I am a private music instructor, not a public-school music teacher, but finding
different ways of presenting basic musical information to students has become a
professional interest of mine. My particular preferred flavor of microtonality
is extended just intonation - I know that many people on this list prefer
various temperaments. It's all cool.

My question is, has anyone experimented with presenting microtonal music to
their students, and if they show interest, how have you dished out the
information in a way that they can dijest and - most importantly - in a way that
enables them to believe that they can play it with practice?

I don't currently have any students who are quite ready yet for extended just
intonation, but one thing that I do occasionally do is to play a drone (I'm a
trombonist) and have them play simple patterns and scales against it, to
practice their ear training and getting those standard intervals in tune. But I
think that more generally, the various flavors of microtonal music that are
possible will be much more successful if it can be presented in a way that
students, in particular children, can follow.

Andrew

On Wed, Feb 22, 2012 at 4:43 AM, lobawad <lobawad@...> wrote:
>
> >
> > Sure, but then I think that chords in first inversion can be ambiguous
> > too then. Consider ||: Cmaj/E | Emaj :||. It's similar to ||: Am/E |
> > Emaj :||, with the same sort of ambiguous root/temporary
> > retonicization thing going on.
>
> Yes, and in your examples you can see that the increasing use of harmonic
> movement by thirds/sixths during the celebrated "collapse of the tonal
> system" makes sense. My original point, which you are now further
> supporting, was that even in justly-intoned "5-limit", roots are not always
> automagically spelled out for us.

I'm not sure this is really the "root" though, maybe more an ambiguous
"tonic." It's kind of in between.

> Yes, but traditionally (which I took pains to point out was what I was
> talking about), function is contextual and an augmented sixth does not have
> the same function or resolution tendency as the minor seventh.

7/4 to me usually sounds like a minor seventh. C G E B E A# makes the
outer note sound like an aug 6. It's the chords I imagine inside some
kind of complex interval like that that dictate the way it sounds like
to me, not the intonation. Maybe it's just me.

> How much of
> this is psychoacoustic and how much is a holdover from 1/4-comma thinking, I
> don't know (and would seriously doubt anyone who claims to "know"). I,
> personally, find it only weakly true that these tendencies are built in
> psychoacoustically; nevertheless, a solid enough phenomenon to consider the
> tradtional assignment of the 7th partial to aug. 6 and 3:2*6:5 to the 7th
> partial superior to what seems to me both 12-tET and naive thinking in
> lumping the two together at 7:4.

What about 16/9? In 22-EDO, dominant 7 chords resolve way better if
you use 16/9 = 7/4 as the minor 7 than 9/5 = 11/6.

> > I don't know if this is really barbershop, but it definitely has >that
> > sort of JI sound
> >
> > http://www.youtube.com/watch?v=l4NafK3NFhA
>
> Four Freshmen are awesome. Definitely Just vertical harmonies all over-
> the roots, it seems to me, are moving in 12-tET, don't you think?

Yeah, more or less.

> > My point is that the psychoacoustic qualities associated with this
> > thing aren't really "objective" because adaptation can train many of
> > them, sometimes in unknown and complex ways. The analogy again is that
> > they're as objective as being able to deadlift 300 pounds is
> > objective. Most people can objectively adapt to be able to do it, but
> > that's not just like an ability that anyone can do at any point in
> > time.
>
> I think this is a very poor analogy, because even if I were to discount
> thousands of years of testimony, except for one guy with pretty severe
> hearing damage, no one to whom I have presented examples, nay, none not
> once, has failed to immediately distinguish between
> "church/choir/ethnic/bluesy/sleepy/etc". intonation and 12-tET intonation.
> 300 lbs? More like 3 lbs.
>
> I think you do not realize that contemporary Western academic musical
> training trains people to listen past these things.

Er, what are we talking about? I was making the point that musical
training can cause actual changes in the cochlea and auditory
brainstem and auditory cortex and so on. If there's some form of
training that teaches you to ignore something that's fine, but my
point was also that if we now, starting a new chapter start training
ourselves to do things like hear really complex VFs (training complex
pitch perception) or pick out individual notes in a cluster (perhaps
training SOAE's) or whatever it is, those sorts of things might result
in actual changes to the auditory system, not just to mental
schematization of stimuli.

