Are microtonal compositions less harmonic in nature?

First of all, I am new at this tuning but beginning to understand
equal,intervallic and just entonations. The raitos and cents throws me
a bit. I am sure if I had a way to measure calcutions, I would fill
more secure in understanding the math nomenclature. But be as it may,
I have a question. I play the harmonica and find certain harmonicas
dissonant to play double stops when harmonising with traditional
players.(some harmonicas are tuned different) Melodically,the notes
seem normal. The only thing I have to remember is what harmonica I am
playing to have better results in harmonising. My question is this: In
microtonal compositions, are there instruments that play well with
harmonising or is the microtonal(alternative tunings)music just
melodic in nature. Perhaps getting use to detuning or dissonance is a
matter of taste or some reason, these tuning will all make sense after
learning to use them with other voicings. Does this question make sense?

--- In tuning@yahoogroups.com, "David A. Lovatto" <slipindave@y...>
wrote:
> First of all, I am new at this tuning but beginning to understand
> equal,intervallic and just entonations. The raitos and cents throws
me
> a bit. I am sure if I had a way to measure calcutions, I would fill
> more secure in understanding the math nomenclature. But be as it
may,
> I have a question. I play the harmonica and find certain harmonicas
> dissonant to play double stops when harmonising with traditional
> players.(some harmonicas are tuned different) Melodically,the notes
> seem normal. The only thing I have to remember is what harmonica I
am
> playing to have better results in harmonising. My question is this:
In
> microtonal compositions, are there instruments that play well with
> harmonising or is the microtonal(alternative tunings)music just
> melodic in nature. Perhaps getting use to detuning or dissonance is
a
> matter of taste or some reason, these tuning will all make sense
after
> learning to use them with other voicings. Does this question make
sense?

From what I can gather, your problem of dissonance with double stops
on the harmonica is rooted in the fact that the tempering errors
inherent in 12-tone equal temperament (12-ET) are emphasized more
with fixed-pitch instruments having timbres that are rich in
harmonics, such as the harpsichord, harmonica, and accordion (my main
instrument; it was only the other day that I was once again
distressed by the dissonance of 12-ET on the accordion after weeks of
listening extensively to more consonant tunings in the electronic
medium). The piano and acoustic organ (flue pipes) are not as rich
in harmonics, which makes 12-ET more tolerable on those instruments.

I should qualify my statement about lumping the harmonica in with
fixed-pitch instruments. If you're playing only one note at a time,
then you have some control over your intonation, but with double
stops I imagine that it would be very tricky to adjust the pitch of
each tone simultaneously by different amounts to detemper your
intervals.

I believe you need an instrument in an alternate tuning, possibly the
meantone temperament (or 19-ET might be interesting). Where can you
get one? Beats me! You may have to learn how to tune reeds and do
the retuning yourself, but I think that it may well be worth the
effort.

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "David A. Lovatto" <slipindave@y...>
> wrote:
> > First of all, I am new at this tuning but beginning to understand
> > equal,intervallic and just entonations. The raitos and cents throws
> me
> > a bit. (snip)
....space....Jumpin' Dave explains: I am aware of dissonance in
playing with the harmonica. Yes, signal note playing is much easier
than double stops.Yes, some modifiers tune their harmonicas
differently than the richter system to obtain different vocings but my
question was: are there instruments dealing with the ET19 tones that
use harmony when playing with others? To me, dissonance would be the
main idea of such instruments because the nature of this non
traditional tunings. A chromatic harmonica could be a candidate for
such tunings. I would assume that after such modifications playing
with instruments tuned with the equal temperment would be counter
productive when playing. Again,are there any instruments with altered
tunings that will blend well with dissonance harmonies.

--- In tuning@yahoogroups.com, "David A. Lovatto" <slipindave@y...>
wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > --- In tuning@yahoogroups.com, "David A. Lovatto"
<slipindave@y...>
> > wrote:
> > > First of all, I am new at this tuning but beginning to
understand
> > > equal,intervallic and just entonations. The raitos and cents
throws me
> > > a bit. (snip)
> ....space....Jumpin' Dave explains: I am aware of dissonance in
> playing with the harmonica. Yes, signal note playing is much easier
> than double stops.Yes, some modifiers tune their harmonicas
> differently than the richter system to obtain different vocings

Yes, but I was not referring to that, but rather to the fine-tuning
of the reeds that would be necessary to make the 3rds and 6ths more
harmonious (i.e., less strident due to a smaller amount of tempering
in the tuning).

