[MMM] Re: 29-HTT Improvisation

Hi George,

>Okay, listen here:
>/tuning/files/secor/
>for the same example in 17 different tunings, including JI, 72-ET,
>and 29-HTT. The score is also there, at the bottom. The only
>significant difference between the 72-ET and Miracle (Stud-loco)
>examples is in how the two ratios of 13 are approximated.

Thanks for providing this. You may want to keep in mind that .mid
files will sound different for different people, depending on their
equipment, and I'm pretty sure I hear a touch of beating in the "JI"
example.

>Paul, you may be interested to compare 22-ET with 152-ET (linear
>temperament using wide fifths). I was surprised to find that the
>latter sounds noticeably better (at least to me), even though the
>fifths have a greater error.

152-equal supports many different linear temperaments (in the most
general sense, where the period need not be 1 octave, but can be 1/2
octave, 1/3 octave, etc.). Thus I have advocated 152-equal (Gene's
false comments on MMM notwithstanding) as a "universal tuning"
encompassing many of the tonal systems than interest me most. Could
you elaborate on what the differences are between the way your
example is tuned in the two files in questions, and what you think
might be hearing that makes you prefer one over the other?

>> > Beating that
>> > occurs with approximated 7-limit consonances is much more
noticeable
>> > than at higher limits, so you had better cut your allowable error
in
>> > half at the 7 limit.
>>
>> I'm not sure exactly what you mean but if you mean that a
>> given 'error' is less noticeable for more complex ratios and more
>> noticeable for simpler ratios,

>Yes.

>> this seems to support the 'TOP' idea
>> for tuning temperaments over the straight minimax-within-an-odd-
limit
>> you seem to have advocated in the past.

You didn't respond. I'd be interested to know your thoughts, since
Dave Keenan has pooh-poohed the TOP idea (in a sense).

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> You didn't respond. I'd be interested to know your thoughts, since
> Dave Keenan has pooh-poohed the TOP idea (in a sense).

Hi Paul,

I'm glad you added "in a sense". But I don't think it's really fair
to say I pooh-poohed it at all. I seem to remember saying it was
brilliant in the way it allows temperaments to be optimised for a
prime limit only (without having to worry about odd limits or
integer limits or any kind of cutoff on the prime exponents), and in
the way it tells us how to temper the octaves. Mathematically
elegant and musically efficient.

I believe I urged you to include words to that effect in your
forthcoming paper.

But of course I then went on and urged you to also mention certain
limitations, thereby tempering the enthusiasm somewhat.

-- Dave Keenan

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> 152-equal supports many different linear temperaments (in the most
> general sense, where the period need not be 1 octave, but can be 1/2
> octave, 1/3 octave, etc.). Thus I have advocated 152-equal (Gene's
> false comments on MMM notwithstanding) as a "universal tuning"
> encompassing many of the tonal systems than interest me most.

Would that mean you do think hemiwuerschmidt is worth discussing? I
think Dave would regard it as too complex, and you seeming have
adopted that point of view for your list.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> But of course I then went on and urged you to also mention certain
> limitations, thereby tempering the enthusiasm somewhat.

What do you regard as its limitations?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > 152-equal supports many different linear temperaments (in the
most
> > general sense, where the period need not be 1 octave, but can be
1/2
> > octave, 1/3 octave, etc.). Thus I have advocated 152-equal
(Gene's
> > false comments on MMM notwithstanding) as a "universal tuning"
> > encompassing many of the tonal systems than interest me most.
>
> Would that mean you do think hemiwuerschmidt is worth discussing?

Hemiwuerschmidt is probably no different from 'JI' in the ways I had
envisioned using 152. Most of the ways involved using a less-than-
ideal approximation, in 152, of at least one prime. Apparently that's
what George did too, since he said the fifth is *wider* than in 22-
equal.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> > Would that mean you do think hemiwuerschmidt is worth discussing?
>
> Hemiwuerschmidt is probably no different from 'JI' in the ways I had
> envisioned using 152.

Which means?

Most of the ways involved using a less-than-
> ideal approximation, in 152, of at least one prime.

That makes your claim that by discussing 152 you've demonstrated an
interest in tempering in the 99-171 range misleading. Through the 11
limit, there is a clear best choice for 152 val, and if you wand 152
to join 99, 130 and 140 (and why not?) you would need to use it.

Apparently that's
> what George did too, since he said the fifth is *wider* than in 22-
> equal.

The best choice of fifth in 152-equal is 89/152 of an octave. This is
2/3 of a cent sharp, not wider than 22-equal, and it is this you'd
need to use to stay in the game with the rest of them.

I think I'll post something to tuning-math on 7 and 11 limit
microtemperaments that 152 supports, there is more to it than just
amity and enneadecal.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> > > Would that mean you do think hemiwuerschmidt is worth
discussing?
> >
> > Hemiwuerschmidt is probably no different from 'JI' in the ways I
had
> > envisioned using 152.
>
> Which means?

That hemiwuerschmidt's commas wouldn't be relevant to my music -- I'd
never go far enough to circumnavigate them.

> > Most of the ways involved using a less-than-
> > ideal approximation, in 152, of at least one prime.
>
> That makes your claim that by discussing 152 you've demonstrated an
> interest in tempering in the 99-171 range misleading.

No, it was your original claim that I'm uninterested in this range
misleading.

> Through the 11
> limit, there is a clear best choice for 152 val, and if you wand 152
> to join 99, 130 and 140 (and why not?) you would need to use it.
>
> Apparently that's
> > what George did too, since he said the fifth is *wider* than in
22-
> > equal.
>
> The best choice of fifth in 152-equal is 89/152 of an octave. This
is
> 2/3 of a cent sharp, not wider than 22-equal,

But George *wasn't* using this 'best choice', and it is in *this*
context that you inserted your claim that I'm uninterested in this
range.

> and it is this you'd
> need to use to stay in the game with the rest of them.

Whatever. I like 152 because it supports meantone, a form of meantone-
based '1/3-comma adaptive-JI', mavila, pajara, injera, dominant, etc.
This may not 'stay in the game', but it's the kind of thing George
and I are clearly more interested in.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> >
> > > > Would that mean you do think hemiwuerschmidt is worth
> discussing?
> > >
> > > Hemiwuerschmidt is probably no different from 'JI' in the ways I
> had
> > > envisioned using 152.
> >
> > Which means?
>
> That hemiwuerschmidt's commas wouldn't be relevant to my music -- I'd
> never go far enough to circumnavigate them.

In my last piece, I circumnavigated these commas over and over and
over and over, to the point people remarked on the harmonic restless
of of it. They are not, in fact, hard to get to.

In cubic lattice coordinates, we have

2401/2400: (2 3 -3)
3136/3125: (-3 2 -5)
6144/6125: (-5 -1 -2)

These are not hard to get to; if you doubt me, compare to

81/80: (-1 4 3)

> But George *wasn't* using this 'best choice', and it is in *this*
> context that you inserted your claim that I'm uninterested in this
> range.

No, George was talking about microtemperaments where the tuning was
comparable to HTT, and this is far more accurate than 22-equal. He was
saying, and I agree, that there is something attractive about this
range of temperaments, which sound so much like JI, but somehow
livilier in a subtle way.

With George and I both having the same reaction I don't think you can
dismiss this degree of tempering out of hand as useless for human
purposes, especially given your exaggerated idea of how complex the
commas involved are. One thing about that to keep in mind is that as
the prime limit goes up, it becomes easier to move around in ways
which involve micro commas, since there are more dimensions to your
movement. Already the 7 limit is quite different from the 5 limit in
that regard; 225/224 is in some sense less complex than 81/80 in the
strict 7 limit:

225/224: (1 1 4)
81/80: (-1 4 3)

> > and it is this you'd
> > need to use to stay in the game with the rest of them.
>
> Whatever. I like 152 because it supports meantone, a form of meantone-
> based '1/3-comma adaptive-JI', mavila, pajara, injera, dominant, etc.
> This may not 'stay in the game', but it's the kind of thing George
> and I are clearly more interested in.

Speak for yourself; from what I have seen from George his standards
and interests are quite different from yours, to the extent that
72-equal might not be quite up to snuff. You seem to believe everyone
shares *your* standards. They simply do not, and I hope you are not
intending to claim, in your paper, that your prejudices amount to laws
of nature.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> > wrote:
> > > > --- In tuning@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> > wrote:
> > >
> > > > > Would that mean you do think hemiwuerschmidt is worth
> > discussing?
> > > >
> > > > Hemiwuerschmidt is probably no different from 'JI' in the
ways I
> > had
> > > > envisioned using 152.
> > >
> > > Which means?
> >
> > That hemiwuerschmidt's commas wouldn't be relevant to my music --
I'd
> > never go far enough to circumnavigate them.
>
> In my last piece, I circumnavigated these commas over and over and
> over and over, to the point people remarked on the harmonic restless
> of of it.

Bravo! Do you think an even more complex comma would fail to
be "restless"? Where does it end? If nowhere for you, that's fine.
But see above. My comment about hemiW. only applied to *my* music.
Can't my music explore a tonal melody, as opposed to following a long-
winded harmonic drive?

> They are not, in fact, hard to get to.
>
> In cubic lattice coordinates, we have
>
> 2401/2400: (2 3 -3)
> 3136/3125: (-3 2 -5)
> 6144/6125: (-5 -1 -2)

I commend you.

> These are not hard to get to; if you doubt me, compare to
>
> 81/80: (-1 4 3)

They're more complex, and you need *two of them together* to justify
hemiwuerschmidt in particular. That takes a rather complicated scale,
hard for listeners to follow . . . in my humble and extremely
insignificant experience.

Oops . . . I passed my deadline . . . the next 120 hours are offline
(except e-mail me if you wanna see the paper in progress).

> With George and I both having the same reaction I don't think you
can
> dismiss this degree of tempering out of hand as useless for human
> purposes,

P.S. I never did any such thing. Hello?

P.P.S.

PLEASE LOOK AGAIN at what I said above.

"To my music" -- not "useless for human purposes" -- is that clear to
you?

> especially given your exaggerated idea of how complex the
> commas involved are.

If anyone recalls, I put the temperament at "#27", one of the
nearest "rocks" along the entire opposite shore of the "moat"
encircling 23 temperaments. I never portrayed this as exaggeratedly
complex or mistuned temperament. Let alone either of the commas on an
individual basis.

> One thing about that to keep in mind is that as
> the prime limit goes up, it becomes easier to move around in ways
> which involve micro commas, since there are more dimensions to your
> movement. Already the 7 limit is quite different from the 5 limit in
> that regard; 225/224 is in some sense less complex than 81/80 in the
> strict 7 limit:
>
> 225/224: (1 1 4)
> 81/80: (-1 4 3)

I don't follow. What are these numbers? This "sense" doesn't
make "sense" to me, in my particular music-making. If I write a piece
based on chords like 1/1-3/2-9/8-27/16 and 1/1-7/6-3/2-7/4 and 1/1-
6/5-3/2-9/5 and connecting them smoothly, does it still make sense?

> > > and it is this you'd
> > > need to use to stay in the game with the rest of them.
> >
> > Whatever. I like 152 because it supports meantone, a form of
meantone-
> > based '1/3-comma adaptive-JI', mavila, pajara, injera, dominant,
etc.
> > This may not 'stay in the game', but it's the kind of thing
George
> > and I are clearly more interested in.
>
> Speak for yourself; from what I have seen from George his standards
> and interests are quite different from yours, to the extent that
> 72-equal might not be quite up to snuff.

Hello! Did you know that at one point, the entire MIRACLE-in-72-equal
discussion was "voted off" the tuning list, and I was the one who
created a new list (miracle tuning) to support the tail end of it?

> You seem to believe everyone
> shares *your* standards. They simply do not, and I hope you are not
> intending to claim, in your paper, that your prejudices amount to
laws
> of nature.

Don't worry.

Bye for now, folks!

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > But of course I then went on and urged you to also mention
certain
> > limitations, thereby tempering the enthusiasm somewhat.
>
> What do you regard as its limitations?

I'll let Paul explain that. Gotta go.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Hi George,
>
> >Okay, listen here:
> >/tuning/files/secor/
> >for the same example in 17 different tunings, including JI, 72-ET,
> >and 29-HTT. The score is also there, at the bottom. The only
> >significant difference between the 72-ET and Miracle (Stud-loco)
> >examples is in how the two ratios of 13 are approximated.
>
> Thanks for providing this. You may want to keep in mind that .mid
> files will sound different for different people, depending on their
> equipment,

True. I also have all of those examples as mp3 files in which subtle
differences can be clearly heard, but they take up too much space.

> and I'm pretty sure I hear a touch of beating in the "JI"
> example.

That may also be true of mp3 JI example in a few spots, but even then
it is extremely slight.

> >Paul, you may be interested to compare 22-ET with 152-ET (linear
> >temperament using wide fifths). I was surprised to find that the
> >latter sounds noticeably better (at least to me), even though the
> >fifths have a greater error.
>
> 152-equal supports many different linear temperaments (in the most
> general sense, where the period need not be 1 octave, but can be
1/2
> octave, 1/3 octave, etc.). Thus I have advocated 152-equal (Gene's
> false comments on MMM notwithstanding) as a "universal tuning"
> encompassing many of the tonal systems than interest me most. Could
> you elaborate on what the differences are between the way your
> example is tuned in the two files in questions, and what you think
> might be hearing that makes you prefer one over the other?

Before doing that, I would just like to mention that my 152-ET
example (using closest approximation to JI) demonstrates that it does
an excellent job of it!

I think I prefer the 152-ET example with wide fifth (linear
temperament with generator one degree more than its best fifth) to 22-
ET because the 7-limit consonances are overall much better (very
close to a local 7-limit minimax). In particular, the ratios of 5
have a much better effect, both harmonically and melodically (since
the major thirds are no longer narrow).

So I think you're onto something good with 152.

> >> ...
> >> I'm not sure exactly what you mean but if you mean that a
> >> given 'error' is less noticeable for more complex ratios and more
> >> noticeable for simpler ratios,
>
> >Yes.
>
> >> this seems to support the 'TOP' idea
> >> for tuning temperaments over the straight minimax-within-an-odd-
limit
> >> you seem to have advocated in the past.
>
> You didn't respond. I'd be interested to know your thoughts, since
> Dave Keenan has pooh-poohed the TOP idea (in a sense).

I haven't been following the TOP discussion, because:
1) I saw something early on about tempering octaves (which idea
doesn't appeal to me), and
2) The discussion was rather lengthy, and I didn't have the time to
follow it, because
3) I've been busy working on notation documentation.

Since I'm not familiar with the details of TOP, I didn't comment. If
you're advocating a weighting of tempering error according to ratio
complexity (with simpler ratios getting more weight), then I suppose
I could go along with that in principle.

But even after after you've worked it all out, an actual listening
test may turn up things you hadn't taken into account. For example,
after listening to these examples many times, I eventually came to
the conclusion that the "best" equal division between 31 and 72 is
probably 46 (taking into account both harmonic and melodic effect
relative to number of tones -- but only my opinion).

--George

--- In MakeMicroMusic@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> > Okay, listen here:
> > /tuning/files/secor/
>
> Whoa dude: rad!
>
> > for the same example in 17 different tunings, including JI,
> > 72-ET, and 29-HTT.
>
> Say, what's the difference between Exmp152w.mid
> and Exmp152.mid?

I thought the file descriptions were sufficient, but it seems not.
Exmp152.mid is 152-ET using the best approximation to JI for each
ratio in the example. Exmp152w uses the linear temperament generated
by the wide fifth of 152-ET (one degree larger than the best fifth)
to approximate 22-ET. I made a comment to Paul that I thought that
the 152 wide-fifth example sounds better than the 22-ET example.

> Ditto Exmp19p3.mid and Exmp19.mid -- does the former
> have 21 notes?

No, 19 plus 3 equals 22. This is the 19-tone well-temperament with 3
additional tones (to get some ratios of 11) that I described here,
/tuning/topicId_38076.html#38287
except that I've made a permanent modication to it, changing the size
of the best fifths so that they are now exactly the same size as in
the equal-beating 5/17-comma meantone temperament.

Exmp19.mid is simply 19-ET.

I feel that 19-ET leaves a lot to be desired, because it doesn't
provide new consonant harmony (above the 5 limit). With my 19-WT+3 I
can have 15-limit otonal harmony in 3 keys -- not a lot of
modulation, but better than no 15-limit harmony at all -- and still
have a complete circle of 19 fifths that will do virtually everything
that 19-ET will, in addition to providing a 5-limit equal-beating
temperament (in a lot of keys) as an alternative to 1/4-comma
meantone. Designed (in 1978) to provide versatility in non-
electronic applications where you can't rapidly change from one
tuning to another (such as a microtonal accordion, metallophone, or
whatever), this is my middle-ground alternative to narrow-fifth ET's.

And of course, 29-HTT, the tuning that started this thread, is my
middle-ground alternative to 15-limit JI.