-Mike

On Wed, Feb 22, 2012 at 7:01 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I have no problem believing that someone like Scarlatti or Gesualdo
> > heard these as categorically different things, reachable by a
> > different path of the circle of fifths or something, or that the most
> > highly trained musicians would have also heard it that way. I'm
> > talking about the way that the average listener might have heard it.
> > And also, if Scarlatti uses a "wolf fifth" as a "deliberately out of
> > tune fifth," that would still be in line with what I'm talking about.
>
> Something else to consider is the vast historical revision that takes
> place, for the most part unconsciously I am sure, in musicology or any other
> historical study in the arts. Did you know that the statuary of the ancient
> Greeks was brightly, garishly by today's standards, painted? The paint was
> deliberately scraped off by European collectors, there are even written
> records of scrapings. Enough remains in cracks and crevices to analize and
> recreate the orignal colors; an exhibition was held in Berlin a few years
> ago. I love it, many are shocked silly. But there is no serious question
> that the originals were painted, the fact is even mentioned in ancient
> literature (a woman stricken with some tragic emotion is described as pale
> as a statue without paint, in Homer iirc, for example).
>
> Same jive happens in musicology, I could do a whole song and dance about
> the deliberate complete rewriting (westernization) of Eastern European music
> in the 19th century. A lot of what you- and I - learned about music history,
> tuning and temperament is probably best described as semi-true. The
> revisionism of the "JI" school, which is perpetuated on this list, is just
> as corny as the party line, beware.

This is a good point. Although I'd argue that the JI school isn't
really perpetuated on this list anymore, at least not since we've been
dominating the conversation with categories in this past year and a
half.

> > I happen to think this is a good principle to consider: quasi-equal
> > chromatic scales allow for regularity in melody and purer harmony than
> > the EDOs. Consider 19-EDO, for instance, which is often used as an
> > ambient enharmonic scale for meantone[12], with meantone[7] being used
> > as a prominent subset of that. One can do the same thing for 22-EDO
> > and use it as an ambient enharmonic scale for porcupine[15], with
> > porcupine[7] and porcupine[8] being used as prominent melodic and
> > diatonic subsets.
>
> Sure- can you put together some examples? Don't worry about making undying
> masterpieces, nobody whose opinion is worth considering is going to write
> you off for failing to write a tuning etude that doesn't save the whales and
> make your jimmy thicker.

LOL what? I'm going to ignore that last line. I have this little thing
I did in porcupine a while ago

http://www.youtube.com/watch?v=XSfnyr1MhXE

Here we can watch me totally botch the explanation of the chord
progression on camera at 5:30 in the morning. Anyway, this chord
progression basically shifts around porcupine modes with the ambient
backdrop being porcupine[15]. There's probably a better example one
could make involving actual melodies that are porcupinally chromatic,
but this is all I have for now.

This was a chord progression I took out of context in the AXiS jam
that I made in 22-edo, which you can also see on my channel.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Feb 22, 2012 at 4:43 AM, lobawad <lobawad@...> wrote:
> >
> > >
> > > Sure, but then I think that chords in first inversion can be ambiguous
> > > too then. Consider ||: Cmaj/E | Emaj :||. It's similar to ||: Am/E |
> > > Emaj :||, with the same sort of ambiguous root/temporary
> > > retonicization thing going on.
> >
> > Yes, and in your examples you can see that the increasing use of harmonic
> > movement by thirds/sixths during the celebrated "collapse of the tonal
> > system" makes sense. My original point, which you are now further
> > supporting, was that even in justly-intoned "5-limit", roots are not always
> > automagically spelled out for us.
>
> I'm not sure this is really the "root" though, maybe more an ambiguous
> "tonic." It's kind of in between.

Yes- in the original post I said that we can even often conflate VFs and roots
in 5-limit JI, but roots are still contextual and subjective. I think Partch
jives like it's going out of business, but he makes some really incisive
observations as well- his take on the old controversy about the "real" root of a
minor triad is right on. Pick that one that sounds right to you and move on.

>
> > Yes, but traditionally (which I took pains to point out was what I was
> > talking about), function is contextual and an augmented sixth does not have
> > the same function or resolution tendency as the minor seventh.
>
> 7/4 to me usually sounds like a minor seventh. C G E B E A# makes the
> outer note sound like an aug 6. It's the chords I imagine inside some
> kind of complex interval like that that dictate the way it sounds like
> to me, not the intonation. Maybe it's just me.

I would be amazed if you hear the 7:4 and 9:5 in the piece I just posted,
"magical thinking", as two intonations of the same interval, though.


>
> What about 16/9? In 22-EDO, dominant 7 chords resolve way better if
> you use 16/9 = 7/4 as the minor 7 than 9/5 = 11/6.