> but my
> question was: are there instruments dealing with the ET19 tones that
> use harmony when playing with others?

Yes, although not many. Some in our group have had guitars refretted
to 19-ET, and the major and minor triads are very definitely
harmonious, so much so that many prefer them to 12-ET. Fretless
string instruments would also be a possibility. (I would think that
a trio consisting of harmonica, guitar, and fretless bass should do
very nicely.)

> To me, dissonance would be the
> main idea of such instruments because the nature of this non
> traditional tunings.

With 19-ET you would get *both* more consonance and more dissonance.
The traditional major and minor triads would be your consonances, and
there are also new intervals that will sound dissonant. One
excellent example of a piece in 19-ET is Aaron Johnson's "Juggler",
which would give you some idea of how this tuning sounds. Please see:

/tuning/topicId_46866.html#46866

> A chromatic harmonica could be a candidate for
> such tunings.

Yes indeed! Note however that enharmonic pairs of sharps and flats
in most alternate tunings are separate pitches that are therefore not
interchangeable. After you have investigated an alternate tuning,
you might also come to the conclusion that you would want to arrange
the tones differently on the instrument, since you may want to have
more than 12 tones available in the octave at one time.

Another idea: since harmonicas tend to be centered around specific
key-notes, you might also want to consider a tuning in just
intonation, which is most harmonious of all (but which also poses
certain challenges). This would require careful planning in
selecting the tones, and refretting a guitar for this would not be as
simple.

> I would assume that after such modifications playing
> with instruments tuned with the equal temperment would be counter
> productive when playing.

Yes, I expect that there would be difficulties unless there is some
way to retune or otherwise modify those instruments for the alternate
tuning.

> Again,are there any instruments with altered
> tunings that will blend well with dissonance harmonies.

I don't quite understand the question (because I tend to think of
dissonant harmonies as those which blend the least), but I will do my
best to answer. Some alternate tunings are *both* more consonant and
more dissonant than 12-ET, i.e., there is a greater range of
consonance to dissonance among their intervals and chords and thus a
greater potential for harmonic expressiveness (19-ET would be one of
those). So my answer to the question in your subject line would be:
No, while some microtonal compositions may be less harmonic in
nature, in general they do not have to be.

If you are open to using electronic instruments, there are
synthesizers that may readily be retuned (though there would be
issues if you wanted to have more than 12 pitches/octave available at
one time).

Most of us have faced problems in getting instruments for alternate
tunings. Some have built their own, while others have gone the
electronic route.

I hope this has been some help.