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> I think I prefer the 152-ET example with wide fifth (linear
> temperament with generator one degree more than its best fifth) to 22-
> ET because the 7-limit consonances are overall much better (very
> close to a local 7-limit minimax). In particular, the ratios of 5
> have a much better effect, both harmonically and melodically (since
> the major thirds are no longer narrow).

Eh? This isn't correct.

We have as best approximatons in 152:

5/4: 49/152 0.528 cents sharp
7/4: 123/152 2.227 cents sharp
11/8: 70/152 1.1317 cents sharp

These are all sharp in a certain range, so the ideal fifth here would
be a little sharp--maybe about a cent sharp. And voila! We have just
such a fifth, perfected suited to the rest of the tuning:

3/2: 89/152 0.677 cents sharp.

This is perfect! On the other hand 90/152, at 8.571 cents sharp, is
far too sharp to work as well as 89/152 with 5 or 11, or even 7. It
makes a good fifth for temperaments which require a fifth in that
range, so for instance it can be used for pajara or augmented/tripletone.

The meantone fifth is 19-equal, which is flat. I think 270 does a
somewhat better job than 152 in pretending to be that mythical
creature, the all-around temperament. For starters, it does a pretty
good version of 13-limit JI. It has a decent meantone of about
1/5-comma, another fifth about 4.7 cents sharp and the 27-et fifth if
needed.

> But even after after you've worked it all out, an actual listening
> test may turn up things you hadn't taken into account. For example,
> after listening to these examples many times, I eventually came to
> the conclusion that the "best" equal division between 31 and 72 is
> probably 46 (taking into account both harmonic and melodic effect
> relative to number of tones -- but only my opinion).

As a fan of the 13-limit, I'd expect you to like 46, but I wonder what
you opinion is of 58?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > I think I prefer the 152-ET example with wide fifth (linear
> > temperament with generator one degree more than its best fifth)
to 22-
> > ET because the 7-limit consonances are overall much better (very
> > close to a local 7-limit minimax). In particular, the ratios of
5
> > have a much better effect, both harmonically and melodically
(since
> > the major thirds are no longer narrow).
>
> Eh? This isn't correct.

I think you misunderstood what I was trying to say. In 22-ET the
major 3rd is ~4.5c narrow (not melodically desirable) and the minor
3rd is ~11.6c wide. With the linear temperament generated by the
wide fifth of 90deg152 (I wish you wouldn't use a slash for degrees
of a division; it's too confusing), the major 3rd is ~8.4c wide (more
acceptable melodically) and the minor 3rd is ~0.1c wide -- an overall
improvement both harmonically and melodically. And all of the 7-
limit consonances are better.

> We have as best approximatons in 152:
>
> 5/4: 49/152 0.528 cents sharp
> 7/4: 123/152 2.227 cents sharp
> 11/8: 70/152 1.1317 cents sharp
>
> These are all sharp in a certain range, so the ideal fifth here
would
> be a little sharp--maybe about a cent sharp. And voila! We have just
> such a fifth, perfected suited to the rest of the tuning:
>
> 3/2: 89/152 0.677 cents sharp.
>
> This is perfect! On the other hand 90/152, at 8.571 cents sharp, is
> far too sharp to work as well as 89/152 with 5 or 11, or even 7.

But I wasn't talking about the *best* approximations in 152-ET. I
was comparing the sound of the wide-fifth (90deg152) linear
temperament with that of 22-ET, which it approximates, and I observed
that, even though 90deg152 has more error than 13deg22, the overall
effect (at the 7 limit) is better, in my opinion.

> It
> makes a good fifth for temperaments which require a fifth in that
> range, so for instance it can be used for pajara or
augmented/tripletone.

Yes.

> The meantone fifth is 19-equal, which is flat. I think 270 does a
> somewhat better job than 152 in pretending to be that mythical
> creature, the all-around temperament. For starters, it does a pretty
> good version of 13-limit JI. It has a decent meantone of about
> 1/5-comma, another fifth about 4.7 cents sharp and the 27-et fifth
if
> needed.

My ideal meantone temperament would be equal-beating, with 5/17-comma
fifths (~695.63c), which lends itself more to a 19-tone than a 12-
tone octave (19 being what Paul was seeking). In an "all-around"
division this would be my narrow fifth. The wide fifth would be
somewhere in the range from 709.59c (for a just 4:5 at +9G) to
~710.5c (for a just 5:6 at -8G). If the best fifth were the average
of the narrow and wide fifths, it would then be somewhat wider than
just. Care to figure out which division will do it?

> > But even after after you've worked it all out, an actual
listening
> > test may turn up things you hadn't taken into account. For
example,
> > after listening to these examples many times, I eventually came
to
> > the conclusion that the "best" equal division between 31 and 72
is
> > probably 46 (taking into account both harmonic and melodic effect
> > relative to number of tones -- but only my opinion).
>
> As a fan of the 13-limit, I'd expect you to like 46,

It's fine for the 17-limit, also. For the 19 limit the numbers look
terrible, but it ultimately comes down to how it actually sounds, and
I think that the representation of the 19th harmonic in 46-ET is
acceptable in spite of this -- at least melodically.

> but I wonder what
> you opinion is of 58?

It has a nice melodic effect, but I think the ratios of 5 are too
heavily tempered. The 5-limit error for 46 vs. 58 isn't a huge
difference, but it seems to be distributed in 46 in such a way that
the triads are more pleasant than in 58. (And I would say the same
thing about 46 vs. 41-ET, with the additional observation that in 41
the best major third is rather narrow -- not melodically desirable,
as a listening test will reveal.)

Another thing that gives me second thoughts about 58 is that
harmonics 11, 13, and 15 have rather large error (relative to the
size of a single degree, going well beyond 30%), even if there is no
inconsistency. (Recall that this is a criticism used in opposition
to 72-ET at the 13 limit.)

And even if it came down to a tossup between 46 and 58, I would
generally go for the division with fewer tones -- unless, of course,
I happened to be interested in some particular tonal relationship(s)
offered by 58 that are not found in 46.

It's nice to think about all the possibilities offered by all of
these different tunings, but I've reached the conclusion that if
anyone is going to compose in alternate tunings, it's best to setttle
on two or three tunings (or four at the most), and concentrate on
developing one's ideas and techniques using the tonal materials
offered by those tunings, rather than jumping around endlessly from
one tuning to another without getting an intimate knowledge of any of
them. Curiously, none of my choices are ET's. (Hmmm, looks like
this thread needs to go back to MMM.)

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> >
> > > I think I prefer the 152-ET example with wide fifth (linear
> > > temperament with generator one degree more than its best fifth)
> to 22-
> > > ET because the 7-limit consonances are overall much better (very
> > > close to a local 7-limit minimax). In particular, the ratios of
> 5
> > > have a much better effect, both harmonically and melodically
> (since
> > > the major thirds are no longer narrow).
> >
> > Eh? This isn't correct.
>
> I think you misunderstood what I was trying to say. In 22-ET the
> major 3rd is ~4.5c narrow (not melodically desirable) and the minor
> 3rd is ~11.6c wide. With the linear temperament generated by the
> wide fifth of 90deg152 (I wish you wouldn't use a slash for degrees
> of a division; it's too confusing), the major 3rd is ~8.4c wide (more
> acceptable melodically) and the minor 3rd is ~0.1c wide -- an overall
> improvement both harmonically and melodically. And all of the 7-
> limit consonances are better.

I use a slash for anything which is a rational number; this would
include fractions of an octave such as 89/152 or 90/152. Think of it
as actually being the number in question, or 2 raised to that power
(2^(89/152), 2^(90/152)).

For a very long time mathematicians were stuck using ratios such as
89:152 instead of fractions, and it did mathematics a lot of harm.
Fractions were represented by Egyptian fractions such as
1/2+1/11+1/836 in place of 89/152. All of this we have grown out of,
and have learned to do better. A fraction such as a/b can be
mulitplied or divided very easily, and can be added without too much
trouble. It can be reduced to lowest terms using Euclid's algorithm,
and compared in size by cross-multiplying very easily. And it has a
specific meaning. It is a number, and presumably we know what a number is.

What I don't know is what the temperament with generator of 90/152 is.
This (being a fraction) can be reduced to lowest terms as 45/76, and
so one way would be to use 76-equal, but you want a 152-equal
temperament. A reasonable choice of 152 temperament would be
<<14 11 9 -15 -25 -10||, with a generator an intermediate minor third,
being in between 6/5 and 7/6, a flat 25/21; it's approximately 13/11.
152 with wide fifths will work for this temperament, but optimally the
fifth is narrower, 2.2 cents or so. One could, of course, explore the
wide, wide world of <152 242 353 427| for other possibilities.

> > The meantone fifth is 19-equal, which is flat. I think 270 does a
> > somewhat better job than 152 in pretending to be that mythical
> > creature, the all-around temperament. For starters, it does a pretty
> > good version of 13-limit JI. It has a decent meantone of about
> > 1/5-comma, another fifth about 4.7 cents sharp and the 27-et fifth
> if
> > needed.
>
> My ideal meantone temperament would be equal-beating, with 5/17-comma
> fifths (~695.63c), which lends itself more to a 19-tone than a 12-
> tone octave (19 being what Paul was seeking).

This is the Wilson fifth, which lends itself to 69-equal very, very
well. My favorite meantone et of 50 isn't too far off.

In an "all-around"
> division this would be my narrow fifth. The wide fifth would be
> somewhere in the range from 709.59c (for a just 4:5 at +9G) to
> ~710.5c (for a just 5:6 at -8G).

The first is the 40^(1/9) fifth, and the second the (80/3)^(1/8)
fifth. Am I to assume the plan is to get close to the Wilson fifth
with one fifth, have another beteen 40^(1/9) and (80/3)^(1/8), and a
third in between?

> It has a nice melodic effect, but I think the ratios of 5 are too
> heavily tempered. The 5-limit error for 46 vs. 58 isn't a huge
> difference, but it seems to be distributed in 46 in such a way that
> the triads are more pleasant than in 58. (And I would say the same
> thing about 46 vs. 41-ET, with the additional observation that in 41
> the best major third is rather narrow -- not melodically desirable,
> as a listening test will reveal.)

I've composed in 41 and 46, but not yet 58. I did like the sound of
46; it's got 126/125 as a comma, which is very useful; also 2048/2025,
245/243 and 1029/1024.

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> It's nice to think about all the possibilities offered by all of
> these different tunings, but I've reached the conclusion that if
> anyone is going to compose in alternate tunings, it's best to
setttle
> on two or three tunings (or four at the most), and concentrate on
> developing one's ideas and techniques using the tonal materials
> offered by those tunings, rather than jumping around endlessly from
> one tuning to another without getting an intimate knowledge of any
of
> them. Curiously, none of my choices are ET's. (Hmmm, looks like
> this thread needs to go back to MMM.)

If I belonged to a religion that routinely shouted "Amen!", I would.
For the moment, how about "Bingo!"? (and if there is a tuning named
Bingo, it's a dog...)

Cheers,
Jon

Hi Jonathan and George!
What George says here has been my own experience and likewise have
suggested the same thing countless times in this forum. Even if our
choices in the end is different (possibly more fruitful for all in the
long run) , it seems it does more to develop a depth that need to be
cultivated.

Jon Szanto wrote:

> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> > It's nice to think about all the possibilities offered by all of
> > these different tunings, but I've reached the conclusion that if
> > anyone is going to compose in alternate tunings, it's best to
> setttle
> > on two or three tunings (or four at the most), and concentrate on
> > developing one's ideas and techniques using the tonal materials
> > offered by those tunings, rather than jumping around endlessly from
> > one tuning to another without getting an intimate knowledge of any
> of
> > them. Curiously, none of my choices are ET's. (Hmmm, looks like
> > this thread needs to go back to MMM.)
>
> If I belonged to a religion that routinely shouted "Amen!", I would.
> For the moment, how about "Bingo!"? (and if there is a tuning named
> Bingo, it's a dog...)
>
> Cheers,
> Jon
>
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> My ideal meantone temperament would be equal-beating, with 5/17-comma
> fifths (~695.63c), which lends itself more to a 19-tone than a 12-
> tone octave (19 being what Paul was seeking). In an "all-around"
> division this would be my narrow fifth. The wide fifth would be
> somewhere in the range from 709.59c (for a just 4:5 at +9G) to
> ~710.5c (for a just 5:6 at -8G).

169 has a narrow fifth of 695.86, a wide fifth of 710.059, and an
intermediate fifth about a cent sharp at 702.959. Speaking of 46-et
commas, it shares 245/243, 1029/1024 and 5120/5103 with 46, which
means it supports supersuper. It's also got 896/891, 385/384, 441/440
and 676/675 going for it. If we use the meantone fifth, we get not
81/80 but 2401/2400, which means it supports squares as well as meantone.

hi Jon,

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> If I belonged to a religion that routinely shouted
> "Amen!", I would. For the moment, how about "Bingo!"?
> (and if there is a tuning named Bingo, it's a dog...)
>
> Cheers,
> Jon

Gene's been so busy naming new tunings that he might
actually have a "bingo" tuning, but i don't know for
sure. but in any case, there's this ...

http://tonalsoft.com/enc/bingo.htm

:)

actually, i'm really glad that you brought up "bingo",
because i've just added a nice new feature to the two
applets at the bottom of the page: now there are lists
of EDOs categorized according to some of the important
unison-vectors ("vanishing commas"). mousing-over the
numbers in any one column will show you all the temperaments
(for which i have lattices) which share that unison-vector.

-monz

Hi George,

I'm not here :)

You wrote,

> > >Paul, you may be interested to compare 22-ET with 152-ET (linear
> > >temperament using wide fifths). I was surprised to find that the
> > >latter sounds noticeably better (at least to me), even though the
> > >fifths have a greater error.

Thanks . . . but I think you might be misunderstanding my favorite
way of using 22-equal, detailed in my papers:

http://lumma.org/tuning/erlich/erlich-decatonic.pdf
http://lumma.org/tuning/erlich/erlich-tFoT.pdf

> I think I prefer the 152-ET example with wide fifth (linear
> temperament with generator one degree more than its best fifth) to
22-
> ET because the 7-limit consonances are overall much better (very
> close to a local 7-limit minimax).

The 22-equal fifth is actually closer than the 152-equal wide fifth
to the 7-(odd-)-limit minimax generator of my system ("pajara", as
Gene just referred to it).

Take a look at this chart:
/tuning/files/perlich/wopaj.gif

The red line shows the 7-(odd-)limit minimax generator. Locate
yourself at "0" on the horizontal axis -- this is the equal-weighted
or "unweighted" case I'm almost sure you're talking about. Notice
that the red line at this point is somewhat below 709.5 cents.

> In particular, the ratios of 5
> have a much better effect, both harmonically and melodically (since
> the major thirds are no longer narrow).

Tell that to the Chopi! Sure, if you write melodies influenced by
Western music of the last couple centuries, you might find a narrow
5:4 approximation melodically unsatisfactory. In other stylistic
contexts, you might find just the opposite.

> So I think you're onto something good with 152.

But not for the reasons you think :) I like 152 because it does other
systems, such as meantone, which 22 can't.

>My ideal meantone temperament would be equal-beating, with 5/17-comma
>fifths (~695.63c), which lends itself more to a 19-tone than a 12-
>tone octave (19 being what Paul was seeking).

Paul who? I must have missed something . . . too busy . . .

>The wide fifth would be
>somewhere in the range from 709.59c (for a just 4:5 at +9G) to
>~710.5c (for a just 5:6 at -8G).

This is the "superpythagorean" system, or "superpyth" for short, that
you're referring to here. It can be derived from a 7-prime-limit
system by "tempering out" 64/63 and 245/243 (1728/1715 can be
substituted for either of these, it makes no difference). This brings
the total dimensionality down from 4 to 2, where dimension 1 would be
an equal temperament.

I've used this system to a limited extent, especially the "no-fives"
version of this system where only 64/63 needs to be "tempered out".

But the main thrust of my 22-equal work has been in "pajara". This
can be obtained from a 7-prime-limit system by "tempering out" 64/63
and 50/49 (225/224 can be substituted for either of these, it makes
no difference). This also brings the total dimensionality down from 4
to 2.

"Superpyth" may be a bit more accurate, or less damaging to
concordance, than "Pajara" in most tuning strategies. But "Pajara" is
simpler, as properly comparing the pairs (or triplets) of "vanishing
commas" I cite above will reveal.

Or, if you prefer, look at the size (# of notes per octave) of the
octave-repeating scales needed to support your favorite 7-prime-limit
harmonic resources. For example, a 12-tone "superpyth" scale will
only contain 1 approximate 4:5:6:7 chord. Meanwhile, a 12-
tone "pajara" scale will contain either 5 or 6 approximate 4:5:6:7
chords (depending on whether the scale is omnitetrachordal or
distributionally even). You would need to go up to the 17-
tone "superpyth" scale to get this many approximate 4:5:6:7 chords.
So "superpyth" certainly looks like a significantly more complex
system than "pajara" on this basis. To me, such complexity is a
compositional hardship.