Yes, that's yet another thing. Basically, conflating tertian chords and harmonic
structures is bogus.



>
> Er, what are we talking about? I was making the point that musical
> training can cause actual changes in the cochlea and auditory
> brainstem and auditory cortex and so on. If there's some form of
> training that teaches you to ignore something that's fine, but my
> point was also that if we now, starting a new chapter start training
> ourselves to do things like hear really complex VFs (training complex
> pitch perception) or pick out individual notes in a cluster (perhaps
> training SOAE's) or whatever it is, those sorts of things might result
> in actual changes to the auditory system, not just to mental
> schematization of stimuli.

My point was that you- and I- are highly prone to hear things in terms of
structures, modalities, what "might" be, what "should" be, etc. Unschooled
listeners can be better, even much better, at hearing raw physical stuff. A
friend of mine who can't carry a tune in a bucket or keep a beat, much less
analize a piece of music, is an excellent professional mixing engineer. Maybe I
shouldn't say unschooled, but schooled otherwise, because you could say he's an
excellent "purely-spectral" musician. When I tried to explain alternative
tunings to him, I realized that he did not know that there are 12 keys to the
octave on the piano. But he spots all these spectral effects of beating, fusing,
blending, etc. better than I do.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Feb 22, 2012 at 7:01 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > I have no problem believing that someone like Scarlatti or Gesualdo
> > > heard these as categorically different things, reachable by a
> > > different path of the circle of fifths or something, or that the most
> > > highly trained musicians would have also heard it that way. I'm
> > > talking about the way that the average listener might have heard it.
> > > And also, if Scarlatti uses a "wolf fifth" as a "deliberately out of
> > > tune fifth," that would still be in line with what I'm talking about.
> >
> > Something else to consider is the vast historical revision that takes
> > place, for the most part unconsciously I am sure, in musicology or any other
> > historical study in the arts. Did you know that the statuary of the ancient
> > Greeks was brightly, garishly by today's standards, painted? The paint was
> > deliberately scraped off by European collectors, there are even written
> > records of scrapings. Enough remains in cracks and crevices to analize and
> > recreate the orignal colors; an exhibition was held in Berlin a few years
> > ago. I love it, many are shocked silly. But there is no serious question
> > that the originals were painted, the fact is even mentioned in ancient
> > literature (a woman stricken with some tragic emotion is described as pale
> > as a statue without paint, in Homer iirc, for example).
> >
> > Same jive happens in musicology, I could do a whole song and dance about
> > the deliberate complete rewriting (westernization) of Eastern European music
> > in the 19th century. A lot of what you- and I - learned about music history,
> > tuning and temperament is probably best described as semi-true. The
> > revisionism of the "JI" school, which is perpetuated on this list, is just
> > as corny as the party line, beware.
>
> This is a good point. Although I'd argue that the JI school isn't
> really perpetuated on this list anymore, at least not since we've been
> dominating the conversation with categories in this past year and a
> half.

Well, that change pretty much boils down to... you.

Gene has always maintained a distance from the tangled perceptions of
"JI"-meets-temperament, not just because mathematical precision safeguards
against this, but because, I am quite sure, of his interest in late Romantic
music. It is not studied much any more, but if you've had to plough through the
thicket of accidentals in Richard Strauss and are aware of the universe outside
of 12-tET, you'll realize that there is a sound and natural connection between
the temperaments created on this list and music that branches off from late
Romantic music. Some of the musical examples I've posted deliberately illustrate
this connection.





> >
> > Sure- can you put together some examples? Don't worry about making undying
> > masterpieces, nobody whose opinion is worth considering is going to write
> > you off for failing to write a tuning etude that doesn't save the whales and
> > make your jimmy thicker.
>
> LOL what? I'm going to ignore that last line.

Why ignore it, it's a good point. I notice on gear forums especially that
there's this whole "hit", "great", blah blah conception of music. And I think
people are really held back by this nonsense, and that this thinking permeates
everything. Like everything is competing with Mozart are something. Believe me
I'm looking forward eagerly to hearing your Porcupine example but I'd puke if I
had to listen to more Mozart right now.


I have this little thing
> I did in porcupine a while ago
>
> http://www.youtube.com/watch?v=XSfnyr1MhXE
>
> Here we can watch me totally botch the explanation of the chord
> progression on camera at 5:30 in the morning. Anyway, this chord
> progression basically shifts around porcupine modes with the ambient
> backdrop being porcupine[15]. There's probably a better example one
> could make involving actual melodies that are porcupinally chromatic,
> but this is all I have for now.
>
> This was a chord progression I took out of context in the AXiS jam
> that I made in 22-edo, which you can also see on my channel.
>
> -Mike
>

Slower so we can hear the harmonies better, man! But the "porcupineness" of it
is clear, that's cool- do I understand you right, that part 1 of the Axis jam in
porcupine tuned to 22-edo?

