead of 26:27?
>
> Because 26:27 is 65 cents where 1024:1053 is 48 cents. And so 26:27
> does not disappear in either 12-tET

i disagree. clearly the best 1:3:5:7:9:11:13 chord in 12-equal is C-E-
G-Bb-D-F#-A, because of the 11:13 and 7:11. so 26:27 *does* disappear
in 12-equal, as far as i'm concerned.

> If you're still planning to assume that certain very small commas
> vanish (so certain combinations of the prime-commas never occur)
then
> they had better be very small (like 1 cent or less) to keep the JI
> folks happy.

but how will you keep the strong-temperament folks happy if you do
this?

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/28/2002 8:15:40 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > > Why was 1024:1053 chosen instead of 26:27?
> >
> > Because 26:27 is 65 cents where 1024:1053 is 48 cents. And so
26:27
> > does not disappear in either 12-tET
>
> i disagree. clearly the best 1:3:5:7:9:11:13 chord in 12-equal is
C-E-
> G-Bb-D-F#-A, because of the 11:13 and 7:11. so 26:27 *does*
disappear
> in 12-equal, as far as i'm concerned.

Hmm. Good point. That's one way of looking at it. In this case, 32;33
(by far the most popular choice for notational 11-comma) _doesn't_
disappear and we'd have to use 704;729, which has 6 fifths in it
instead of 1, and is 60 cents instead of 53.

But of course 12-tET is not consistent with 13s, so why take that
chord as the decider. I was looking at the best 1:3:9:13 and not all
the other ratios of 13.

But, even ignoring my arguments above, what do you think of the other
reasons I gave for favouring 1024:1053, namely smaller size and it
vanishes in Pythagorean-12 which is what the tuning is actually based
on (not 12-tET)?

> > If you're still planning to assume that certain very small commas
> > vanish (so certain combinations of the prime-commas never occur)
> then
> > they had better be very small (like 1 cent or less) to keep the JI
> > folks happy.
>
> but how will you keep the strong-temperament folks happy if you do
> this?

I'm not really recommending the above, but I don't see the problem.
Please explain.

🔗paulerlich <paul@stretch-music.com>

2/28/2002 8:20:13 PM

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

> But, even ignoring my arguments above, what do you think of the
other
> reasons I gave for favouring 1024:1053, namely smaller size and it
> vanishes in Pythagorean-12 which is what the tuning is actually
based
> on (not 12-tET)?

why pythagorean-12? i thought it was based on pythagorean-7?

>
> > > If you're still planning to assume that certain very small
commas
> > > vanish (so certain combinations of the prime-commas never
occur)
> > then
> > > they had better be very small (like 1 cent or less) to keep the
JI
> > > folks happy.
> >
> > but how will you keep the strong-temperament folks happy if you
do
> > this?
>
> I'm not really recommending the above, but I don't see the problem.
> Please explain.

2401:2400 is a very, very small comma, but its a full step for
example in 12-equal.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/28/2002 10:11:02 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > But, even ignoring my arguments above, what do you think of the
> other
> > reasons I gave for favouring 1024:1053, namely smaller size and it
> > vanishes in Pythagorean-12 which is what the tuning is actually
> based
> > on (not 12-tET)?
>
> why pythagorean-12? i thought it was based on pythagorean-7?

Sure. Take it to be pythag-7. It doesn't really matter since # and b
are defined as the apotome (2^11;3^7). It's just that I tend not to go
_beyond_ chains of 12 notes (Eb to G#) in the "canonical" (ignoring
enharmonics) notation of a given ET, so as to ensure monotonic
letters.

So, now, what about the other reasons for favouring 1024;1053 over
26;27?

> > > > If you're still planning to assume that certain very small
> commas
> > > > vanish (so certain combinations of the prime-commas never
> occur)
> > > then
> > > > they had better be very small (like 1 cent or less) to keep
the
> JI
> > > > folks happy.
> > >
> > > but how will you keep the strong-temperament folks happy if you
> do
> > > this?
> >
> > I'm not really recommending the above, but I don't see the
problem.
> > Please explain.
>
> 2401:2400 is a very, very small comma, but its a full step for
> example in 12-equal.

Aha! Excellent point. Don't do it George.

🔗paulerlich <paul@stretch-music.com>

2/28/2002 10:15:05 PM

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> >
> > > But, even ignoring my arguments above, what do you think of the
> > other
> > > reasons I gave for favouring 1024:1053, namely smaller size and
it
> > > vanishes in Pythagorean-12 which is what the tuning is actually
> > based
> > > on (not 12-tET)?
> >
> > why pythagorean-12? i thought it was based on pythagorean-7?
>
> Sure. Take it to be pythag-7. It doesn't really matter since # and
b
> are defined as the apotome (2^11;3^7). It's just that I tend not to
go
> _beyond_ chains of 12 notes (Eb to G#) in the "canonical" (ignoring
> enharmonics) notation of a given ET, so as to ensure monotonic
> letters.

oh.