Best,

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "David A. Lovatto" <slipindave@y...>
> wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > > --- In tuning@yahoogroups.com, "David A. Lovatto"
> <slipindave@y...>
> > > wrote:
> > > > First of all, I am new at this tuning but beginning to
> understand
> > > > equal,intervallic and just entonations. The raitos and cents
> throws me
> > > > a bit. (snip)
> > ....space....Jumpin' Dave explains: I am aware of dissonance in
> > playing with the harmonica. Yes, signal note playing is much easier
> > than double stops.Yes, some modifiers tune their harmonicas
> > differently than the richter system to obtain different vocings
>
> Yes, but I was not referring to that, but rather to the fine-tuning
> of the reeds that would be necessary to make the 3rds and 6ths more
> harmonious (i.e., less strident due to a smaller amount of tempering
> in the tuning).
>
> > but my
> > question was: are there instruments dealing with the ET19 tones that
> > use harmony when playing with others?
>
> Yes, although not many. Some in our group have had guitars refretted
> to 19-ET, and the major and minor triads are very definitely
> harmonious, so much so that many prefer them to 12-ET. Fretless
> string instruments would also be a possibility. (I would think that
> a trio consisting of harmonica, guitar, and fretless bass should do
> very nicely.)
>
> > To me, dissonance would be the
> > main idea of such instruments because the nature of this non
> > traditional tunings.
>
> With 19-ET you would get *both* more consonance and more dissonance.
> The traditional major and minor triads would be your consonances, and
> there are also new intervals that will sound dissonant. One
> excellent example of a piece in 19-ET is Aaron Johnson's "Juggler",
> which would give you some idea of how this tuning sounds. Please see:
>
> /tuning/topicId_46866.html#46866
>
> > A chromatic harmonica could be a candidate for
> > such tunings.
>
> Yes indeed! Note however that enharmonic pairs of sharps and flats
> in most alternate tunings are separate pitches that are therefore not
> interchangeable. After you have investigated an alternate tuning,
> you might also come to the conclusion that you would want to arrange
> the tones differently on the instrument, since you may want to have
> more than 12 tones available in the octave at one time.
>
> Another idea: since harmonicas tend to be centered around specific
> key-notes, you might also want to consider a tuning in just
> intonation, which is most harmonious of all (but which also poses
> certain challenges). This would require careful planning in
> selecting the tones, and refretting a guitar for this would not be as
> simple.
>
> > I would assume that after such modifications playing
> > with instruments tuned with the equal temperment would be counter
> > productive when playing.
>
> Yes, I expect that there would be difficulties unless there is some
> way to retune or otherwise modify those instruments for the alternate
> tuning.
>
> > Again,are there any instruments with altered
> > tunings that will blend well with dissonance harmonies.
>
> I don't quite understand the question (because I tend to think of
> dissonant harmonies as those which blend the least), but I will do my
> best to answer. Some alternate tunings are *both* more consonant and
> more dissonant than 12-ET, i.e., there is a greater range of
> consonance to dissonance among their intervals and chords and thus a
> greater potential for harmonic expressiveness (19-ET would be one of
> those). So my answer to the question in your subject line would be:
> No, while some microtonal compositions may be less harmonic in
> nature, in general they do not have to be.
>
> If you are open to using electronic instruments, there are
> synthesizers that may readily be retuned (though there would be
> issues if you wanted to have more than 12 pitches/octave available at
> one time).
>
> Most of us have faced problems in getting instruments for alternate
> tunings. Some have built their own, while others have gone the
> electronic route.
>
> I hope this has been some help.
>
> Best,
>
> --George
....space....Jumpin' Dave says: Thank you for your insights. For some
reason, I assumed that inorder to play alternative tunings one had to
have a special instrument only. After, investigating and listening to
some recordings. I can see now that it's not as completed as I
expected. I for one wouldn't modify a chromatic harp, although some do
with a diminished tuning. I was awed with some of the diagrams I
found, which, When I was a kid I use to make such drawings but didn't
know the reason behind it. When I seen these geometric drawing they
put a chill up my spine. I have always had a craft for unusual
intervals with traditional instruments. I still have my synthezier and
a few effects units that allow me to play detune intervals and melodic
motifs just messing around. I am lol because, when I was learning to
bend on the harmonica at first, not knowing that there were different
key centers for each harmonica in the major and minor keys, I sounded
pretty much like some of the recordings I was listening too this
morning. Once again, thanks for your post and insights. I am still
working on the math.Reading a little each day on the links. Time for
college again.

Speaking in broad generalites, just intonation will sound more clean when played in block chords (in the right keys at least), but are more messy from a melodic perspective. Viewed in terms of major/minor modes, JIs involve a variety of different sizes of whole- and half-steps and, arrayed melodically, the choices between them are not always intuitively obvious. Those choices are more apparent played harmonically against a drone, for example. Equal temperaments, again speaking in broad generalities, tend to be exactly the reverse: Their melodic step sizes are very consistent and thus easily predictable melodically, but are less placid when placed in block chords.

Those two goals in tuning - cleanliness in block harmony vs. cleanliness in melody - are impossible to reconcile completely, and for that I'm eternally grateful! If there existed a single ideal solution, there would no longer be choices of myriads of tunings to choose from, each with its own unique, insightful way to balance those trade-offs, and similarly for other trade-offs. It's every bit as interesting for a tuning to have what are, from one viewpoint or another, "bad" attributes as it is for them to have "good" attributes. It's even more interesting when those "bad" attributes from one viewpoint are "good" from some other viewpoint, because you can then use that one attribute to convey greater variety of impressions to your audience, each in a different context.

On a different, but somewhat related, topic, you might perhaps find Bill Sethares' research into the interactions between tuning and tone qualities interesting. In short, the question is why certain harmonies sound better on certain timbres than on others. He described his results in his book entitled, "Tuning Timbre Spectrum Scale." On the downside, the math is even more involved than the basics, but on the upside, the accompanying CD does a good job of illustrating these effects in the form of actual sounds and music.

--- Paul Erlich wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
>
> > From what I can gather, your problem of dissonance with double
stops
> > on the harmonica is rooted in the fact that the tempering errors
> > inherent in 12-tone equal temperament
>
> George, the harmonica is *not* tuned in 12-equal. If you don't
> believe me, check for yourself! For example, the "draw" diminished
> chord is typically tuned very close to 5:6:7 -- much closer to
that,
> anyway, than to 12-equal.