Let's include within our sights a 7-limit version of the system you
discovered in 1974, now known as "Miracle" (225/224, 1029/1024 [or
2401/2400] "vanish"), into our considerations. This gives us three
different ways of bringing the dimensionality of the 7-prime-limit
from 4 down to 2. There are 10 or 20 other such systems which are no
worse than these three in terms of mistuning damage and complexity.
In fact, my XH18 paper (which I'm sending out tomorrow night)
presents 28 such systems (I include even higher-mistuning systems,
which can be very useful for some timbres).

(Plus a bonus system -- ennealimmal -- which, while almost twice as
complex as Miracle in the 7-limit, is barely mistuned at all. In
fact, ennealimmal's mistunings are smaller than those in the 5-
limit "schismic" temperament advocated by Helmholtz and Eivind
Groven -- systems that have been historically referred to as "just".)

Speaking of which, I have to go finish the paper.

- He who is not here

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > My ideal meantone temperament would be equal-beating, with 5/17-
comma
> > fifths (~695.63c), which lends itself more to a 19-tone than a 12-
> > tone octave (19 being what Paul was seeking). In an "all-around"
> > division this would be my narrow fifth. The wide fifth would be
> > somewhere in the range from 709.59c (for a just 4:5 at +9G) to
> > ~710.5c (for a just 5:6 at -8G).
>
> 169 has a narrow fifth of 695.86, a wide fifth of 710.059, and an
> intermediate fifth about a cent sharp at 702.959. Speaking of 46-et
> commas, it shares 245/243, 1029/1024 and 5120/5103 with 46, which
> means it supports supersuper. It's also got 896/891, 385/384,
441/440
> and 676/675 going for it. If we use the meantone fifth, we get not
> 81/80 but 2401/2400, which means it supports squares as well as
meantone.

Unfortunately, 169 is not very good for approximating JI, so there's
no really good "ideal" such as I specified (but it was fun trying).

Perhaps the next best thing would be a foil to Paul's 152-ET -- a
division that is a multiple of 22 and has a decent approximation of
the 5/17-comma fifth: 176-ET.

--George

Hi Monz,

I'm not here.

Well, that's really fun, but I'm sorry to have to report an error.

Sweep over the tunings where the kleisma ([-5 6>) vanishes, and
you'll probably see what I mean. 40-equal doesn't belong.

Of the three places 40-equal can be found on my charts which you
refer to as my zoom applet, none of them lies on the line where the
kleisma vanishes. None of the three resulting "bingo-cards" of 40-
equal would therefore show a zero at coordinates (-5,6).

Back to nonexistence,
Paul

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Jon,
>
>
> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
>
> > If I belonged to a religion that routinely shouted
> > "Amen!", I would. For the moment, how about "Bingo!"?
> > (and if there is a tuning named Bingo, it's a dog...)
> >
> > Cheers,
> > Jon
>
>
>
> Gene's been so busy naming new tunings that he might
> actually have a "bingo" tuning, but i don't know for
> sure. but in any case, there's this ...
>
> http://tonalsoft.com/enc/bingo.htm
>
>
> :)
>
>
> actually, i'm really glad that you brought up "bingo",
> because i've just added a nice new feature to the two
> applets at the bottom of the page: now there are lists
> of EDOs categorized according to some of the important
> unison-vectors ("vanishing commas"). mousing-over the
> numbers in any one column will show you all the temperaments
> (for which i have lattices) which share that unison-vector.
>
>
>
> -monz

The Chopi interval in question is probably closer in practice to a neutral
third than anything

wallyesterpaulrus wrote:

>
> Tell that to the Chopi! Sure, if you write melodies influenced by
> Western music of the last couple centuries, you might find a narrow
> 5:4 approximation melodically unsatisfactory. In other stylistic
> contexts, you might find just the opposite.
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

Monz,

Ah, yessssss. It was bingo *cards*, not a bingo tuning. Didn't have
any interest for me, just remembered the term.

Cheers,
Jon

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Hi George,
>
> I'm not here :)

I haven't been officially here for a while, either -- but I was
experiencing tuning list withdrawal symptoms, and with nothing else
to read during lunch, I eventually succumbed to the temptation of
answering a message. Grrrrr!

> You wrote,
>
> > > >Paul, you may be interested to compare 22-ET with 152-ET
(linear
> > > >temperament using wide fifths). I was surprised to find that
the
> > > >latter sounds noticeably better (at least to me), even though
the
> > > >fifths have a greater error.
>
> Thanks . . . but I think you might be misunderstanding my favorite
> way of using 22-equal, detailed in my papers:
>
> http://lumma.org/tuning/erlich/erlich-decatonic.pdf
> http://lumma.org/tuning/erlich/erlich-tFoT.pdf

No, it just wasn't relevant to my point, which is that setting an
arbitrary limit for how much tempering in a fifth might be considered
acceptable (such as no more than about the 7 cents of 19 or 22-ET)
can be overridden by other considerations, as demonstrated by the
90deg152 linear temperament, with fifths ~8 cents wide.

> ...
> > In particular, the ratios of 5
> > have a much better effect, both harmonically and melodically
(since
> > the major thirds are no longer narrow).
>
> Tell that to the Chopi! Sure, if you write melodies influenced by
> Western music of the last couple centuries, you might find a narrow
> 5:4 approximation melodically unsatisfactory.

Yes, in the past some have rejected 19-ET for that very reason. Joel
Mandelbaum's doctoral dissertation mentions an individual whom he
identified as "McClure", who, after going to the trouble of building
a 19-tone harmonium, was disappointed with the tuning, because he
thought that the fifths and major thirds were too small.

> In other stylistic
> contexts, you might find just the opposite.

True.

> ...
> >My ideal meantone temperament would be equal-beating, with 5/17-
comma
> >fifths (~695.63c), which lends itself more to a 19-tone than a 12-
> >tone octave (19 being what Paul was seeking).
>
> Paul who? I must have missed something . . . too busy . . .

Paul you! Your (152-ET) "all-around" tuning has 19-tone, 22-tone,
and 11-limit near-JI capability, so 19 is what you seek in a meantone
system.

> ...
> Speaking of which, I have to go finish the paper.
>
> - He who is not here

Taking that into account, I'll read (but won't respond to) the rest
of your message.

But when you get a chance, I would be interested in your reaction to
this last paragraph:
> Perhaps the next best thing would be a foil to Paul's 152-ET -- a
> division that is a multiple of 22 and has a decent approximation of
> the 5/17-comma fifth: 176-ET.
from /tuning/topicId_53712.html#53791

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> > Perhaps the next best thing would be a foil to Paul's 152-ET -- a
> > division that is a multiple of 22 and has a decent approximation of
> > the 5/17-comma fifth: 176-ET.
> from /tuning/topicId_53712.html#53791

It doesn't do a very plausible JI, but it has other good features. It
has both a 22-equal fifth and a Lucy meantone fifth (51/88) as well as
a slightly sharp fifth which works as, among other things, a cassandra
fifth using the 22-equal major third and the Lucy meantone 7 which is
0.644 cents flat.

It also has a few specialty items: <<25 7 2 -47 -65 -16|| and
<<11 -11 22 -43 4 82||. The latter has a mapping

[<11 17 26 30|, <0 1 -1 2|]

and 99-equal is a more plausible choice as a tuning.

Something else along these lines is 198, which is both nine times 22
and twice 99, and which is a good 11 and 13 limit system. It does a
much better job for JI than 176 does. It has a 3/13-comma meantone
fifth a touch sharper than that of 31, and a 1/2-comma fifth which
works for flattone.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > > Perhaps the next best thing would be a foil to Paul's 152-ET --
a
> > > division that is a multiple of 22 and has a decent
approximation of
> > > the 5/17-comma fifth: 176-ET.
> > from /tuning/topicId_53712.html#53791
>
> It doesn't do a very plausible JI,

True (unfortunately). I'll have to admit that 152 does sound better.

> ...
> and 99-equal is a more plausible choice as a tuning.

But really good only up to the 9-limit.

> Something else along these lines is 198, which is both nine times 22
> and twice 99, and which is a good 11 and 13 limit system. It does a
> much better job for JI than 176 does. It has a 3/13-comma meantone
> fifth a touch sharper than that of 31, and a 1/2-comma fifth which
> works for flattone.

Well, since you're upping the ante, then I should mention 217, which
is seven times 31, and which is a good 19-limit system. It also
offers a good 17-tone well-temperament (a 13-limit non-5 tuning) with
11 wide fifths (of 128deg) and 6 near-just fifths (of 127deg). (The
best keys of the well-temperament have wide fifths.)

--George

Hi George! Well, I plan to officially "return" tomorrow, so we might
as well keep this up . . .

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> > >My ideal meantone temperament would be equal-beating, with 5/17-
> comma
> > >fifths (~695.63c), which lends itself more to a 19-tone than a
12-
> > >tone octave (19 being what Paul was seeking).
> >
> > Paul who? I must have missed something . . . too busy . . .
>
> Paul you! Your (152-ET) "all-around" tuning has 19-tone, 22-tone,
> and 11-limit near-JI capability, so 19 is what you seek in a
>meantone
> system.

It isn't. 152 contains a lot of systems I use, including meantone, so
it's great "all-around". But it's certainly not the ideal for
meantone. 19 is an acceptable meantone, and 152 also contains an
acceptable adaptive-JI scheme (based on 1/3-comma, as opposed to
Vicentino's 1/4-comma, shifts) for "improving" meantone compositions.
(This works because I find its 8-cent retuning shifts acceptable,
while retuning shifts of 11 cents or so are unacceptable to my ears.)
But neither case is the quite "what I seek" in those particular
systems.

> > ...
> > Speaking of which, I have to go finish the paper.
> >
> > - He who is not here
>
> Taking that into account, I'll read (but won't respond to) the rest
> of your message.

Please do respond -- it would mean a lot to me.

> But when you get a chance, I would be interested in your reaction
to
> this last paragraph:
> > Perhaps the next best thing would be a foil to Paul's 152-ET -- a
> > division that is a multiple of 22 and has a decent approximation
of
> > the 5/17-comma fifth: 176-ET.
> from /tuning/topicId_53712.html#53791
>
> --George

Wouldn't 88-equal -- every other note of 176-equal -- fulfill both
these functions as well?

Anyway, this tuning is a bit closer than 19-equal to what I
would "seek" in a meantone. 176 would also work almost as well as 152
for a meantone-based adaptive-JI system. But 152 is better for
several other systems I care about, such as injera, mavila, and pure
11-limit JI. So 152 certainly seems more "all-around" to me than 176.

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> > and 99-equal is a more plausible choice as a tuning.
>
> But really good only up to the 9-limit.

That was in connection with a 7-limit temperament.

> Well, since you're upping the ante, then I should mention 217, which
> is seven times 31, and which is a good 19-limit system. It also
> offers a good 17-tone well-temperament (a 13-limit non-5 tuning) with
> 11 wide fifths (of 128deg) and 6 near-just fifths (of 127deg). (The
> best keys of the well-temperament have wide fifths.)

If that's the way you're going to play, then 224 is a much better
13-limit system (which is about all I care about) and it has divisors
of 7, 8, 14, 16, 32, 56, and 112. The 65/112 meantone fifth is
excellent, and the 56-equal fifth 5.19 cents sharp works as a pajara
tuning. The 59/224 minor third is slightly sharp and can serve as a
kleismic minor third, though the 7 is nearly as flat as in 19-equal.
It also does a fine version of shismic (what I used to call
countershismic) and octoid.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> If that's the way you're going to play, then 224 is a much better
> 13-limit system (which is about all I care about) and it has divisors
> of 7, 8, 14, 16, 32, 56, and 112.

And 28, with which it shares a major third.

Paul tells us in another posting:

{Anyway, this tuning is a bit closer than 19-equal to what I
would "seek" in a meantone. 176 would also work almost as well as 152
for a meantone-based adaptive-JI system. But 152 is better for
several other systems I care about, such as injera, mavila, and pure
11-limit JI. So 152 certainly seems more "all-around" to me than 176.}

If I take the rms generator for 7-limit mavila, m = 0.443463, and
multiply by these various numbers, I get

152 m = 67.406

176 m = 78.050

198 m = 87.806

217 m = 96.231

224 m = 99.336

270 m = 119.735

Not only does 152 come out on bottom in terms of absolute error, it is
the worst (using this definition of optimum, at any rate) in terms of
relative error. If 152 is acceptable, so are the others.

I'm procrastinating . . .

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Paul tells us in another posting:
>
> {Anyway, this tuning is a bit closer than 19-equal to what I
> would "seek" in a meantone. 176 would also work almost as well as
152
> for a meantone-based adaptive-JI system. But 152 is better for
> several other systems I care about, such as injera, mavila, and pure
> 11-limit JI. So 152 certainly seems more "all-around" to me than
176.}
>
> If I take the rms generator for 7-limit mavila, m = 0.443463,

I'm unfamiliar with "7-limit mavila". I meant 5-limit.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> I'm procrastinating . . .

Good, because you should give us a chance to look at the paper before
sending it off.

> I'm unfamiliar with "7-limit mavila". I meant 5-limit.

Number 19 Mavilla {21/20, 135/128}

[1, -3, -4, -7, -9, -1] [[1, 2, 1, 1], [0, -1, 3, 4]]
TOP tuning [1209.734056, 1886.526887, 2808.557731, 3341.498957]
TOP generators [1209.734056, 532.9412251]
bad: 39.824125 comp: 2.022675 err: 9.734056

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > I'm procrastinating . . .
>
> Good, because you should give us a chance to look at the paper
before
> sending it off.

Well, I'm in the middle of revising the whole thing, and haven't
written the parts about temperament complexity and combining commas
yet (I may have to give the latter extremely short shrift, due to
space limitations and John's desire to keep things relatively non-
mathematical). But here it is, chicken-scratch and all . . .

/tuning/files/perlich/coyotepaper1.doc

I have 46 horagrams printed out which I'm going to cut out and paste
onto as few pages as possible. They look much better printed out
directly than if saved and then printed.

> > I'm unfamiliar with "7-limit mavila". I meant 5-limit.
>
> Number 19 Mavilla {21/20, 135/128}
>
> [1, -3, -4, -7, -9, -1] [[1, 2, 1, 1], [0, -1, 3, 4]]
> TOP tuning [1209.734056, 1886.526887, 2808.557731, 3341.498957]
> TOP generators [1209.734056, 532.9412251]
> bad: 39.824125 comp: 2.022675 err: 9.734056

Ouch -- kind of a rough tuning. TOP 7-limit Blackwood (whose horagram
I'm calling Blacksmith, as a nod to you) already strains my tolerance
unless I keep the music moving, moving, moving. This is worse. BTW,
the whole idea of 21:20 vanishing made Dave very uncomfortable at one
point.

wallyesterpaulrus wrote:

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>>>I'm unfamiliar with "7-limit mavila". I meant 5-limit.
>>
>>Number 19 Mavilla {21/20, 135/128}
>>
>>[1, -3, -4, -7, -9, -1] [[1, 2, 1, 1], [0, -1, 3, 4]]
>>TOP tuning [1209.734056, 1886.526887, 2808.557731, 3341.498957]
>>TOP generators [1209.734056, 532.9412251]
>>bad: 39.824125 comp: 2.022675 err: 9.734056
> > > Ouch -- kind of a rough tuning. TOP 7-limit Blackwood (whose horagram > I'm calling Blacksmith, as a nod to you) already strains my tolerance > unless I keep the music moving, moving, moving. This is worse. BTW, > the whole idea of 21:20 vanishing made Dave very uncomfortable at one > point.

"Hexadecimal" <<1, -3, 5, -7, 5, 20]] makes a better 7-limit temperament, but neither of these is all that close to 5-limit mavila (TOP tuning [1206.548265, 1891.576247, 2771.109114]). The problem with <<1, -3, -4, -7, -9, -1]] is that the 7 approximation is very flat, which only gets worse as a 7/2 or 7/4 because of the stretched octaves. If one of these two gets to keep the name "mavila", it should be <<1, -3, 5, -7, 5, 20]], which has a more consistent mapping. The other possibility is <<2, -6, -6, -14, -15, 3]], but that's a half-octave temperament.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Hi George! Well, I plan to officially "return" tomorrow, so we
might
> as well keep this up . . .
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> [PE:]
> > > Speaking of which, I have to go finish the paper.
> > >
> > > - He who is not here
> >
> > Taking that into account, I'll read (but won't respond to) the
rest
> > of your message.
>
> Please do respond -- it would mean a lot to me.

Well, I don't know that there's much that I can say at this point.
You've been analyzing, classifying, and naming families of tunings in
much more detail than I ever had the time or inclination to go into
(especially not having access to a computer years ago). And since I
haven't been following your recent work-in-progress on these things
on tuning-math (due to time constraints involving other
responsibilities and commitments), I haven't yet made any concerted
effort to familiarize myself with a lot of the names you're using --
and thought that it would be good not to as long as you, Gene, and
the others hadn't yet settled some of those.