> So, now, what about the other reasons for favouring 1024;1053 over
> 26;27?

i'll leave that up to you guys.

>
> > > > > If you're still planning to assume that certain very small
> > commas
> > > > > vanish (so certain combinations of the prime-commas never
> > occur)
> > > > then
> > > > > they had better be very small (like 1 cent or less) to keep
> the
> > JI
> > > > > folks happy.
> > > >
> > > > but how will you keep the strong-temperament folks happy if
you
> > do
> > > > this?
> > >
> > > I'm not really recommending the above, but I don't see the
> problem.
> > > Please explain.
> >
> > 2401:2400 is a very, very small comma, but its a full step for
> > example in 12-equal.
>
> Aha! Excellent point. Don't do it George.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

2/28/2002 10:27:06 PM

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > So, now, what about the other reasons for favouring 1024;1053 over
> > 26;27?
>
> i'll leave that up to you guys.

Paul, would you be more inclined to get involved if we moved this
discussion to tuning-math? We could use your brain power and
experience. Thanks heaps for pointing out those bloopers so far.

Anyone else want us to move this discussion to tuning-math? I offered
to do this ages ago, but no-one has said they wanted it to happen. (No
one said they didn't either).

🔗genewardsmith <genewardsmith@juno.com>

3/1/2002 12:17:26 AM

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

> Anyone else want us to move this discussion to tuning-math? I offered
> to do this ages ago, but no-one has said they wanted it to happen. (No
> one said they didn't either).

Tuning-math could use the traffic, but it seems to me the math part has been pretty well taken care of, which is why I haven't been contributing of late.

🔗jpehrson2 <jpehrson@rcn.com>

3/1/2002 7:58:04 AM

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_34071.html#35067

> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > Anyone else want us to move this discussion to tuning-math? I
offered
> > to do this ages ago, but no-one has said they wanted it to
happen. (No
> > one said they didn't either).
>
> Tuning-math could use the traffic, but it seems to me the math part
has been pretty well taken care of, which is why I haven't been
contributing of late.

***Wow. You mean everybody's figured out all the possible math for
tuning? I'm impressed. :)

🔗gdsecor <gdsecor@yahoo.com>

3/11/2002 8:47:15 AM

Dave,

This is just to let you know that I have taken some time off from the
Tuning List to work on the sagittal notation per our last
conversation. I've eliminated a number of possibilities that didn't
work to my satisfaction and am now much closer to a final solution.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > I am very impressed by the semantics you have shown above, and it
has
> > caused me to completely rethink my sagittal notation, which I
want to
> > conform to this as closely as possible (leaving aside the issue
of
> > single vs. double symbols for the moment).
>
> Great.
>
> > One question: Is the choice for the 13-comma graven in stone?
>
> Nothing is graven in stone yet.
>
> > Why was 1024:1053 chosen instead of 26:27?
>
> Because 26:27 is 65 cents where 1024:1053 is 48 cents. And so 26:27
> does not disappear in either 12-tET or a true Pythagorean chain. It
> maps to a sharp or flat in both these systems. You could notate
26:27
> as pairs like "b}" and "#{", but this could lead to ugly things
like
> F#b}. I consider 8:13 to be a narrow neutral sixth (11:18 being the
> ordinary one). Ask yourself, is it more like a kind of C:Ab or a
kind
> of C:A; more like a kind of A:F or a kind of A:F#. Based purely on
> distance in cents the answer in both 12-tET and Pythagorean is
C:Eb}
> and A:F{.

It depends on the context. I hear 8:11 primarily as an augmented
fourth (rather than a perfect fourth), and when the 8:11:13 is
sounded, the 13 will sound more like an A than an A-flat. (I noticed
that Paul Erlich said something to this effect in his reply.)
Anyway, this is beside the point, in light of what I have to say
below.