I would be surprised to find something close to 5:6:7 (although I
don't discount your report), because the top tone in the triad would
make something close to 7:9 with its upper neighbor -- although
something such as a very wide (and therefore dissonant) major 3rd
would account for the problem with dissonant double-stops that David
described.

It's been very many years since I've tried playing a harmonica, and
the ones I played were definitely in 12-ET, so I don't think you can
make a blanket statement that harmonicas are *not* in 12-equal. But
since they're often pitched in specific keys, I would think that
someone might have tried a non-12-ET tuning somewhere along the line,
so I'm not surprised at what you have to say. (But I *would* expect
chromatic harmonicas to be in 12-ET.)

After re-reading part of David's original question (which I repeat
here):

> I have a question. I play the harmonica and find certain harmonicas
> dissonant to play double stops when harmonising with traditional
> players.(some harmonicas are tuned different) ...

So we would need more information to determine whether the particular
harmonicas that produce dissonant double stops:
1) Are in 12-equal (with the dissonance of the tuning made more
apparent by rich harmonic content), or
2) Are really intervals in non-equal tuning that suffered in order to
improve other intervals.

Whatever the case, I would think that a meantone or 19-ET tuning
could have possibilities. Imagine a 19-ET two-decker "chromatic"
instrument with naturals and sharps (on one level) and possibly flats
and naturals (on the other level, 1 degree lower than the first
level) that would allow enharmonic scales. The instrument could be
called an "enharmonica". :-)

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- Paul Erlich wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> > wrote:
(snip)
> ....space....Jumpin' Dave explains: When I wrote about this
dissonance, I referring to non chromatic harmonicas, although diatonic
can be modified to play chromatics, although I find these notes
distubing,nontheless, praticable. I just prefer intonation to be in
tuned to other players, unless we're opting to be crazy and play
anything that is dissonant. Your idea of a double decker harmonica
with a 19-ET tuning sounds(I haven't heard yet) intriquing. The
"Enharmonic harmonica"Hmmm? By the way this certain harmonica is tuned
just a bit sharp from A-440 pitch, which makes this harmonica nice
for single note playing. Not for double stops,3rds,4th's,5ths' and
octave's. I am not sure which tuning but I will find out.
>
> David wrote:
> > I have a question. I play the harmonica and find certain harmonicas
> > dissonant to play double stops when harmonising with traditional
> > players.(some harmonicas are tuned different) ...
> ....space....

George wrote:
> So we would need more information to determine whether the particular
> harmonicas that produce dissonant double stops:
> 1) Are in 12-equal (with the dissonance of the tuning made more
> apparent by rich harmonic content), or
> 2) Are really intervals in non-equal tuning that suffered in order to
> improve other intervals.
>
> Whatever the case, I would think that a meantone or 19-ET tuning
> could have possibilities. Imagine a 19-ET two-decker "chromatic"
> instrument with naturals and sharps (on one level) and possibly flats
> and naturals (on the other level, 1 degree lower than the first
> level) that would allow enharmonic scales. The instrument could be
> called an "enharmonica". :-)
>
> --George

I build and modify harmonicas for a living, so perhaps I might be able
to help clarify things a little.

George D. Secor wrote:
>
>--- Paul Erlich wrote:
>> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
>> wrote:
>>
>> > From what I can gather, your problem of dissonance with double stops
>> > on the harmonica is rooted in the fact that the tempering errors
>> > inherent in 12-tone equal temperament
>>
>> George, the harmonica is *not* tuned in 12-equal. If you don't
>> believe me, check for yourself! For example, the "draw" diminished
>> chord is typically tuned very close to 5:6:7 -- much closer to that,
>> anyway, than to 12-equal.
>
>I would be surprised to find something close to 5:6:7 (although I
>don't discount your report), because the top tone in the triad would
>make something close to 7:9 with its upper neighbor -- although
>something such as a very wide (and therefore dissonant) major 3rd
>would account for the problem with dissonant double-stops that David
>described.

Paul is referring to the typical diatonic harmonicas which were
traditionally tuned to 7 limit JI, making the draw notes
3:4:5:6:7:9:10:12:14:18 on a typical 10-hole diatonic.

However, these days very few manufacturers make them in strict JI any
more, the Brazilian firm Hering behing a notable exception. There are
quite a few models available in 12TET (Lee Oskar, Hohner's Golden
Melody and most of those made in Japan), but most other diatonic
harmonicas use some sort of compromise temperament somewhere between
JI and 12TET.