> > But when you get a chance, I would be interested in your reaction
to
> > this last paragraph:
> > > Perhaps the next best thing would be a foil to Paul's 152-ET --
a
> > > division that is a multiple of 22 and has a decent
approximation of
> > > the 5/17-comma fifth: 176-ET.
> > from /tuning/topicId_53712.html#53791
> >
> > --George
>
> Wouldn't 88-equal -- every other note of 176-equal -- fulfill both
> these functions as well?

Yes, but then you wouldn't want 76-equal -- every other note of 152-
equal -- for your all-around tuning, would you?

> Anyway, this tuning is a bit closer than 19-equal to what I
> would "seek" in a meantone. 176 would also work almost as well as
152
> for a meantone-based adaptive-JI system.

Ah, yes, that almost-dead-on minor 3rd of 19-ET serves you well in
that regard. I wasn't thinking about adaptive JI as part of
your "all-around" requirements.

> But 152 is better for
> several other systems I care about, such as injera, mavila,

Sorry, no habla espanol! ;-) I guess I'll have to read your XH18
paper to see what these names refer to. (Looking forward to that,
BTW!)

> and pure
> 11-limit JI.

JI purists will probably take issue with that statement, but there's
no denying that it's very close.

> So 152 certainly seems more "all-around" to me than 176.

Well, I believe that you've made your point, except -- when can we
look for a 152-ET keyboard design? ;-)

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > Hi George! Well, I plan to officially "return" tomorrow, so we
> might
> > as well keep this up . . .
> >
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > [PE:]
> > > > Speaking of which, I have to go finish the paper.
> > > >
> > > > - He who is not here
> > >
> > > Taking that into account, I'll read (but won't respond to) the
> rest
> > > of your message.
> >
> > Please do respond -- it would mean a lot to me.
>
> Well, I don't know that there's much that I can say at this point.
> You've been analyzing, classifying, and naming families of tunings
in
> much more detail than I ever had the time or inclination to go into
> (especially not having access to a computer years ago). And since
I
> haven't been following your recent work-in-progress on these things
> on tuning-math (due to time constraints involving other
> responsibilities and commitments), I haven't yet made any concerted
> effort to familiarize myself with a lot of the names you're using --

> and thought that it would be good not to as long as you, Gene, and
> the others hadn't yet settled some of those.
>
> > > But when you get a chance, I would be interested in your
reaction
> to
> > > this last paragraph:
> > > > Perhaps the next best thing would be a foil to Paul's 152-ET -
-
> a
> > > > division that is a multiple of 22 and has a decent
> approximation of
> > > > the 5/17-comma fifth: 176-ET.
> > > from /tuning/topicId_53712.html#53791
> > >
> > > --George
> >
> > Wouldn't 88-equal -- every other note of 176-equal -- fulfill
both
> > these functions as well?
>
> Yes, but then you wouldn't want 76-equal -- every other note of 152-
> equal -- for your all-around tuning, would you?

I've advocated 76-equal as a lesser sort of all-around tuning (as you
can see on Monz's equal temeprament encyclopaedia page), yes. It does
do Meantone, Pajara, and Injera, at least. But it doesn't do many of
the things, such as adaptive JI based off meantone and straight 11-
limit JI, that 152 does quite well.

Mavila is a sort of "anti-meantone" and was discussed by Erv Wilson:

http://www.anaphoria.com/meantone-mavila.PDF

Pajara is the system that produces the scales that the bulk of my
XH17 paper is concerned with, and Injera is the system that produces
the 26-equal scales I mention in that same paper.

> Well, I believe that you've made your point, except -- when can we
> look for a 152-ET keyboard design? ;-)

The smiley makes the point . . . the whole thing about 152 is likely
going to be useless to me in a practical sense. But it's a curiosity
of the sort that tends to stick in my mind for some reason . . .

Cheers,
Paul

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> "Hexadecimal" <<1, -3, 5, -7, 5, 20]] makes a better 7-limit
> temperament, but neither of these is all that close to 5-limit mavila
> (TOP tuning [1206.548265, 1891.576247, 2771.109114]). The problem with
> <<1, -3, -4, -7, -9, -1]] is that the 7 approximation is very flat,
> which only gets worse as a 7/2 or 7/4 because of the stretched octaves.
> If one of these two gets to keep the name "mavila", it should be <<1,
> -3, 5, -7, 5, 20]], which has a more consistent mapping. The other
> possibility is <<2, -6, -6, -14, -15, 3]], but that's a half-octave
> temperament.

Probably nothing in the 7-limit mavila family is close enough to
5-limit mavila to deserve the name. Here's the family; the number on
the second line is TOP error times the square of Graham complexity. So
what names should they carry?

135/128 [1206.548265, 521.520283]

7-limit mavila family

[1, -3, 5, -7, 5, 20] {36/35, 135/128}
[1208.959293, 530.1637287] 573.394816

[1, -3, 3, -7, 2, 15] {28/27, 35/32}
[1215.315953, 511.8117400] 551.374308

[1, -3, -2, -7, -6, 4] {15/14, 64/63}
[1194.329967, 516.2390269] 298.143022

[1, -3, -4, -7, -9, -1] {21/20, 135/128}
[1209.734056, 532.9412251] 243.351404

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> I've advocated 76-equal as a lesser sort of all-around tuning (as you
> can see on Monz's equal temeprament encyclopaedia page), yes. It does
> do Meantone, Pajara, and Injera, at least.

Both 76 and 88 show up in a search for things which do those three
well; presumably 398 is taking it too far, though 230 steps gives an
exellent injera fifth, 231 steps gives meantone, 233
garibaldi/cassandra, 235 pajara.

Hi Kraig,

The "optimal" Mavila horagram in the present paper puts the interval
in question at 358.01 cents (and the "octave" at 1206.55 cents, so
the 5:2 and 5:1 approximations are better).

So yes, indeed, in theory it should be close to a neutral third, and
if so, it perfectly illustrates my point below.

-Paul

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> The Chopi interval in question is probably closer in practice to a
neutral
> third than anything
>
> wallyesterpaulrus wrote:
>
> >
> > Tell that to the Chopi! Sure, if you write melodies influenced by
> > Western music of the last couple centuries, you might find a
narrow
> > 5:4 approximation melodically unsatisfactory. In other stylistic
> > contexts, you might find just the opposite.
> >
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>

> It's nice to think about all the possibilities offered by all of
> these different tunings, but I've reached the conclusion that if
> anyone is going to compose in alternate tunings, it's best to
setttle
> on two or three tunings (or four at the most), and concentrate on
> developing one's ideas and techniques using the tonal materials
> offered by those tunings, rather than jumping around endlessly from
> one tuning to another without getting an intimate knowledge of any
of
> them.

Agreed entirely. But if an array of possibilities is presented, it's
more likely that any given musician will be able to find the one or
two (or at most four) novel tunings that inspire him or her in
particular to develop an intimate familiarity with them.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Agreed entirely. But if an array of possibilities is presented,
it's
> more likely that any given musician will be able to find the one or
> two (or at most four) novel tunings that inspire him or her in
> particular to develop an intimate familiarity with them.

If, and only if, they are presented in a manner that allows said
musician a ghost of a chance to sort through the myriad of tunings. I
say this from recent experience, as I saw that I couldn't simply load
up every one of the thousands of tunings in Scala and try them out.

Nor will overly and predominantly (not to mention inscrutably)
mathematical descriptions of them help. I really wonder, sometimes,
how many people can look at the recent 'standard' of presenting a
tuning with generators, wedgies, and the other lines of numbers (that
it seems mostly Gene and Herman can comprehend readily) and have any
gleaning whatsoever. 3 or 4? 7 or 9, maybe? It can't be many.

Maybe your paper will help, Paul. Maybe floragrams or horagrams or
some other pictorials will also assist. But the absolute abundance,
the veritable mountain of tunings that have been shown on
these 'pages' over the last couple of years, seem overwhelming and
pretty well indistinguishable to all but a few. I bet there are good
things in there, but for the life of me I wouldn't know where to
start.

And, as you might expect, I figure the one thing that could really
allow a *musician* to understand differences between some of these
(maybe between differing types) would be music that was so
inextricably tied to a tuning that you couldn't think of one without
the other. An impossible task, I'm sure, but it would be interesting
to see. Most of the comparison tests between tunings have been far
too small in victories for me - and I can only speak for myself - to
gravitate heavily in one direction or another.

I can't tall - are you here? :)

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> Maybe your paper will help, Paul. Maybe floragrams or horagrams or
> some other pictorials will also assist. But the absolute abundance,
> the veritable mountain of tunings that have been shown on
> these 'pages' over the last couple of years, seem overwhelming and
> pretty well indistinguishable to all but a few. I bet there are good
> things in there, but for the life of me I wouldn't know where to
> start.

I'd suggest people start by asking themselves what they want in a
tuning. For instance, how close would you like it to come to JI and in
what limit? Are there any "puns", or approximations, you think you
might want? Do you like flat fifths or sharp fifths, flat major thirds
or sharp ones, and is detuning the octave on your radar screen?

If you don't yourself know the answer to these questions it becomes
doubly difficult to sort through this stuff.

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I'd suggest people start by asking themselves what they want in a
> tuning.

Beautiful. The only thing that I can add is that this is very much
the left brain end of things, and the right brain side needs to play
through tunings and find what 'feels' good.

> For instance, how close would you like it to come to JI and in
> what limit?

Or, would you like it to BE JI, right? :)

> Are there any "puns", or approximations, you think you
> might want? Do you like flat fifths or sharp fifths, flat major
thirds
> or sharp ones, and is detuning the octave on your radar screen?
>
> If you don't yourself know the answer to these questions it becomes
> doubly difficult to sort through this stuff.

Absolutely. But one must be prepared for the person who literally,
with no explicit purpose, has somehow decided that the prison of 12
black-and-white pitches will not work for them, intellectually or
artistically. It would be of value to have some way to navigate the
(apparently) endless stream of tunings that a group like this seems
to produce.

Possibly not a question that has an answer, admittedly.

Cheers,
Jon

Jon Szanto wrote:

> If, and only if, they are presented in a manner that allows said > musician a ghost of a chance to sort through the myriad of tunings. I > say this from recent experience, as I saw that I couldn't simply load > up every one of the thousands of tunings in Scala and try them out.

There does seem to be an overabundance of tunings, especially the 7-limit temperaments; it's hard to know which ones are worth pursuing. I recently dug up an old reference to the 13-limit Lemba mapping that I mentioned a while back, but it was buried at the end of a list of tunings in an old post on the tuning-math list, and no one noticed it at the time. When I originally found the 7-limit version of lemba, it was just "Number 82" in a list of 114 7-limit temperaments. Now it's turning into one of my favorite tuning systems. There must be more treasures like it buried in lists of temperaments on the tuning-math list, but it took me long enough to find this one; I think I'll stick with it for a while.

> Nor will overly and predominantly (not to mention inscrutably) > mathematical descriptions of them help. I really wonder, sometimes, > how many people can look at the recent 'standard' of presenting a > tuning with generators, wedgies, and the other lines of numbers (that > it seems mostly Gene and Herman can comprehend readily) and have any > gleaning whatsoever. 3 or 4? 7 or 9, maybe? It can't be many.

Well, I spent quite a lot of time trying to figure out wedgies because I was finally convinced they might be useful for something. But the only way to really get familiar with a tuning is to use it to tune an instrument, and until generalized keyboards are widely available and reasonably priced, most of these alternate tunings will still be really hard to get a feel for. I frequently have the feeling that some of these tunings are really great, after accidentally stumbling across some nice bit of harmonic progression or melodic inflection, but that the limitations of the 12-note keyboard prevent me from being able to use them fluently. Miracle[31], for instance, is really nice in theory, but just try to play with it on a standard keyboard! I went back to the old method of manually entering pitch bends in MIDI files when I was playing around with that one.

> Maybe your paper will help, Paul. Maybe floragrams or horagrams or > some other pictorials will also assist. But the absolute abundance, > the veritable mountain of tunings that have been shown on > these 'pages' over the last couple of years, seem overwhelming and > pretty well indistinguishable to all but a few. I bet there are good > things in there, but for the life of me I wouldn't know where to > start.

That's the real trick, knowing where to start. I've only played with a small fraction of the total number of tunings, and I'm only just starting to get a feeling for whether a tuning will be "interesting". I'll play around with it for a minute or so and if nothing "interesting" happens, set it aside and try the next one. I'm sure I overlook lots of perfectly fine temperaments that way.

> And, as you might expect, I figure the one thing that could really > allow a *musician* to understand differences between some of these > (maybe between differing types) would be music that was so > inextricably tied to a tuning that you couldn't think of one without > the other. An impossible task, I'm sure, but it would be interesting > to see. Most of the comparison tests between tunings have been far > too small in victories for me - and I can only speak for myself - to > gravitate heavily in one direction or another.

I think there've been some steps in that direction: Joseph Pehrson's Blackjack music for instance. Paul's _Glassic_ certainly caught my attention for the unique sound of its tuning, and there are early hints of interest in unusual commas back in some of Easley Blackwood's etudes. Blackwood was exploring the tonal resources of EDO's, but much of his work should be adaptable to linear temperaments as well.

Jon Szanto wrote:

> Gene,
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> >>I'd suggest people start by asking themselves what they want in a
>>tuning.
> > > Beautiful. The only thing that I can add is that this is very much > the left brain end of things, and the right brain side needs to play > through tunings and find what 'feels' good.

There's always that aspect of music. In theory 21-ET isn't a very good tuning, but it can actually be appropriate for setting a particular mood. I originally wrote Galticeran in 12-ET for the piano, but found that it sounded quite nice in 21-ET, very dark and mysterious.

http://www.io.com/~hmiller/midi/Galticeran21.mid

>>For instance, how close would you like it to come to JI and in
>>what limit?
> > > Or, would you like it to BE JI, right? :)

That's within zero cents of JI. :-)

hi Paul (and George),

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:

> > Well, I believe that you've made your point, except --
> > when can we look for a 152-ET keyboard design? ;-)
>
> The smiley makes the point . . . the whole thing about
> 152 is likely going to be useless to me in a practical
> sense. But it's a curiosity of the sort that tends to
> stick in my mind for some reason . . .
>
> Cheers,
> Paul

you certainly *will* be able to easily compose music
on the computer in 152-ET using the Tonalsoft software.

Chris (my Tonalsoft partner) and i are hoping that
some intrepid instrument designers out there will be
wanting to make microtonal controllers to work with
our software. i think that a keyboard like the Microzone
would be able to handle 152-ET quite well.

(Paul knows, but for those who don't: click on
"keyboards" at http://starrlabs.com)

that would make jamming / improvising etc. with our
software in 152-ET feasible.

-monz

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> There does seem to be an overabundance of tunings, especially the
> 7-limit temperaments; it's hard to know which ones are worth pursuing.

It's easier to get a handle on 5 and 7 limit linear temperaments, but
lately there's been some attention paid to the 13-limit. Where does
one stop? If you keep going, the linear temperaments get so complex
that one wants to turn to planar, spacial, etc. If we do that, the
result is harder to understand (no MOS!) and the number of
possibilities is rather overwhelming.

>There must be more treasures
> like it buried in lists of temperaments on the tuning-math list, but it
> took me long enough to find this one; I think I'll stick with it for a
> while.

Looking at the complexity range you favor (low) still seems like good
advice here.

> Well, I spent quite a lot of time trying to figure out wedgies
because I
> was finally convinced they might be useful for something. But the only
> way to really get familiar with a tuning is to use it to tune an
> instrument, and until generalized keyboards are widely available and
> reasonably priced, most of these alternate tunings will still be really
> hard to get a feel for.

I think there are other ways. One approach is to look at the commas.
If I needed to tune an instrument, I'd never be able to compose
anything in the tunings I favor.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> There's always that aspect of music. In theory 21-ET isn't a very good
> tuning, but it can actually be appropriate for setting a particular
> mood. I originally wrote Galticeran in 12-ET for the piano, but found
> that it sounded quite nice in 21-ET, very dark and mysterious.

12 and 21 share what Paul is calling "august", a 7-limit version of
augmented. 21 has the flat fifth of 7, and excellent 7s, whereas 12
has an excellent fifth and lousy 7s. Since they share the commas 36/35
and 128/125, and hence their ratio 225/224, translation from 12 to 21
is logical for certain types of music. If you really want to be brave,
you could try to wean such a piece of music from these commas and only
leave the ratio 225/224, and the 21-et comma 1029/1024 (and 385/384 if
you want), which would turn your 21-et piece into Blackjack. If you
could manage to convert Galticeran into a Blackjack piece without too
much damage, it would be an impressive tour de force, 12-->21-->Blackjack.