> We have enough large commas already in the 11-limit. To notate as
many
> ETs as possible without going too far up the primes, we need
smaller
> commas, not larger. With the choice I've given, I've noticed that
11
> and 13 commas are rarely needed together, in case that's relevant.
>
> > I have a specific reason for
> > asking this: I have an idea for the sagittal symbols that would
> > notate primes 7 and 13 in combination (with curved flags). Only
> > primes 5 and 11 (and NOT 7) would be notated by the straight
flags
> > (/ and \). The curved flags would not show up in the native
notations
> > for the simpler EDO's, such as 17, 22, 24, 31, and 41. A FULL
ARROW
> > with CURVED lines would indicate alteration by 26:27, while a
RIGHT
> > CURVED flag would indicate alteration by 63:64. Left-right
> > confusibility for the 72-EDO native notation could still be
avoided
> > by a carefully chosen selection from both the curved and straight-
> > flag symbols. (While it would also be possible to mix straight
and
> > curved flags in the same symbol, I would think very long and hard
> > about this before doing it, even though it would present an
> > additional alternative for theoretical or analytical purposes.)
>
> I'm hoping you can come up with an alternative that can use the
> 1024:1053.

As it turns out, neither variation of the approach that I am now
taking pairs the 7 and 13 factors together, and the one that looks
most promising at the moment requires all defining commas to be no
more than half of an apotome, so it *must* use 1024:1053 instead of
26:27.

I was wondering whether you had a particular comma in mind when you
said this, because a very useful one that I found is around 0.4 cents.
>
> > > ... These 17 and 19 commas just happen to step down in size
from the
> > > syntonic and septimal comma in an almost perfect trinary
system!: 27c,
> > > 9c, 3c. To get the idea, notice how you can make up all the
numbers
> > > from -13 to +13 just using combinations of 0,-1,+1,-3,+3,-9,+9
without
> > > using more than 3 of them and never using any of them more than
once.
> > >
> Except that as Manuel pointed out, it's considered bad form to
combine
> an up accidental with a down. In that case you'd need a binary
> sequence like 1, 2, 4, 8. At least we do have that with the larger
> commas (and hence lower numbered ETs).

That's something that I don't like about the Sims notation -- down
arrows used in conjunction with sharps, and up arrows with flats.
Anyway, I'm not concerned with trying to get a trinary sequence. I
just want a good JI notation to at least the 17 limit that will
handle EDOs up to 94, and at the moment it appears that the 19 limit
and higher EDOs are within reach.

--George

🔗dkeenanuqnetau <d.keenan@uq.net.au>

3/11/2002 6:09:45 PM

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> Dave,
>
> This is just to let you know that I have taken some time off from
the
> Tuning List to work on the sagittal notation per our last
> conversation. I've eliminated a number of possibilities that didn't
> work to my satisfaction and am now much closer to a final solution.

Thanks for letting me know. I'm glad someone's still working on it.
Johny Reinhard took the wind right out of my sails.

> It depends on the context. [whether 8:13 is more of a major or minor
6th]

True. So what is it in the most common contexts?

I hear 8:11 primarily as an augmented
> fourth (rather than a perfect fourth),

Me too, although I call it a super fourth, leaving "augmented" for
5:7.

> and when the 8:11:13 is
> sounded, the 13 will sound more like an A than an A-flat. (I
noticed
> that Paul Erlich said something to this effect in his reply.)

Yes.

> Anyway, this is beside the point, in light of what I have to say
> below.

OK.

> As it turns out, neither variation of the approach that I am now
> taking pairs the 7 and 13 factors together, and the one that looks
> most promising at the moment requires all defining commas to be no
> more than half of an apotome,

This seems like a sensible criterion to me too, perhaps for other
reasons.

> so it *must* use 1024:1053 instead of
> 26:27.

OK.

> > If you're still planning to assume that certain very small commas
> > vanish (so certain combinations of the prime-commas never occur)
> then
> > they had better be very small (like 1 cent or less) to keep the JI
> > folks happy.
>
> I was wondering whether you had a particular comma in mind when you
> said this, because a very useful one that I found is around 0.4
cents.

No I didn't. So what are the smallest ETs in which this comma
consistently fails to vanish?

> > Except that as Manuel pointed out, it's considered bad form to
> combine
> > an up accidental with a down. In that case you'd need a binary
> > sequence like 1, 2, 4, 8. At least we do have that with the larger
> > commas (and hence lower numbered ETs).
>
> That's something that I don't like about the Sims notation -- down
> arrows used in conjunction with sharps, and up arrows with flats.

I think Manuel exempts sharps and flats from this criticism.

If you had a ruler with only inch marks, what could you find quicker
(a) two and a half, less an eighth, or
(b) two and three eights?

> Anyway, I'm not concerned with trying to get a trinary sequence. I
> just want a good JI notation to at least the 17 limit that will
> handle EDOs up to 94, and at the moment it appears that the 19 limit
> and higher EDOs are within reach.

I look forward to it.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

3/11/2002 6:13:02 PM

By the way George Secor, and anyone, when you do post more on this
topic, could you please post it to tuning-math. Thanks.