11 maps to -8 generators in Magic. Lower primes are positive. If 11 is the
tonic, the other pitches will be above it, measured by generators.
The third section involves iv chords. They will go down in generators. You can't
fit both II9 and iv in the same 22 note Magic but it is a close fit.
Yes, there are things you can't do with an MOS. I don't see much point in
talking about things we can't do.
9/5 sevenths are no problem in a Magic  MOS. They lie in the same direction on
the spiral of thirds. It's a theorem that if you have a 7/4 on a degree of a
Magic MOS, you must also have a 9/5.

Graham

------Original message------
From: lobawad <lobawad@...>
To: <tuning@yahoogroups.com>
Date: Thursday, February 23, 2012 6:52:35 AM GMT-0000
Subject: [tuning] Re: Moving on [to Cameron and others]



--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> If you're using runs of 36:35 or 25:24 then yes you'll tend towards >Magic
temperament. But you didn't say that before so I didn't >comment on it.

I see by the dates on my Soundcloud page that it must be about nine months (!)
since I mentioned on this list tempering 36/35 and 25/24 to one step for
septimal music.  So I can hardly expect anyone to remember that.

>You'll also tend towards the MOS scales.

If that were the only consideration, yes. Introducing the syntonic comma via
Pythagorean structures messes up this tidiness, however.

> The message was "Seventh chords, intonation, and function." The >chords as I
worked them out use twenty thirds piled up above the >tonic. All but one
outlying pitch fit in the sixteen note MOS. >Seventh degrees above ii would be
more remote but I don't know if >they're required or how they're tuned.

But the chords are not all "above the tonic". I explained this carefully, but
okay, more slowly this time.

(When we say above or below, we are of course talking about first or root
position).

Let us call our tonic C. A tertian chord is built on, above, this C. Now, this C
remains as a pedal tone, and a tertian chord forms BELOW the C. In the example I
presented, C became the 11th partial of the following chord.

In traditional terms, a common-tone modulation which is also an enharmonic
modulation.

Even in tempered systems using 41 or 53 tones, you already have both an "F#" and
a "Gb", and a lot of different pitches. In the example I more recently
presented, in which the "C" is a pedal and the chords move such that C is the
eleventh partial, then the ninth, then seventh, and so on down, more than 30
discrete pitches are required even without full 11th chords at each new identity
for C.

The scheme itself is obviously very simple. But it generates masses of pitches
very quickly, and adding root movement by 5ths/4ths will generate even more,
offset by syntonic commas.

53-edo- all of it- is perfect for implementing this scheme up to the 11th
partial and probably the 13th as well.

The case of distinguishing between harmonic and "dominant" seventh chords also
generates many tones and easily steps out of MOS structures. You need numerous
instances of full harmonic structures, and Pythagorean root movement will entail
needing these structures offset by the syntonic comma as well.

Once again, not once have I criticized the temperaments themselves. Quite the
contrary- the examples I give could be titled "reasons to use temperament"
(specifically 41 and 53 equal temperaments).

No, the problem is that of practical application, and the unavoidable fact that
temperaments cannot both reach every prime at lightening speed and be accurate
at the same time.









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--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> 11 maps to -8 generators in Magic. Lower primes are positive. If 11 is the
tonic, the other pitches will be above it, measured by generators.
> The third section involves iv chords. They will go down in generators. You
can't fit both II9 and iv in the same 22 note Magic but it is a close fit.
> Yes, there are things you can't do with an MOS. I don't see much point in
talking about things we can't do.

There's a hell of a lot you *can* do in 22 notes of Magic:

http://xenharmonic.wikispaces.com/Chords+of+magic

Ummmmm, does this mean that no one on here can contribute to this topic?