> http://www.io.com/~hmiller/midi/Galticeran21.mid

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > Agreed entirely. But if an array of possibilities is presented,
> it's
> > more likely that any given musician will be able to find the one
or
> > two (or at most four) novel tunings that inspire him or her in
> > particular to develop an intimate familiarity with them.
>
> If, and only if, they are presented in a manner that allows said
> musician a ghost of a chance to sort through the myriad of tunings.
I
> say this from recent experience, as I saw that I couldn't simply
load
> up every one of the thousands of tunings in Scala and try them out.
>
> Nor will overly and predominantly (not to mention inscrutably)
> mathematical descriptions of them help. I really wonder, sometimes,
> how many people can look at the recent 'standard' of presenting a
> tuning with generators, wedgies, and the other lines of numbers
(that
> it seems mostly Gene and Herman can comprehend readily) and have
any
> gleaning whatsoever. 3 or 4? 7 or 9, maybe? It can't be many.
>
> Maybe your paper will help, Paul. Maybe floragrams or horagrams or
> some other pictorials will also assist.

My paper will have 46 horagrams in it, though I didn't include them
in the .doc I uploaded. I completely agree with your comments here,
and I'd greatly appreciate any comments, even if only remotely
constructive, you might have on my paper.

> And, as you might expect, I figure the one thing that could really
> allow a *musician* to understand differences between some of these
> (maybe between differing types) would be music that was so
> inextricably tied to a tuning that you couldn't think of one
without
> the other. An impossible task, I'm sure, but it would be
interesting
> to see.

That'll be the next project ;) Not a paper, of course.

> I can't tall - are you here? :)

Yup :(

Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> My paper will have 46 horagrams in it, though I didn't include them
> in the .doc I uploaded. I completely agree with your comments here,
> and I'd greatly appreciate any comments, even if only remotely
> constructive, you might have on my paper.

Well, I always strive for at least _remotely_ constructive comments!
Only question: do you mean I should wait for the final article, or
take a look now?

> That'll be the next project ;) Not a paper, of course.

Sigh. Music: the poor step-child of music theory. ;-)

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Paul,
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > My paper will have 46 horagrams in it, though I didn't include
them
> > in the .doc I uploaded. I completely agree with your comments
here,
> > and I'd greatly appreciate any comments, even if only remotely
> > constructive, you might have on my paper.
>
> Well, I always strive for at least _remotely_ constructive
comments!
> Only question: do you mean I should wait for the final article, or
> take a look now?

Take a look now. It's not complete, there are some typos and a lot
of "*******"s which mean I need to insert elaborations, but it's at
this (75% or so) point where critiques could do the most good. And,
of course, this is the worst time to get into big, heated arguments
of opinion, and the best time to say, "Well, you should take this
whole section of the paper and move it over there" or "you need to
insert a sentence defining . . ." and stuff like that.

I'm praying that this paper won't induce a complete shut-out response
in you the way _The Forms Of Tonality_ did. But if it does, I'll
(<choke>) understand.

> > That'll be the next project ;) Not a paper, of course.
>
> Sigh. Music: the poor step-child of music theory. ;-)

Hee hee. Then I'm really looking forward to becoming an "adoptive
parent".

Gene Ward Smith wrote:

> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> > >>There's always that aspect of music. In theory 21-ET isn't a very good >>tuning, but it can actually be appropriate for setting a particular >>mood. I originally wrote Galticeran in 12-ET for the piano, but found >>that it sounded quite nice in 21-ET, very dark and mysterious.
> > > 12 and 21 share what Paul is calling "august", a 7-limit version of
> augmented. 21 has the flat fifth of 7, and excellent 7s, whereas 12
> has an excellent fifth and lousy 7s. Since they share the commas 36/35
> and 128/125, and hence their ratio 225/224, translation from 12 to 21
> is logical for certain types of music. If you really want to be brave,
> you could try to wean such a piece of music from these commas and only
> leave the ratio 225/224, and the 21-et comma 1029/1024 (and 385/384 if
> you want), which would turn your 21-et piece into Blackjack. If you
> could manage to convert Galticeran into a Blackjack piece without too
> much damage, it would be an impressive tour de force, 12-->21-->Blackjack.

Galticeran is based on a 9-note augmented temperament MOS, in different transpositions (two different ones at the same time, in one part towards the end). This explains why it works so well in 21-ET (also 27 and 15-et for that matter -- http://www.io.com/~hmiller/midi/Galticeran27.mid and http://www.io.com/~hmiller/midi/Galticeran15.mid), but not particularly well in 22-ET (http://www.io.com/~hmiller/midi/Galticeran22.mid). It's not very likely that I could get it to work with Blackjack. But you could start with something written in Blackjack and warp it to 21 and 12, if it doesn't use any miracle-specific commas.

Of course I didn't know about MOS's or augmented temperament when I wrote it (1986); it was just a particularly good 9-note scale I hadn't seen before.

The 27-ET version is an interesting contrast to the 21; the same notes but with a distinctly different mood.

Gene Ward Smith wrote:

> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> > >>There does seem to be an overabundance of tunings, especially the >>7-limit temperaments; it's hard to know which ones are worth pursuing. > > > It's easier to get a handle on 5 and 7 limit linear temperaments, but
> lately there's been some attention paid to the 13-limit. Where does
> one stop? If you keep going, the linear temperaments get so complex
> that one wants to turn to planar, spacial, etc. If we do that, the
> result is harder to understand (no MOS!) and the number of
> possibilities is rather overwhelming. Looking at it from another point of view, 11- and 13-limit temperaments are interesting because there's fewer of them that are any good within a particular complexity range; they have more constraints on what makes a good temperament.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> Gene Ward Smith wrote:
>
> > --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> >
> >
> >>There's always that aspect of music. In theory 21-ET isn't a very
good
> >>tuning, but it can actually be appropriate for setting a
particular
> >>mood. I originally wrote Galticeran in 12-ET for the piano, but
found
> >>that it sounded quite nice in 21-ET, very dark and mysterious.
> >
> >
> > 12 and 21 share what Paul is calling "august", a 7-limit version
of
> > augmented. 21 has the flat fifth of 7, and excellent 7s, whereas
12
> > has an excellent fifth and lousy 7s. Since they share the commas
36/35
> > and 128/125, and hence their ratio 225/224, translation from 12
to 21
> > is logical for certain types of music. If you really want to be
brave,
> > you could try to wean such a piece of music from these commas and
only
> > leave the ratio 225/224, and the 21-et comma 1029/1024 (and
385/384 if
> > you want), which would turn your 21-et piece into Blackjack. If
you
> > could manage to convert Galticeran into a Blackjack piece without
too
> > much damage, it would be an impressive tour de force, 12-->21--
>Blackjack.
>
> Galticeran is based on a 9-note augmented temperament MOS,

This is known to the world out there as the Tcherepnin scale:

http://www.tcherepnin.com/alex/basic_elem1.htm

Apparently Tcherepnin conceived of chords like C-Eb-E-G as his
fundamental harmonic units for this scale. Dan Stearns would love
this.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> (also 27 and 15-et
> for that matter -- http://www.io.com/~hmiller/midi/Galticeran27.mid
> and

I listed to the first half of this -- stellar! I guess it grows on
you. And the Mizarian Porcupine Overture sounds different than I
remembered it -- have you revised it lately? BTW, I love the
progression in the *first* part of Mizarian . . . did you ever
discuss that one? I think you really should . . .

--- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:

> i think that the past decade has seen a great expansion
> of the study of tuning, thanks largely to the internet.

i just realized after i wrote that that the tuning
list is now exactly 10 years old, +/- 6 months.

does anyone know exactly when the tuning list began
on the Mills College Server?

was that the first electronic one? was there ever
a bulletin board for tuning before that? i know that
the tuning list was an outgrowth of the
Xenharmonic Alliance, which i believe was started
by Ivor Darreg ... is that correct?

-monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
>
> > (also 27 and 15-et for that matter --
> > http://www.io.com/~hmiller/midi/Galticeran27.mid
>
> I listed to the first half of this -- stellar! I guess
> t grows on you.

i really love this, Herman!!! i listened to it in 21 also,
but like 27 much more.

> and the Mizarian Porcupine Overture sounds different than I
> remembered it -- have you revised it lately? BTW, I love the
> progression in the *first* part of Mizarian . . . did you ever
> discuss that one? I think you really should . . .

can we please have a score of Galticeran27?
and a nice long explanation of how you used the tuning.
i would really love that -- i like this piece a lot.

-monz

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> Looking at it from another point of view, 11- and 13-limit temperaments
> are interesting because there's fewer of them that are any good
within a
> particular complexity range; they have more constraints on what makes a
> good temperament.

I think my way of putting it--that they are more complex--gets to the
heart of the matter. If you take any fixed equal temperament and go
uplimit, there will be a tendency for the complexity to increase for
the best approximations until you've pretty well covered the whole
thing, no matter what you are using as a generator. Two of these taken
together give you a linear temperament, which inherits the tendency
for the complexity to become greater.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > i think that the past decade has seen a great expansion
> > of the study of tuning, thanks largely to the internet.
>
>
> i just realized after i wrote that that the tuning
> list is now exactly 10 years old, +/- 6 months.
>
> does anyone know exactly when the tuning list began
> on the Mills College Server?

Here's your answer:

http://www.mills.edu/LIFE/CCM/ftp/tuning/list/archive/feb941

Looks like Feb 1, 1994.

Hey monz, listen to this . . .

http://www.io.com/~hmiller/music/ex/hanaki.mid

Herman's got a lot of great stuff under his sleeve!

BTW, this tuning was panned, in a sense, by Dave K. ;)

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Hey monz, listen to this . . .
>
> http://www.io.com/~hmiller/music/ex/hanaki.mid
>
> Herman's got a lot of great stuff under his sleeve!
>
> BTW, this tuning was panned, in a sense, by Dave K. ;)

Not 27, but the tuning the above example is in . . . which BTW needs
a better English name. I suggest "Mork" ;)

hi Jon and Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> > > That'll be the next project ;) Not a paper, of course.
> >
> > Sigh. Music: the poor step-child of music theory. ;-)
>
> Hee hee. Then I'm really looking forward to becoming an
> "adoptive parent".

Jon keeps towing the party line! ;-)

(and good for you to do so ... as is only right for the
list-mom of MMM and park-ranger of Corporeal Meadows)

but, even tho i like most of Paul's music that i've heard,
i'm glad he spends so much time writing theory.
he's one of the best tuning theorists around.

-monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> >
> > i just realized after i wrote that that the tuning
> > list is now exactly 10 years old, +/- 6 months.
> >
> > does anyone know exactly when the tuning list began
> > on the Mills College Server?
>
> Here's your answer:
>
> http://www.mills.edu/LIFE/CCM/ftp/tuning/list/archive/feb941
>
> Looks like Feb 1, 1994.

too bad we already missed the chance to celebrate the
actual anniversary date. :(

-monz

monz wrote:

> can we please have a score of Galticeran27?
> and a nice long explanation of how you used the tuning.
> i would really love that -- i like this piece a lot.

The original 12-ET piano score is on my web page:
http://www.io.com/~hmiller/png/Galticeran-p1.png
http://www.io.com/~hmiller/png/Galticeran-p2.png
http://www.io.com/~hmiller/png/Galticeran-p3.png
http://www.io.com/~hmiller/png/Galticeran-p4.png

I used MIDICONV to retune the original 12-ET MIDI file to 27-ET.

! 12 notes of 27-TET (Galticeran scale)
coords 3
octave 1.0
fifth 0.592592592
third 0.333333333
notes 12
0 0 0 0 ! C
1 -2 3 1 ! C#
2 -1 2 0 ! D
3 0 1 -1 ! Eb
4 0 0 1 ! E
5 -1 3 -1 ! F
6 -1 2 1 ! F#
7 0 1 0 ! G
8 1 0 -1 ! Ab
9 -1 3 0 ! A
10 0 2 -1 ! Bb
11 0 1 1 ! B
12 1 0 0 ! C

So essentially it's in a slightly retuned 12-ET with sharp fifths; only 12 of the 27 notes are used. The other augmented versions are the same, but with different values for the fifth.

E B F# C#
C G D A
Ab Eb Bb F

Hmm, since it looks like I still have all the files I need, I'm tempted to do a TOP augmented[12] version.

octave 0.999980525
fifth 0.577227706
third 0.333326841

http://www.io.com/~hmiller/midi/galticeran-top-augmented.mid

Hi Herman,

Couple of questions:

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> The original 12-ET piano score is on my web page:

So, when you compose this in 12, are you actually thinking 12, or are
you working it out with a midi relay or something? If composing in
twelve, do you then just 'try' converting to differing tunings to see
what works for you?

> I used MIDICONV to retune the original 12-ET MIDI file to 27-ET.
>
> ! 12 notes of 27-TET (Galticeran scale)
> coords 3
> octave 1.0
> fifth 0.592592592
> third 0.333333333
> notes 12
> 0 0 0 0 ! C
> 1 -2 3 1 ! C#

Somehow I hadn't come across that format for a Scala file - I'll
check in Scala before asking questions...

> So essentially it's in a slightly retuned 12-ET with sharp fifths;
only
> 12 of the 27 notes are used.

I wonder if other people have been confused in this way before: when
you mentioned a piece in 27, I usually think that all (or the
majority) of the notes would have been used, but I see that it is a
subset. If you do restrict to a limited set of the pitches
(essentially a twelve note scale/tuning *derived* from 27et), maybe
it would be cool to have a way to document that. I believe I've seen
Gene do it with magic[13] or some similar convention.

I *do* enjoy your pieces, and hope that comments haven't led you to
think to the contrary; I really do hope, someday, that you'll find it
of value to create your own recordings of them, so they aren't just
bare .mid files. I can hear a lot of instrumental
and 'orchestrational' effects that would really enhance them with
some of the tools available to musicians right now...

Cheers,
Jon

Jon Szanto wrote:

> Hi Herman,
> > Couple of questions:
> > --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> >>The original 12-ET piano score is on my web page:
> > > So, when you compose this in 12, are you actually thinking 12, or are > you working it out with a midi relay or something? If composing in > twelve, do you then just 'try' converting to differing tunings to see > what works for you?

I wrote this in 1986, and I was still very much thinking in 12 at the time. It was shortly after that time that I started playing with 19-ET and other meantone scales. But it was only a few years ago that I started trying to retune some of my old 12-ET music, and realized that Galticeran was in augmented temperament (which at that time was still only a 5-limit temperament; I don't think anyone had come up with the 7-limit version yet).

> Somehow I hadn't come across that format for a Scala file - I'll > check in Scala before asking questions...

It's not Scala; it's Graham Breed's Midiconv utility:
http://x31eq.com/software.htm

Herman,

Ta for all the info - I probably have Graham's utility somewhere but
never used it!

Cheers,
Jon

hi Jon,

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> > I used MIDICONV to retune the original 12-ET MIDI file to 27-ET.
> >
> > ! 12 notes of 27-TET (Galticeran scale)
> > coords 3
> > octave 1.0
> > fifth 0.592592592
> > third 0.333333333
> > notes 12
> > 0 0 0 0 ! C
> > 1 -2 3 1 ! C#
>
> Somehow I hadn't come across that format for a Scala file - I'll
> check in Scala before asking questions...
>
> > So essentially it's in a slightly retuned 12-ET with
> > sharp fifths; only 12 of the 27 notes are used.
>
> I wonder if other people have been confused in this way
> before: when you mentioned a piece in 27, I usually think
> that all (or the majority) of the notes would have been used,
> but I see that it is a subset. If you do restrict to a
> limited set of the pitches (essentially a twelve note
> scale/tuning *derived* from 27et), maybe it would be cool
> to have a way to document that. I believe I've seen
> Gene do it with magic[13] or some similar convention.