Sadly, the tuning of most mass-produced harmonicas is so variable it
is often hard to tell what the tuning is meant to be.

>It's been very many years since I've tried playing a harmonica, and
>the ones I played were definitely in 12-ET, so I don't think you can
>make a blanket statement that harmonicas are *not* in 12-equal. But
>since they're often pitched in specific keys, I would think that
>someone might have tried a non-12-ET tuning somewhere along the line,
>so I'm not surprised at what you have to say. (But I *would* expect
>chromatic harmonicas to be in 12-ET.)

Almost all chromatic harmonicas are in 12TET, or at least they are
supposed to be.

>After re-reading part of David's original question (which I repeat
>here):
>
>> I have a question. I play the harmonica and find certain harmonicas
>> dissonant to play double stops when harmonising with traditional
>> players.(some harmonicas are tuned different) ...
>
>So we would need more information to determine whether the particular
>harmonicas that produce dissonant double stops:
>1) Are in 12-equal (with the dissonance of the tuning made more
>apparent by rich harmonic content), or
>2) Are really intervals in non-equal tuning that suffered in order to
>improve other intervals.
>
>Whatever the case, I would think that a meantone or 19-ET tuning
>could have possibilities. Imagine a 19-ET two-decker "chromatic"
>instrument with naturals and sharps (on one level) and possibly flats
>and naturals (on the other level, 1 degree lower than the first
>level) that would allow enharmonic scales. The instrument could be
>called an "enharmonica". :-)

I hate to put a damper on the enthusiasm, but such an instrument would
introduce many other problems, particularly efficiency of air usage,
to say nothing of the retail price. There have been patents for
instruments along these lines, but none of them have ever made it as
far as a commercial model. The harmonica market is a very conservative
one, for the most part, although there are a few customisers (such as
myself) that cater to a more discerning bunch of customers. If anyone
is interested in a Bohlen-Pierce harmonica, I'd be more than happy to
take on the job... but I digress.

As regards temperament for the convention chromatic harmonica, there
are a few things to keep in mind. One is that single notes (and
double-stops to a limited extent) can be played into tune by slight
degree of note bending, although obviously this requires that the note
to be played is lower than the tuning of the instrument itself, as
notes can only be bend downwards in pitch. The other thing is that
only certain note combinations can be played at any given time. For
example, on a typical C harmonica C E and G are blow notes and D F and
A are draw notes. This means that you don't have to worry too much
about getting the A to make both a 3/2 with D and a 5/3 with C, just
provided the note combinations that you ~can~ play sound reasonably
good with each other and not too out of tune with any accompanying
instruments.

-- Pat Missin.

--- In tuning@yahoogroups.com, Pat Missin <pat@p...> wrote:
> I build and modify harmonicas for a living, so perhaps I might be
able
> to help clarify things a little.

Hey, just the man we need!

> Paul is referring to the typical diatonic harmonicas which were
> traditionally tuned to 7 limit JI, making the draw notes
> 3:4:5:6:7:9:10:12:14:18 on a typical 10-hole diatonic.

Assuming that 4 is the dominant of the scale, then a player could
attempt to use 7:9 and 14:18 as major thirds on the (too-low)
subdominant of the scale but find that these are more dissonant than
expected (as David might have).

> However, these days very few manufacturers make them in strict JI
any
> more, the Brazilian firm Hering behing a notable exception. There
are
> quite a few models available in 12TET (Lee Oskar, Hohner's Golden
> Melody and most of those made in Japan), but most other diatonic
> harmonicas use some sort of compromise temperament somewhere between
> JI and 12TET.
>
> ... The harmonica market is a very conservative
> one, for the most part, although there are a few customisers (such
as
> myself) that cater to a more discerning bunch of customers. If
anyone
> is interested in a Bohlen-Pierce harmonica, I'd be more than happy
to
> take on the job... but I digress.

Now you've started the gears in my head turning -- see idea below.

> As regards temperament for the convention chromatic harmonica, there
> are a few things to keep in mind. One is that single notes (and
> double-stops to a limited extent) can be played into tune by slight
> degree of note bending, although obviously this requires that the
note
> to be played is lower than the tuning of the instrument itself, as
> notes can only be bend downwards in pitch. The other thing is that
> only certain note combinations can be played at any given time. For
> example, on a typical C harmonica C E and G are blow notes and D F
and
> A are draw notes. This means that you don't have to worry too much
> about getting the A to make both a 3/2 with D and a 5/3 with C, just
> provided the note combinations that you ~can~ play sound reasonably
> good with each other and not too out of tune with any accompanying
> instruments.