Graham's method does indeed give a complete documentation
of the tuning Herman used -- it's just very cryptic.
i haven't used MIDIconv myself for many years now, and
it took me a while to figure it out again.

the lattice Herman drew in the post you quoted
relates directly to the MIDIconv output table which
he quoted above his lattice.

in that MIDIconv output table, the first 5 lines define
the parameters of the scale:

the first line, "coords 3":
there are 3 coordinates, which sort-of-equate to the
prime-factors of the harmony, in this case 2, 3, and 5.

the next 3 lines each define the logarithmic size of
the coordinates in terms of "octaves", or more generally,
in terms of the period:

octave 1.0
fifth 0.592592592
third 0.333333333

just multiply these by 1200 to find the cents:

octave 1200
fifth 711.11 ... (exact value: 711 & 1/9 cents)
third 400

finally, "notes 12" says that this is a 12-note scale.

the last 12 rows simply: itemize each note (in the first
column), then show the mapping according to the 3 coordinates
(in the 2nd, 3rd, and 4th columns), then finally after the
exclamation point the last column gives the letter-name.

if you look at the 3rd and 4th columns of those 12 rows,
you'll see that they give the same coordinates where the
corresponding letter-names appear in Herman's lattice:

(i'll redraw both, in an attempt to circumvent Yahoo's
stupid "space saving feature" and keep the columns aligned)

. note . 8ves 5ths . 3rds
... 0 ... 0 ... 0 ... 0 ! C
... 1 .. -2 ... 3 ... 1 ! C#
... 2 .. -1 ... 2 ... 0 ! D
... 3 ... 0 ... 1 .. -1 ! Eb
... 4 ... 0 ... 0 ... 1 ! E
... 5 .. -1 ... 3 .. -1 ! F
... 6 .. -1 ... 2 ... 1 ! F#
... 7 ... 0 ... 1 ... 0 ! G
... 8 ... 1 ... 0 .. -1 ! Ab
... 9 .. -1 ... 3 ... 0 ! A
.. 10 ... 0 ... 2 .. -1 ! Bb
.. 11 ... 0 ... 1 ... 1 ! B
.. 12 ... 1 ... 0 ... 0 ! C

lattice:

5ths ------------
E .. B .. F# . C# .. |
C .. G .. D .. A ... 3rds
Ab . Eb . Bb . F ... |

if you multiply the coordinate-values in the table
by the cents-values of each coordinate-definition
(as i gave above), and add the 3 coordinates in
each column together, you get the cents-value of
each note in the scale.

for example:

note 7 is "7 0 1 0 ! G". this means that this note
is calculated as one "5th", with no "octaves" or "3rds".
we saw above that a "5th" is defined as 711&1/9 cents,
so that is the cents-value of note 7 ("G") in this scale.
hence, as Herman said: "essentially it's in a slightly
retuned 12-ET with sharp fifths".

note 1 is "1 -2 3 1 ! C#". so it's three "5ths" plus
one "3rd" minus two "8ves". in cents-values, that
would be: (3 * 711&1/9) + 400 - (2 * 1200)
= 2133&1/3 + 400 - 2400 = 133&1/3 cents.

etc.

the full list of cents-values for the scale is thus
very easy to calculate ... but i'll give it here anyway.
the decimal values are actually Excel's best attempt
at rendering simple fractions, so i give those too:

note .. ~cents .... exact cents
C ...... 0 ............. 0
C# ... 133.3333308 ... 133 1/3
D .... 222.2222208 ... 222 2/9
Eb ... 311.1111108 ... 311 1/9
E .... 399.9999996 ... 400
F .... 533.3333316 ... 533 1/3
F# ... 622.2222204 ... 622 2/9
G .... 711.1111104 ... 711 1/9
Ab ... 800.0000004 ... 800
A .... 933.3333312 ... 933 1/3
Bb .. 1022.222221 ... 1022 2/9
B ... 1111.11111 .... 1111 1/9
C ... 1200 .......... 1200

hope that helps you unravel the mystery of Herman's tuning.
:)

(why didn't i think of that when Herman retuned the
Ravel "Pavane"?)

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

...well, he wrote quite a lot! Thanks for the excessive typing, Joe,
I am sure you have other things to do, but I appreciate the lucid
manner of description. Will be filed for future consideration.

Cheers,
Jon

i had a heck of a time finding the post in which Paul
gave the link to his new paper, so i'm simply making
it easier for everyone else to find it now, and to keep
discussion of it with the proper subject heading.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> Well, I'm in the middle of revising the whole thing, and haven't
> written the parts about temperament complexity and combining commas
> yet (I may have to give the latter extremely short shrift, due to
> space limitations and John's desire to keep things relatively non-
> mathematical). But here it is, chicken-scratch and all . . .
>
> /tuning/files/perlich/coyotepaper1.doc

-monz

hi Paul,

near the bottom of page 6 ("Temperaments"), you wrote:

>> "The vanishing of the Pythagorean comma now implies that
>> moving 19 rungs in the positive direction along the two-axis
>> is equivalent to moving 12 rungs in the positive direction
>> along the three-axis;

unless i'm misunderstanding something, that should say
"moving 19 rungs in the *negative* direction along the two-axis".

and two opinionated comments from me:

1) i really think the axes should be labeled with the
Arabic-numeral figures rather than the English words,
i.e., "2-axis" instead of "two-axis", etc. can't really
give a good reason for this, other than that it just
seems better to me.

2) selfish, yes ... but i also really think that where you
introduce the term "vector" in connection with measuring
lattice distance, you should mention that Gene and i use
"monzo" to mean the vector which specifically contains
exponents of prime-factors, which *is* exactly the kind
you are using here. i think that at least he and i are
determined to make it a part of tuning theory terminology.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> i had a heck of a time finding the post in which Paul
> gave the link to his new paper, so i'm simply making
> it easier for everyone else to find it now, and to keep
> discussion of it with the proper subject heading.
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > Well, I'm in the middle of revising the whole thing,
> > and haven't written the parts about temperament complexity
> > and combining commas yet (I may have to give the latter
> > extremely short shrift, due to space limitations and John's
> > desire to keep things relatively non-mathematical).
> > But here it is, chicken-scratch and all . . .
> >
> > /tuning/files/perlich/coyotepaper1.
doc
>
>
>
> -monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> 2) selfish, yes ... but i also really think that where you
> introduce the term "vector" in connection with measuring
> lattice distance, you should mention that Gene and i use
> "monzo" to mean the vector which specifically contains
> exponents of prime-factors, which *is* exactly the kind
> you are using here. i think that at least he and i are
> determined to make it a part of tuning theory terminology.

I want *some* word which means this. I also want some word for the
dual notion, "val", and so far I've resisted changing that to "breed".
Paul's big opportunity to force me to do that is this paper, but Paul
I think is trying to avoid any difficulties, which would include
introducing new terminology. Questions about whether the components of
his vector need to be integers, and whether we are talking about
abelian groups or vector spaces, I think is the sort of stuff he wants
to bail from.

>I want *some* word which means this.

Monzo and Val are in use and I don't think they
should be "changed". This of course doesn't
obligate any authors, such as Paul, to anything.
And if he uses other terms for some reason, and
those catch on, and five years from now nobody
is using Monzo and Val, so be it.

And Joe, I understand sky writing is very
affordable these days. If it makes you feel
better I'm sure your name could be written in
the clouds over a major city.

-Carl

Carl Lumma wrote:

>And Joe, I understand sky writing is very
>affordable these days. If it makes you feel
>better I'm sure your name could be written in
>the clouds over a major city.
>
>-Carl
>
He could sell hot pink t-shirts that have monzo
written in silver sparkle from his web site too.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

hi Gene (and Paul),

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > 2) selfish, yes ... but i also really think that where you
> > introduce the term "vector" in connection with measuring
> > lattice distance, you should mention that Gene and i use
> > "monzo" to mean the vector which specifically contains
> > exponents of prime-factors, which *is* exactly the kind
> > you are using here. i think that at least he and i are
> > determined to make it a part of tuning theory terminology.
>
> I want *some* word which means this. I also want some word
> for the dual notion, "val", and so far I've resisted changing
> that to "breed". Paul's big opportunity to force me to do
> that is this paper, but Paul I think is trying to avoid any
> difficulties, which would include introducing new terminology.
> Questions about whether the components of his vector need to
> be integers, and whether we are talking about abelian groups
> or vector spaces, I think is the sort of stuff he wants
> to bail from.

i can understand all of that, especially given the constraints
within which John Chalmers asked him to keep his paper (not
too much math).

but at the point where Paul introduces "vector" to describe
the routes around the lattice "road map", it *has* already
become unavoidably mathematical.

all i'm saying is that we're already using "monzo" to refer
specifically to the types of vectors that we use in tuning theory,
and Paul has already described what a vector is, so why not
just pop the new term in?

-monz

hi Carl,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> > I want *some* word which means this.
>
> Monzo and Val are in use and I don't think they
> should be "changed". This of course doesn't
> obligate any authors, such as Paul, to anything.
> And if he uses other terms for some reason, and
> those catch on, and five years from now nobody
> is using Monzo and Val, so be it.

perfectly understandable.

> And Joe, I understand sky writing is very
> affordable these days. If it makes you feel
> better I'm sure your name could be written in
> the clouds over a major city.
>
> -Carl

that gave me a chuckle ... but i'm not seeking to
have everyone in a major city know my name.

... only other musicians and music-theorists. ;-)

-monz

--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:

> Carl Lumma wrote:
>
> >And Joe, I understand sky writing is very
> >affordable these days. If it makes you feel
> >better I'm sure your name could be written in
> >the clouds over a major city.
> >
> >-Carl
> >
> He could sell hot pink t-shirts that have monzo
> written in silver sparkle from his web site too.
>
>
>
> --
> * David Beardsley
> * microtonal guitar
> * http://biink.com/db

i probably will. thanks for the idea.

-monz

monz wrote:

>--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
>
> >
>>Carl Lumma wrote:
>>
>>>nd Joe, I understand sky writing is very
>>>affordable these days. If it makes you feel
>>>better I'm sure your name could be written in
>>>the clouds over a major city.
>>>
>>>-Carl
>>>
>>e could sell hot pink t-shirts that have monzo
>>written in silver sparkle from his web site too.
>>
>>-- >>* David Beardsley
>>* microtonal guitar
>>* http://biink.com/db
>> >>
>
>i probably will. thanks for the idea.
>
Thongs and baseball hats too.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> monz wrote:
>
> >--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> >
> >
> >
> >>Carl Lumma wrote:
> >>
> >>>nd Joe, I understand sky writing is very
> >>>affordable these days. If it makes you feel
> >>>better I'm sure your name could be written in
> >>>the clouds over a major city.
> >>>
> >>>-Carl
> >>>
> >>e could sell hot pink t-shirts that have monzo
> >>written in silver sparkle from his web site too.
> >>
> >>--
> >>* David Beardsley
> >>* microtonal guitar
> >>* http://biink.com/db
> >>
> >>
> >
> >i probably will. thanks for the idea.
> >
> Thongs and baseball hats too.

and coffee mugs, pens, etc. keep sending ideas.

-monz

--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> Carl Lumma wrote:
>
> >And Joe, I understand sky writing is very
> >affordable these days. If it makes you feel
> >better I'm sure your name could be written in
> >the clouds over a major city.
> >
> >-Carl
> >
> He could sell hot pink t-shirts that have monzo
> written in silver sparkle from his web site too.

I want one!

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Paul,
>
>
> near the bottom of page 6 ("Temperaments"), you wrote:
>
> >> "The vanishing of the Pythagorean comma now implies that
> >> moving 19 rungs in the positive direction along the two-axis
> >> is equivalent to moving 12 rungs in the positive direction
> >> along the three-axis;
>
>
> unless i'm misunderstanding something, that should say
> "moving 19 rungs in the *negative* direction along the two-axis".

You're misunderstanding something. How can adding 19 intervals
*downward* add up to the same thing as adding 12 other intervals
*upward*?

To spare our poor readers, I'll reply to the rest of the comments in
a single post.

monz wrote:

>--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> >
>>monz wrote:
>>
>> >>
>>>--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
>>>
>>> >>>
>>> >>>
>>>>Carl Lumma wrote:
>>>>
>>>> >>>>
>>>>>nd Joe, I understand sky writing is very
>>>>>affordable these days. If it makes you feel
>>>>>better I'm sure your name could be written in
>>>>>the clouds over a major city.
>>>>>
>>>>>-Carl
>>>>>
>>>>> >>>>>
>>>>e could sell hot pink t-shirts that have monzo
>>>>written in silver sparkle from his web site too.
>>>>
>>>>-- >>>>* David Beardsley
>>>>* microtonal guitar
>>>>* http://biink.com/db
>>>> >>>>
>>>> >>>>
>>>i probably will. thanks for the idea.
>>>
>>> >>>
>>Thongs and baseball hats too.
>> >>
>
>
>and coffee mugs, pens, etc. keep sending ideas.
>
>
>
>-monz
> >
How about those large nylon signs we have on the sides of buildings in NYC?

Maybe some billboards too....

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

Paul,

Just to note that I've started reading the paper. I'll wait a bit
with comments until I can either get through all of it or get stopped.

And this is the version with as little math as possible? OK...

Cheers,
Jon

Gene wrote,

>Questions about whether the components of
>his vector need to be integers, and whether we are talking about
>abelian groups or vector spaces, I think is the sort of stuff he
wants
>to bail from.

Reading my paper, where might someone get the idea that they might
not be integers? I'd like to fix that part.

> Paul,
>
> Just to note that I've started reading the paper. I'll wait a bit
> with comments until I can either get through all of it or get
stopped.
>
> And this is the version with as little math as possible? OK...

Well, i'm thinking it's as little math as possible to avoid requiring
readers to take the results "on faith". I'm giving enough information
for more sophisticated readers, say John Chalmers or George Secor, to
begin their own process of exploration, and generate new results for
themselves. But I know that it's coming with a lot of verbal baggage
that I'd love for you and everyone to help me "unload".

Anyhow, the more criticism, the better, folks!

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Gene wrote,
>
> >Questions about whether the components of
> >his vector need to be integers, and whether we are talking about
> >abelian groups or vector spaces, I think is the sort of stuff he
> wants
> >to bail from.
>
> Reading my paper, where might someone get the idea that they might
> not be integers? I'd like to fix that part.

A vector is an element of a vector space, which by definition is
defined over a field, not an integral domain. Hence if you say
for instance |-4 4 1> is a "vector" you are implicitly stating it
lives inside a vector space and that the coefficients at minimum are
allowed to be rational numbers (which should make Monz happy) and
probably are allowed to be real numbers. If you want to make it clear
the coefficients are not allowed to be rational or real numbers, etc.,
you can say it is a member of an abelian group or Z-module. Your
nonmathematical readers, however, will not thank you.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> but at the point where Paul introduces "vector" to describe
> the routes around the lattice "road map", it *has* already
> become unavoidably mathematical.

Not to mention confusing if Paul wants his vectors to only have
integer coefficients, in which case he has to make it clear that they
must represent rational numbers only, and therefore have only integer
coefficients. "Vector" without additional commentary will generally be
taken to mean real number coefficients are allowable.

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> --- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> > Carl Lumma wrote:
> >
> > >And Joe, I understand sky writing is very
> > >affordable these days. If it makes you feel
> > >better I'm sure your name could be written in
> > >the clouds over a major city.
> > >
> > >-Carl
> > >
> > He could sell hot pink t-shirts that have monzo
> > written in silver sparkle from his web site too.
>
> I want one!

i used to be really good at making T-shirts with
my name painted on them in acrylic in 3-D "Gothic"
style metallic-look graffiti, complete with
New-York-subway-car sparkles and clouds.
(a genre of c.1980s american folk art).

i guess it's time to resurrect them. :)

-monz

hi Gene and Paul,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> > Gene wrote,
> >
> > >Questions about whether the components of
> > >his vector need to be integers, and whether we are talking about
> > >abelian groups or vector spaces, I think is the sort of stuff he
> > wants
> > >to bail from.
> >
> > Reading my paper, where might someone get the idea that they might
> > not be integers? I'd like to fix that part.
>
> A vector is an element of a vector space, which by definition is
> defined over a field, not an integral domain. Hence if you say
> for instance |-4 4 1> is a "vector" you are implicitly stating it
> lives inside a vector space and that the coefficients at minimum are
> allowed to be rational numbers (which should make Monz happy) and
> probably are allowed to be real numbers. If you want to make it clear
> the coefficients are not allowed to be rational or real numbers, etc.,
> you can say it is a member of an abelian group or Z-module. Your
> nonmathematical readers, however, will not thank you.

actually i've argued with Paul in the past because i believe
that the coefficients of tuning monzos can be real.

i've often used fractions in my explanations of meantones.
see, for example, my webpage on Zarlino's advocation of
2/7-comma meantone, which uses fractional exponents to
map the meantone as a straight line across the 3,5 ratio-space:

http://www.tonalsoft.com/monzo/zarlino/1558/zarlino1558-2.htm

Paul never liked this. of course, it's because there are
infinitely many different ways to pivot that meantone line
around 1/1, and i know that. but the idea of a "best-fit"
temperament is something that appeals to me:

http://tonalsoft.com/monzo/meantone/lattices/PB-MT.htm

... and i suspect that it also appeals to Gene ... perhaps
in a different way.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> > --- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> > > Carl Lumma wrote:
> > >
> > > >And Joe, I understand sky writing is very
> > > >affordable these days. If it makes you feel
> > > >better I'm sure your name could be written in
> > > >the clouds over a major city.
> > > >
> > > >-Carl
> > > >
> > > He could sell hot pink t-shirts that have monzo
> > > written in silver sparkle from his web site too.
> >
> > I want one!
>
>
> i used to be really good at making T-shirts with
> my name painted on them in acrylic in 3-D "Gothic"
> style metallic-look graffiti, complete with
> New-York-subway-car sparkles and clouds.
> (a genre of c.1980s american folk art).
>
> i guess it's time to resurrect them. :)

Please do that and I mean it!

I'm in love with the 80s and this has nothing to do with trends. Been
like that all my life even if I was born 1978.

Kalle

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > but at the point where Paul introduces "vector" to describe
> > the routes around the lattice "road map", it *has* already
> > become unavoidably mathematical.
>
> Not to mention confusing if Paul wants his vectors to only have
> integer coefficients, in which case he has to make it clear that
they
> must represent rational numbers only, and therefore have only
integer
> coefficients. "Vector" without additional commentary will generally
be
> taken to mean real number coefficients are allowable.

Except that the readers of the paper won't generally be
mathematicians, and they'll construe the paper's exposition of
the "vector" concept by analogy.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> Except that the readers of the paper won't generally be
> mathematicians, and they'll construe the paper's exposition of
> the "vector" concept by analogy.

They are not going to be mathematicians, but I've got to be kidding
you that both bimonzos and bivals will just be meaningless lists of
numbers and therefore there is no reason not to use bivals for wedgies??

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > Except that the readers of the paper won't generally be
> > mathematicians, and they'll construe the paper's exposition of
> > the "vector" concept by analogy.
>
> They are not going to be mathematicians, but I've got to be kidding
> you that both bimonzos and bivals will just be meaningless lists of
> numbers and therefore there is no reason not to use bivals for
>wedgies??

Maybe you missed something -- two parts of the paper aren't there
yet. In one of them, I'm planning to explain the 12-equal bivector
(which you call "bimonzo"). Not too different from what's in the
gentle introduction to periodicity blocks, but in a 12-equal context.

Nowhere in the paper do I plan to introduce vals, let alone multivals.

(But actually I'm reconsidering -- I might re-organize the paper and
excise all the real math to the back. Then we might squeeze in vals
and even be able to introduce the complement, for the few people who
will read that far. I can't wait to get Jon's feedback!)

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> But actually I'm reconsidering -- I might re-organize the paper and
> excise all the real math to the back. Then we might squeeze in vals
> and even be able to introduce the complement, for the few people
who
> will read that far.

I guess it bears asking: what is the audience you intend for this
paper? No one can write a paper that speaks to all segments of a
diverse group without some significant compromises, or really really
clever organization (seems like you're going for the latter). But
you've got me confused as to the knowledge base of your target reader.

> I can't wait to get Jon's feedback!

Heh... I'll tell you what: I don't think I've ever seen anyone on the
list with a deeply mathematical background trot out their "non-
musician-ness" the way I feel I end up showing my "non-mathematician-
ness"! :-) It is uncomfortable and profoundly embarassing, so I
hope it ends up being useful, and not just an easy laugh at my
expense.

I'll take another swack at it this evening, I lost the last two days.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > But actually I'm reconsidering -- I might re-organize the paper
and
> > excise all the real math to the back. Then we might squeeze in
vals
> > and even be able to introduce the complement, for the few people
> who
> > will read that far.
>
> I guess it bears asking: what is the audience you intend for this
> paper?

The readers of Xenharmonikon 18. This is the journal which brought us
articles like the following by Erv Wilson:

http://www.anaphoria.com/xen1.PDF

http://www.anaphoria.com/xen2.PDF

http://www.anaphoria.com/xen3a.PDF

http://www.anaphoria.com/xen3b.PDF

http://www.anaphoria.com/xen456.PDF

http://www.anaphoria.com/xen9mar.PDF

http://www.anaphoria.com/xen10pur.PDF

http://www.anaphoria.com/dal.PDF

> It is uncomfortable and profoundly embarassing, so I
> hope it ends up being useful, and not just an easy laugh at my
> expense.

I'll assume there's at least one reader of Xenharmonikon like you,
and I'll do my best to make the results presentable to you, even if
that means putting the more technical material further back.

Thanks!

P,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> The readers of Xenharmonikon 18. This is the journal which brought
us
> articles like the following by Erv Wilson:
>
> http://www.anaphoria.com/xen1.PDF

... and so on. Chill - one or two examples would have sufficed, or
just the mention of one of Erv's papers. I find it surprising John C.
would be asking you to take it easy on the math end of things, but I
also didn't know if you had a multiple purpose for the paper.

> I'll assume there's at least one reader of Xenharmonikon like you,
> and I'll do my best to make the results presentable to you, even if
> that means putting the more technical material further back.

Just don't dumb it down so much that it dulls the impact to the large
core of your intended audience. A paper can't be all things to all
people, so make it the best paper for the group you most want it read
by.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> P,
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > The readers of Xenharmonikon 18. This is the journal which
brought
> us
> > articles like the following by Erv Wilson:
> >
> > http://www.anaphoria.com/xen1.PDF
>
> ... and so on. Chill - one or two examples would have sufficed, or
> just the mention of one of Erv's papers. I find it surprising John
C.
> would be asking you to take it easy on the math end of things, but
I
> also didn't know if you had a multiple purpose for the paper.
>
> > I'll assume there's at least one reader of Xenharmonikon like
you,
> > and I'll do my best to make the results presentable to you, even
if
> > that means putting the more technical material further back.
>
> Just don't dumb it down so much that it dulls the impact to the
large
> core of your intended audience. A paper can't be all things to all
> people, so make it the best paper for the group you most want it
read
> by.
>
> Cheers,
> Jon

***This seems like excellent advice, Jon. After all, Paul can
always write the "dummies explanation" paper later for people
like... er... nevermind...(yours truly)

J. Pehrson

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Paul (and George),
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > > Well, I believe that you've made your point, except --
> > > when can we look for a 152-ET keyboard design? ;-)
> >
> > The smiley makes the point . . . the whole thing about
> > 152 is likely going to be useless to me in a practical
> > sense. But it's a curiosity of the sort that tends to
> > stick in my mind for some reason . . .
> >
> > Cheers,
> > Paul
>
> you certainly *will* be able to easily compose music
> on the computer in 152-ET using the Tonalsoft software.
>
> Chris (my Tonalsoft partner) and i are hoping that
> some intrepid instrument designers out there will be
> wanting to make microtonal controllers to work with
> our software. i think that a keyboard like the Microzone
> would be able to handle 152-ET quite well.

Yes, given a sufficient number of keys, you could theoretically get
all of the tones of 152-ET on a Bosanquet arrangement, using its best
fifth as generator, with these primes in the following positions in
the chain of fifths:

5 +33G
7 +27G
11 -18G

But chords would be a bit of a stretch for the fingers (along the Y-
axis).

Another (more practical) strategy would be to map various subsets of
152-ET in appropriate arrangements on the keys, switching from one
mapping to another on the fly. Here I am assuming that many
different pitches would not be required within a single passage of
music.

> (Paul knows, but for those who don't: click on
> "keyboards" at http://starrlabs.com)
>
> that would make jamming / improvising etc. with our
> software in 152-ET feasible.

Also possible would be a polyphonic linear controller that allowed
only discrete steps of 152-ET (and which, of course, could also be
programmed to other discrete steps, either equal or unequal, that
others might desire). Assuming that equal intervals span equal
lateral distances, the player would become accustomed to positioning
the fingers in specific ways to play common chords.

--George

hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

re: http://www.tonalsoft.com/enc/bingo.htm

> Well, that's really fun, but I'm sorry to have to report an error.
>
> Sweep over the tunings where the kleisma ([-5 6>) vanishes, and
> you'll probably see what I mean. 40-equal doesn't belong.
>
> Of the three places 40-equal can be found on my charts which you
> refer to as my zoom applet, none of them lies on the line where the
> kleisma vanishes. None of the three resulting "bingo-cards" of 40-
> equal would therefore show a zero at coordinates (-5,6).

wow, i can't believe it took me over a week to fix that.
thanks, Paul.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> re: http://www.tonalsoft.com/enc/bingo.htm
>
>
> > Well, that's really fun, but I'm sorry to have to report an error.
> >
> > Sweep over the tunings where the kleisma ([-5 6>) vanishes, and
> > you'll probably see what I mean. 40-equal doesn't belong.
> >
> > Of the three places 40-equal can be found on my charts which you
> > refer to as my zoom applet, none of them lies on the line where
the
> > kleisma vanishes. None of the three resulting "bingo-cards" of 40-
> > equal would therefore show a zero at coordinates (-5,6).
>
>
>
> wow, i can't believe it took me over a week to fix that.
> thanks, Paul.

So why is 40 still listed under the kleisma ([-5 6>)?

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > hi Paul,
> >
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > re: http://www.tonalsoft.com/enc/bingo.htm
> >
> >
> > > Well, that's really fun, but I'm sorry to have to report
> > > an error.
> > >
> > > Sweep over the tunings where the kleisma ([-5 6>) vanishes,
> > > and you'll probably see what I mean. 40-equal doesn't belong.
> > >
> > > Of the three places 40-equal can be found on my charts
> > > which you refer to as my zoom applet, none of them lies
> > > on the line where the kleisma vanishes. None of the three
> > > resulting "bingo-cards" of 40-equal would therefore show
> > > a zero at coordinates (-5,6).
> >
> >
> >
> > wow, i can't believe it took me over a week to fix that.
> > thanks, Paul.
>
> So why is 40 still listed under the kleisma ([-5 6>)?

big oops! just fixed it. thanks.

-monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_53712.html#53887

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > --- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > > i think that the past decade has seen a great expansion
> > > of the study of tuning, thanks largely to the internet.
> >
> >
> > i just realized after i wrote that that the tuning
> > list is now exactly 10 years old, +/- 6 months.
> >
> > does anyone know exactly when the tuning list began
> > on the Mills College Server?
>
> Here's your answer:
>
> http://www.mills.edu/LIFE/CCM/ftp/tuning/list/archive/feb941
>
> Looks like Feb 1, 1994.

***Wow. This was interesting in that one of the very first proposals
was the invention of a FAQ. Regrettably that seems to have been a
difficult undertaking...

J. Pehrson

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_53712.html#53896

> Hey monz, listen to this . . .
>
> http://www.io.com/~hmiller/music/ex/hanaki.mid
>
> Herman's got a lot of great stuff under his sleeve!
>
> BTW, this tuning was panned, in a sense, by Dave K. ;)

***This is interesting... there's almost a kind of gamelan sound to
it... Would there be a reason for that??

Thanks!

J. Pehrson

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_53712.html#53899

> hi Jon and Paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
>
> > > > That'll be the next project ;) Not a paper, of course.
> > >
> > > Sigh. Music: the poor step-child of music theory. ;-)
> >
> > Hee hee. Then I'm really looking forward to becoming an
> > "adoptive parent".
>
>
> Jon keeps towing the party line! ;-)
>
> (and good for you to do so ... as is only right for the
> list-mom of MMM and park-ranger of Corporeal Meadows)
>
>
> but, even tho i like most of Paul's music that i've heard,
> i'm glad he spends so much time writing theory.
> he's one of the best tuning theorists around.
>
>
>
> -monz

***Some musicians on this list have always felt that composing is
inherently superior to theorizing. That's just an opinion. It may
or may not be. It may also depend upon the quality of the *music* as
well... :)

J. Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Wow. This was interesting in that one of the very first
proposals
> was the invention of a FAQ. Regrettably that seems to have been a
> difficult undertaking...

Not difficult, just unpopular (with personal phone calls and
all . . .)

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_53712.html#53896
>
> > Hey monz, listen to this . . .
> >
> > http://www.io.com/~hmiller/music/ex/hanaki.mid
> >
> > Herman's got a lot of great stuff under his sleeve!
> >
> > BTW, this tuning was panned, in a sense, by Dave K. ;)
>
>
> ***This is interesting... there's almost a kind of gamelan sound to
> it...

Cool, I wasn't hearing that, but thought monz would love this piece.
Not sure if he listened to it . . .

> Would there be a reason for that??
>
> Thanks!
>
> J. Pehrson

Yes, the 9-note MOS that is representative of this tuning system was
described by Herman as having a 5-note (3-step-size) subset closely
resembling some pelog stuff he'd heard. Kraig has also discussed
pelog in terms of such (3-step-size) subsets of a 9-note MOS with
specifications quite similar to this one.

If I'm not mistaken, the tuning Herman used here had a generator of
260.6 cents and a period of 1200 cents.

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> /tuning/topicId_53712.html#53899
>
> > hi Jon and Paul,
> >
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > > --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...>
wrote:
> >
> > > > > That'll be the next project ;) Not a paper, of course.
> > > >
> > > > Sigh. Music: the poor step-child of music theory. ;-)
> > >
> > > Hee hee. Then I'm really looking forward to becoming an
> > > "adoptive parent".
> >
> >
> > Jon keeps towing the party line! ;-)
> >
> > (and good for you to do so ... as is only right for the
> > list-mom of MMM and park-ranger of Corporeal Meadows)
> >
> >
> > but, even tho i like most of Paul's music that i've heard,
> > i'm glad he spends so much time writing theory.
> > he's one of the best tuning theorists around.
> >
> >
> >
> > -monz
>
>
> ***Some musicians on this list have always felt that composing is
> inherently superior to theorizing. That's just an opinion. It may
> or may not be. It may also depend upon the quality of the *music*
as
> well... :)
>
> J. Pehrson

I missed this post by Monz. Thanks for the kind words. I'm planning
to (and I have no doubt of success) make even better music, both the
kinds you've heard and kinds you haven't from me. I'm asking on
MakeMicroMusic for advice as to which computer to ask my parents for
(they're insisting on a birthday present this year, as I've refused
for so many). The primary purpose, by far, is making music. Advice
appreciated.

As for theory, Monz, thanks for those other kinds words. I could
really use more feedback on the paper I'm working on, which I believe
you've printed out. I have to get it in pretty soon, and I'd like to
make it as comprehensible as possible.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_53712.html#54261

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > /tuning/topicId_53712.html#53899
> >
> > > hi Jon and Paul,
> > >
> > >
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> > wrote:
> > >
> > > > --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...>
> wrote:
> > >
> > > > > > That'll be the next project ;) Not a paper, of course.
> > > > >
> > > > > Sigh. Music: the poor step-child of music theory. ;-)
> > > >
> > > > Hee hee. Then I'm really looking forward to becoming an
> > > > "adoptive parent".
> > >
> > >
> > > Jon keeps towing the party line! ;-)
> > >
> > > (and good for you to do so ... as is only right for the
> > > list-mom of MMM and park-ranger of Corporeal Meadows)
> > >
> > >
> > > but, even tho i like most of Paul's music that i've heard,
> > > i'm glad he spends so much time writing theory.
> > > he's one of the best tuning theorists around.
> > >
> > >
> > >
> > > -monz
> >
> >
> > ***Some musicians on this list have always felt that composing is
> > inherently superior to theorizing. That's just an opinion. It
may
> > or may not be. It may also depend upon the quality of the
*music*
> as
> > well... :)
> >
> > J. Pehrson
>
> I missed this post by Monz. Thanks for the kind words. I'm planning
> to (and I have no doubt of success) make even better music, both
the
> kinds you've heard and kinds you haven't from me.

***Hi Paul,

Actually, I wasn't implying *anything* about your *own* music making
here, although it struck me after writing my post that it could be
interpreted that way. It was totally a *general* comment about
theory "vs." composing...

JP

wallyesterpaulrus wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

>>***This is interesting... there's almost a kind of gamelan sound to >>it...
>>Would there be a reason for that??
>>
>>Thanks!
>>
>>J. Pehrson
> > > Yes, the 9-note MOS that is representative of this tuning system was > described by Herman as having a 5-note (3-step-size) subset closely > resembling some pelog stuff he'd heard. Kraig has also discussed > pelog in terms of such (3-step-size) subsets of a 9-note MOS with > specifications quite similar to this one.
> > If I'm not mistaken, the tuning Herman used here had a generator of > 260.6 cents and a period of 1200 cents.

That sounds about right for the 5-limit TOP. I get <1200.000000, 1879.486406, 2819.229610] for the prime approximations. The Scala archive includes a scale "pelog_pb.scl", attributed to von Hornbostel, with a generator of a similar size (261.0 cents). Scales with a generator in this range sound more similar to actual pelog scales to me than the mavila-type scales (which are too regularly spaced).

hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > /tuning/topicId_53712.html#53896
> >
> > > Hey monz, listen to this . . .
> > >
> > > http://www.io.com/~hmiller/music/ex/hanaki.mid
> > >
> > > Herman's got a lot of great stuff under his sleeve!
> > >
> > > BTW, this tuning was panned, in a sense, by Dave K. ;)
> >
> >
> > ***This is interesting... there's almost a kind of
> > gamelan sound to it...
>
> Cool, I wasn't hearing that, but thought monz would love
> this piece. Not sure if he listened to it . . .

yep, i did ... just didn't get around to posting anything.
i was so taken by Galticeran27, and this sounds so different.

i didn't recognize anything "gamelanish" about it ...
to me it sounds kind of like a "warped Penny Lane".

... but you're right, i do like it.

-monz

hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> I missed this post by Monz. Thanks for the kind words.
> I'm planning to (and I have no doubt of success) make
> even better music, both the kinds you've heard and kinds
> you haven't from me. I'm asking on MakeMicroMusic for advice
> as to which computer to ask my parents for (they're
> insisting on a birthday present this year, as I've refused
> for so many). The primary purpose, by far, is making music.
> Advice appreciated.

the only advice i can give about a computer is: make
sure it's a Windows machine -- Chris and i are releasing
our software later this year, and that's the only platform
version 1.0 will run on.

(we do hope that Mac and Linux folks will help us port
it over for future releases.)