Since JI lends itself so well to key centers, how about a 13-limit
otonal JI instrument with 12 tones/octave built into a chromatic
frame with the following pitches:

unshifted:
blow: 1/1 3/2 1/1 5/4 3/2 7/4 9/8 11/8 13/8 1/1
draw: 3/2 7/4 9/8 11/8 13/8 1/1 5/4 3/2 7/4 9/8

shifted:
blow: 4/3 5/3 1/1 7/6 3/2 11/6 13/12 4/3 5/3 1/1
draw: 3/2 11/6 13/12 4/3 5/3 1/1 7/6 3/2 11/6 13/12

With otonalities on C and F, 1/1 on hole 3 would be middle C. (I
would miss having 15/8, but I guess you can't have everything.)

--George

George D. Secor wrote"
>
>--- In tuning@yahoogroups.com, Pat Missin <pat@p...> wrote:
>> I build and modify harmonicas for a living, so perhaps I might be
>able
>> to help clarify things a little.
>
>Hey, just the man we need!

I've been on the tuning list for over eight years now, but it's not
that often that topics come up where I have more experience than most.

>> Paul is referring to the typical diatonic harmonicas which were
>> traditionally tuned to 7 limit JI, making the draw notes
>> 3:4:5:6:7:9:10:12:14:18 on a typical 10-hole diatonic.
>
>Assuming that 4 is the dominant of the scale, then a player could
>attempt to use 7:9 and 14:18 as major thirds on the (too-low)
>subdominant of the scale but find that these are more dissonant than
>expected (as David might have).

This is precisely the reason that many harmonica companies moved away
from JI. I also suspect that as electronic tuners became more
affordable and more commonplace, they were getting all sorts of
complaints that there harmonicas were "not in tune"!

>Since JI lends itself so well to key centers, how about a 13-limit
>otonal JI instrument with 12 tones/octave built into a chromatic
>frame with the following pitches:
>
>unshifted:
>blow: 1/1 3/2 1/1 5/4 3/2 7/4 9/8 11/8 13/8 1/1
>draw: 3/2 7/4 9/8 11/8 13/8 1/1 5/4 3/2 7/4 9/8
>
>shifted:
>blow: 4/3 5/3 1/1 7/6 3/2 11/6 13/12 4/3 5/3 1/1
>draw: 3/2 11/6 13/12 4/3 5/3 1/1 7/6 3/2 11/6 13/12
>
>With otonalities on C and F, 1/1 on hole 3 would be middle C. (I
>would miss having 15/8, but I guess you can't have everything.)

It would be tough to do on a 10-hole (40 reed) chromatic, but if you
added a couple of pitches to each row it could probably be done on a
12-hole (48 reed) instrument.

-- Pat Missin.

--- In tuning@yahoogroups.com, Pat Missin <pat@p...> wrote:
> George D. Secor wrote"
>
> >Since JI lends itself so well to key centers, how about a 13-limit
> >otonal JI instrument with 12 tones/octave built into a chromatic
> >frame with the following pitches:
> >
> >unshifted:
> >blow: 1/1 3/2 1/1 5/4 3/2 7/4 9/8 11/8 13/8 1/1
> >draw: 3/2 7/4 9/8 11/8 13/8 1/1 5/4 3/2 7/4 9/8
> >
> >shifted:
> >blow: 4/3 5/3 1/1 7/6 3/2 11/6 13/12 4/3 5/3 1/1
> >draw: 3/2 11/6 13/12 4/3 5/3 1/1 7/6 3/2 11/6 13/12
> >
> >With otonalities on C and F, 1/1 on hole 3 would be middle C. (I
> >would miss having 15/8, but I guess you can't have everything.)
>
> It would be tough to do on a 10-hole (40 reed) chromatic, but if you
> added a couple of pitches to each row it could probably be done on a
> 12-hole (48 reed) instrument.

As you noted before, observing which pitches are assigned to adjacent
holes of the same blow/draw group is a major consideration. I would
want 15/8 adjacent to 3/2, but I already have 3/2 adjacent to 7/4 and
11/6 (in different rows, above), so it's a matter of picking and
choosing which combinations are more important.

Oh, well, back to the drawing board.

--George