> As for theory, Monz, thanks for those other kinds words.
> I could really use more feedback on the paper I'm working
> on, which I believe you've printed out. I have to get it
> in pretty soon, and I'd like to make it as comprehensible
> as possible.

i did print a copy, and have been perusing it on and off
for about a week now. i've been so busy with the Tonalsoft
website and software for over a year now that i haven't
been following the tuning lists closely until just recently,
and i've missed a lot.

have you included the hora-/floragrams yet? you know me,
Paul -- diagrams are worth a thousand tables of numbers.

-monz

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Hi Paul,
>
> Actually, I wasn't implying *anything* about your *own* music
making
> here,

I know that -- Monz was. I was replying to him, not you. Sorry for
the confusion, but I didn't see Monz's remarks when he originally
posted them, only when you replied to them.

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> >
> > I missed this post by Monz. Thanks for the kind words. I'm
planning
> > to (and I have no doubt of success) make even better music, both
the
> > kinds you've heard and kinds you haven't from me.
>
> ***Hi Paul,
>
> Actually, I wasn't implying *anything* about your *own* music
making
> here, although it struck me after writing my post that it could be
> interpreted that way. It was totally a *general* comment about
> theory "vs." composing...

Joseph, I thought it appropriate that this thread (which I started
while you were away) has finally begun to swing back towards its
original topic about *making microtonal music*. In case you're
interested, here's where it started (complete with an mp3 file):

/makemicromusic/topicId_6820.html#6889

--George

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Paul,
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> > wrote:
> > >
> > > /tuning/topicId_53712.html#53896
> > >
> > > > Hey monz, listen to this . . .
> > > >
> > > > http://www.io.com/~hmiller/music/ex/hanaki.mid
> > > >
> > > > Herman's got a lot of great stuff under his sleeve!
> > > >
> > > > BTW, this tuning was panned, in a sense, by Dave K. ;)
> > >
> > >
> > > ***This is interesting... there's almost a kind of
> > > gamelan sound to it...
> >
> > Cool, I wasn't hearing that, but thought monz would love
> > this piece. Not sure if he listened to it . . .
>
>
>
> yep, i did ... just didn't get around to posting anything.
> i was so taken by Galticeran27, and this sounds so different.
>
> i didn't recognize anything "gamelanish" about it ...
> to me it sounds kind of like a "warped Penny Lane".
>
> ... but you're right, i do like it.
>
>
>
> -monz

There was kind of a debate about whether this temperament should be
considered a temperament at all, since its approximations are so
rough. Dave Keenan argued strongly that it shouldn't, so I didn't
include it in my paper. I'm not so sure, though . . .

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> have you included the hora-/floragrams yet?

They're printed out on paper, but not electronically. They don't look
as good when saved first and then printed as they do when directly
printed out.

> you know me,
> Paul -- diagrams are worth a thousand tables of numbers.

Many of the horagrams have been posted previously to this list. Take
a look at:

/tuning/files/miracle.gif
/tuning/files/pajara.gif
/tuning/files/Erlich/sevenlimit.zip

as well as most of the files in

/tuning/files/Erlich/
with "horagram" as the description (these are 5-limit ones).

Note that a few names have changed -- my paper uses "Mavila" for what
used to be "pelogic", "Hanson" for what used to be (5-
limit) "kleismic", and "Keenan" for what used to be (7-
limit) "kleismic", for example . . . There are reasons for all these
names, of course . . .

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > >
> > > I missed this post by Monz. Thanks for the kind words. I'm
> planning
> > > to (and I have no doubt of success) make even better music,
both
> the
> > > kinds you've heard and kinds you haven't from me.
> >
> > ***Hi Paul,
> >
> > Actually, I wasn't implying *anything* about your *own* music
> making
> > here, although it struck me after writing my post that it could
be
> > interpreted that way. It was totally a *general* comment about
> > theory "vs." composing...
>
> Joseph, I thought it appropriate that this thread (which I started
> while you were away) has finally begun to swing back towards its
> original topic about *making microtonal music*. In case you're
> interested, here's where it started (complete with an mp3 file):
>
> /makemicromusic/topicId_6820.html#6889
>
> --George

What happened to the music?

/tuning/files/secor/improv29.mp3

appears to be gone.

I really wanted to listen to it!

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> > wrote:
> > > >
> > > > I missed this post by Monz. Thanks for the kind words. I'm
> > planning
> > > > to (and I have no doubt of success) make even better music,
> both
> > the
> > > > kinds you've heard and kinds you haven't from me.
> > >
> > > ***Hi Paul,
> > >
> > > Actually, I wasn't implying *anything* about your *own* music
> > making
> > > here, although it struck me after writing my post that it could
> be
> > > interpreted that way. It was totally a *general* comment about
> > > theory "vs." composing...
> >
> > Joseph, I thought it appropriate that this thread (which I
started
> > while you were away) has finally begun to swing back towards its
> > original topic about *making microtonal music*. In case you're
> > interested, here's where it started (complete with an mp3 file):
> >
> > /makemicromusic/topicId_6820.html#6889
> >
> > --George
>
> What happened to the music?
>
>
/tuning/files/secor/improv29.mp3
>
> appears to be gone.
>
> I really wanted to listen to it!

Oh, so sorry -- it's gone forever! :-O

Just joking!!! Try this message to read about the "wrong note" that
improved the improv.:

/makemicromusic/topicId_6820.html#6897

which will also give you the link to where it was moved:

http://lumma.org/tuning/secor/improv29.mp3

--George

hi Paul and Joe,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Hi Paul,
> >
> > Actually, I wasn't implying *anything* about your *own*
> > music making here,
>
> I know that -- Monz was. I was replying to him, not you.
> Sorry for the confusion, but I didn't see Monz's remarks
> when he originally posted them, only when you replied to them.

good thing that i recommend you guys call me "monz"
instead of "Joe". ;-)

-monz

hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > have you included the hora-/floragrams yet?
>
> They're printed out on paper, but not electronically.
> They don't look as good when saved first and then printed
> as they do when directly printed out.
>
> > you know me,
> > Paul -- diagrams are worth a thousand tables of numbers.
>
> Many of the horagrams have been posted previously to this list. Take
> a look at:
>
> /tuning/files/miracle.gif
> /tuning/files/pajara.gif
> /tuning/files/Erlich/sevenlimit.
zip
>
> as well as most of the files in
>
> /tuning/files/Erlich/
> with "horagram" as the description (these are 5-limit ones).

thanks for those links. i've seen some of them before,
but really haven't taken the time to study and understand
them.

> Note that a few names have changed -- my paper uses "Mavila"
> for what used to be "pelogic", "Hanson" for what used to be
> (5-limit) "kleismic", and "Keenan" for what used to be
> (7-limit) "kleismic", for example . . . There are reasons
> for all these names, of course . . .

hmm ... so then now i have to go into my webpages and
change "kleismic" to "Hanson" or "Keenan" etc.?

that's not a problem ... but i am dismayed to see
each of these names being capitalized. i like to keep
things simple, and am in the process of trying to do away
with capitalization as much as possible in my Encyclopaedia.
(which, i note with irony, i capitalize all the time ...)

... while at the same time, promoting hyphenization.

-monz

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> http://lumma.org/tuning/secor/improv29.mp3

Wow -- a lot of great ideas in there. With about 2/5 of the piece
having the melody playing in "micro-clusters", for that wacky
accordion sound, I'm imagining all sorts of non-just tunings that
would be great for you . . .

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> that's not a problem ... but i am dismayed to see
> each of these names being capitalized.

Oh -- didn't mean to dismay you . . . (what should I do?)

> i like to keep
> things simple, and am in the process of trying to do away
> with capitalization as much as possible in my Encyclopaedia.

Well, that's certainly a nice idea, and I support it wholeheartedly,
but I wouldn't equate it with "keeping things simple", at least as
far as the reader is concerned . . .

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> that's not a problem ... but i am dismayed to see
> each of these names being capitalized. i like to keep
> things simple, and am in the process of trying to do away
> with capitalization as much as possible in my Encyclopaedia.

I use lower case for temperaments, and upper case for MOS in those
temperaments.

aul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> As for theory, Monz, thanks for those other kinds words.
> I could really use more feedback on the paper I'm working on,
> which I believe you've printed out. I have to get it in
> pretty soon, and I'd like to make it as comprehensible
> as possible.

maybe some footnotes citing these entries in the Encyclopaedia of
Tuning (in the order they appear in your paper) ...

http://tonalsoft.com/enc/

- Sumerian tuning
- accordance, concord, discord
- just intonation
- syntonic comma
- lattice
- meantone
- diesis, diaschisma, schisma, Pythagorean comma
- vector, monzo
- MOS, myhill

if you do put links to the Encyclopaedia, we prefer
that you give the main URL as above, and the entry
as a separate word in quotes.

and people who read your paper and are exposed to the
Tonalsoft website will be able to download the free demo
(when it's available later this year) and play around
with the concepts you write about.

you should also have a link to the Sagittal website
at the point where you mention that.

also, i think i'll be perpetually confused over the
differences/similarities between period and
equivalence-interval. your _Middle Path_ paper
has spelled it out for me better than anything else
i've ever read, but i'm still confused ... a little
more on that would be very welcome to me.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> you should also have a link

There are no live links, as XH is a paper-only journal.

> to the Sagittal website
> at the point where you mention that.

Rather than that, there will be a footnote referring to the Sagittal
article appearing in the same magazine.

> also, i think i'll be perpetually confused over the
> differences/similarities between period and
> equivalence-interval. your _Middle Path_ paper
> has spelled it out for me better than anything else
> i've ever read, but i'm still confused ... a little
> more on that would be very welcome to me.

What more can I say? As far as the relevant section of my paper is
concerned, the octave is assumed to be the interval of equivalence,
even before you create any scales or tuning systems. But when you
create an octave-repeating scale, the period of repetition can be 1
octave, 1/2 octave, 1/3 octave, etc. . . . regardless of which it is,
the scale will still repeat itself at the octave.

Can you help me understand where/how this trips you up?

hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > you should also have a link
>
> There are no live links, as XH is a paper-only journal.

right, of course i know that -- bad wording on my part.
i mean for you to included footnotes citing the URLs.

> > to the Sagittal website
> > at the point where you mention that.
>
> Rather than that, there will be a footnote referring to
> the Sagittal article appearing in the same magazine.

duh, of course. but still, the website has that nice
story by Hermes, which is very different from the exposition
on the notation given in the paper. cite both.

> > also, i think i'll be perpetually confused over the
> > differences/similarities between period and
> > equivalence-interval. your _Middle Path_ paper
> > has spelled it out for me better than anything else
> > i've ever read, but i'm still confused ... a little
> > more on that would be very welcome to me.
>
> What more can I say? As far as the relevant section of
> my paper is concerned, the octave is assumed to be the
> interval of equivalence, even before you create any scales
> or tuning systems. But when you create an octave-repeating
> scale, the period of repetition can be 1 octave, 1/2 octave,
> 1/3 octave, etc. . . . regardless of which it is,
> the scale will still repeat itself at the octave.
>
> Can you help me understand where/how this trips you up?

i dunno, i guess i understand it better now. so the
period is significant simply because the intervallic
structure of the scale repeats at that interval.

i guess i'm confused because the equivalence-interval
is *also* a period, on a higher level, but no-one ever
calls it that ... like the way the period is also a
generator, but no-one ever calls it that ...

-monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Hey monz, listen to this . . .
>
> http://www.io.com/~hmiller/music/ex/hanaki.mid
>
> Herman's got a lot of great stuff under his sleeve!
>
> BTW, this tuning was panned, in a sense, by Dave K. ;)

In what ;) sense?

Of course I have no idea what tuning you're talking about. :-)

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Paul,
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:

> > Note that a few names have changed -- my paper uses "Mavila"
> > for what used to be "pelogic", "Hanson" for what used to be
> > (5-limit) "kleismic", and "Keenan" for what used to be
> > (7-limit) "kleismic", for example . . . There are reasons
> > for all these names, of course . . .
>
>
>
> hmm ... so then now i have to go into my webpages and
> change "kleismic" to "Hanson" or "Keenan" etc.?

Paul,

I really don't want any temperament (or comma) named after me.

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

/tuning/topicId_53712.html#54298

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > >
> > > I missed this post by Monz. Thanks for the kind words. I'm
> planning
> > > to (and I have no doubt of success) make even better music,
both
> the
> > > kinds you've heard and kinds you haven't from me.
> >
> > ***Hi Paul,
> >
> > Actually, I wasn't implying *anything* about your *own* music
> making
> > here, although it struck me after writing my post that it could
be
> > interpreted that way. It was totally a *general* comment about
> > theory "vs." composing...
>
> Joseph, I thought it appropriate that this thread (which I started
> while you were away) has finally begun to swing back towards its
> original topic about *making microtonal music*. In case you're
> interested, here's where it started (complete with an mp3 file):
>
> /makemicromusic/topicId_6820.html#6889
>
> --George

***Hello "George..." (or committee... :)

Thanks. I wanted to listen to this but this file is GONE! (Jon
Szanto probably did some housecleaning...)

JP

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

/tuning/topicId_53712.html#54321

> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> > wrote:
> > > > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
<paul@s...>
> > > wrote:
> > > > >
> > > > > I missed this post by Monz. Thanks for the kind words. I'm
> > > planning
> > > > > to (and I have no doubt of success) make even better music,
> > both
> > > the
> > > > > kinds you've heard and kinds you haven't from me.
> > > >
> > > > ***Hi Paul,
> > > >
> > > > Actually, I wasn't implying *anything* about your *own* music
> > > making
> > > > here, although it struck me after writing my post that it
could
> > be
> > > > interpreted that way. It was totally a *general* comment
about
> > > > theory "vs." composing...
> > >
> > > Joseph, I thought it appropriate that this thread (which I
> started
> > > while you were away) has finally begun to swing back towards
its
> > > original topic about *making microtonal music*. In case you're
> > > interested, here's where it started (complete with an mp3 file):
> > >
> > > /makemicromusic/topicId_6820.html#6889
> > >
> > > --George
> >
> > What happened to the music?
> >
> >
>
/tuning/files/secor/improv29.mp3
> >
> > appears to be gone.
> >
> > I really wanted to listen to it!
>
> Oh, so sorry -- it's gone forever! :-O
>
> Just joking!!! Try this message to read about the "wrong note"
that
> improved the improv.:
>
> /makemicromusic/topicId_6820.html#6897
>
> which will also give you the link to where it was moved:
>
> http://lumma.org/tuning/secor/improv29.mp3
>
> --George

***Hello "Committee!"

Actually, the ol' Scalatron doesn't sound half bad... fascinating
stuff...

J. Pehrson

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> i guess i'm confused because the equivalence-interval
> is *also* a period, on a higher level,

One could conceivably come up with a scale where it isn't. For
example, you could take the scale

C D E F G A B c d e f g

and repeat it at the perfect twelfth (so the scale continues a b c d
e f# g a b c' d') but still treat the *octave* as the interval of
equivalence . . . why not?

> ... like the way the period is also a
> generator, but no-one ever calls it that ...

Well, that's different, the period is sometimes called a generator,
especially when focusing on infinite tuning systems and each
generator is a period as well.

>
>
>
> -monz

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Paul,
>
> I really don't want any temperament (or comma) named after me.

Aiggh! OK, it's back to the photocopier with Herman's suggestion,
then . . .

Dave Keenan wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> >>Hey monz, listen to this . . .
>>
>>http://www.io.com/~hmiller/music/ex/hanaki.mid
>>
>>Herman's got a lot of great stuff under his sleeve!
>>
>>BTW, this tuning was panned, in a sense, by Dave K. ;)
> > > In what ;) sense?
> > Of course I have no idea what tuning you're talking about. :-)

"Beep", although I'd like to revive the old name "bug" from an old tuning-math post.

4&5, 2/9 generator
vanishing comma: 27;25 (133.238c)
map: [<1, 2, 3|, <0, -2, -3|]
TOP tuning: <1200.000000, 1879.486406, 2819.229610]

http://x31eq.com/cgi-bin/temperament.cgi?et1=4&et2=5&limit=5

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> Dave Keenan wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> >
> >>Hey monz, listen to this . . .
> >>
> >>http://www.io.com/~hmiller/music/ex/hanaki.mid
> >>
> >>Herman's got a lot of great stuff under his sleeve!
> >>
> >>BTW, this tuning was panned, in a sense, by Dave K. ;)
> >
> >
> > In what ;) sense?
> >
> > Of course I have no idea what tuning you're talking about. :-)
>
> "Beep", although I'd like to revive the old name "bug" from an old
> tuning-math post.
>
> 4&5, 2/9 generator
> vanishing comma: 27;25 (133.238c)
> map: [<1, 2, 3|, <0, -2, -3|]
> TOP tuning: <1200.000000, 1879.486406, 2819.229610]
>
> http://x31eq.com/cgi-bin/temperament.cgi?
et1=4&et2=5&limit=5

This diagram:

/tuning-math/files/dualzoomk.gif

shows its relationship with other 5-limit 2-dimensional
temperaments. "Mavila" was still called "pelogic" when this was drawn.