:/


--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> As Ryan said - contact Jacob and Andrew
>
> Leave a comment on there site - probably the best way outside of facebook.
>
> http://oddmusicuc.wordpress.com/programs/xenharmonic-praxis-summer-camp/
>
> Chris
>
> On Thu, Feb 23, 2012 at 2:24 AM, bigAndrewM <bigandrewm@...> wrote:
>
> > **
> >
> >
> > I am a private music instructor, not a public-school music teacher, but
> > finding different ways of presenting basic musical information to students
> > has become a professional interest of mine. My particular preferred flavor
> > of microtonality is extended just intonation - I know that many people on
> > this list prefer various temperaments. It's all cool.
> >
> > My question is, has anyone experimented with presenting microtonal music
> > to their students, and if they show interest, how have you dished out the
> > information in a way that they can dijest and - most importantly - in a way
> > that enables them to believe that they can play it with practice?
> >
> > I don't currently have any students who are quite ready yet for extended
> > just intonation, but one thing that I do occasionally do is to play a drone
> > (I'm a trombonist) and have them play simple patterns and scales against
> > it, to practice their ear training and getting those standard intervals in
> > tune. But I think that more generally, the various flavors of microtonal
> > music that are possible will be much more successful if it can be presented
> > in a way that students, in particular children, can follow.
> >
> > Andrew
> >
> >
> >
>

Hello, dear In-Tuners :) ...

I've just searched in the archives for what I need to ask you now, but I see
that I hardly have the vocabulary to find what you may most hopefully guide me
to within a glimpse :)


If I have two frequencies

i.e. 100 Hz and 151 Hz

and want to let a program decide wether the closest approximate equivalent ratio
is i.e.
- ?/?
- x/y
- 3/2

So I am searching something like [http://www.djehuti.com/pitchcalc/]- but
calculating the closest approach within a limited range of denominators,
resulting in a fraction - which program could do that, or how could I calculate
that?

I have installed Scala and tried to find what I look for in the Tools or
Approximate menu's, but I am to weak to peek through these terminologies to
discover what I cannot see: Can Scala do this?

Of course the example above is a bit weak, but what with frequencies that are
not so easily traceable? I create my scales through singing what I feel to be
right and I want to be able to sweep away "the dust" with your help ...

:-)

Thanks for any little help
Clemens

p.s. If any of you are tuning scales primarily with using "the inner ear" and
less in connection with theory, I'd like to receive a little hint to your works,
if you'd share :-) ...

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> Ummmmm, does this mean that no one on here can contribute to this topic?
>
> :/

I don't think any of us here have students.  I certainly have plenty of ideas on
how to teach this stuff, but I've never actually taught anyone, so I can't say
what works and what doesn't.  I might suggest playing them some barbershop
music, and then playing the same piece on the piano, and asking them if they can
hear the difference.

-Igs

--- In tuning@yahoogroups.com, "soymilkismycoffee" <listening.inn@...> wrote:

> So I am searching something like [http://www.djehuti.com/pitchcalc/]- but
calculating the
> closest approach within a limited range of denominators, resulting in a
fraction - which
> program could do that, or how could I calculate that?

If you have a limited range of denominators, that suggests a finite number of
ratios, so I'd suggest making a table of them and their corresponding cents
values.  Then, whatever two frequencies you have, use
http://www.sengpielaudio.com/calculator-centsratio.htm to convert them to cents,
and look up the nearest cents value in the table you made.  There's probably a
more efficient way to to do it, but I do everything brute-force due to my lack
of mathematical education and my inability to even rudimentarily program my
computer to do anything.

-Igs

 

Hello, dear In-Tuners :) ...

I've just searched in the archives for what I need to ask you now, but I see that I hardly have the vocabulary to find what you may most hopefully guide me to within a glimpse :)

If I have two frequencies

i.e. 100 Hz and 151 Hz

and want to let a program decide wether the closest approximate equivalent ratio is i.e.
- ?/?
- x/y
- 3/2

So I am searching something like [http://www.djehuti.com/pitchcalc/]- but calculating the closest approach within a limited range of denominators, resulting in a fraction - which program could do that, or how could I calculate that?

I have installed Scala and tried to find what I look for in the Tools or Approximate menu's, but I am to weak to peek through these terminologies to discover what I cannot see: Can Scala do this?

Of course the example above is a bit weak, but what with frequencies that are not so easily traceable? I create my scales through singing what I feel to be right and I want to be able to sweep away "the dust" with your help ...

:-)

Thanks for any little help
Clemens

p.s. If any of you are tuning scales primarily with using "the inner ear" and less in connection with theory, I'd like to receive a little hint to your works, if you'd share :-) ...

Wow, surprised to see the not-so-helpful comments otherwise, I thought lots of
people would have ideas...

I'm a private music teacher, and I teach JI and other tuning issues to my
students.

In my experience, teaching has been extremely valuable in showing *me* that
tuning isn't really so fundamental all the time. It's easy as a connoisseur to
get all wrapped up in the tuning details. However, students appreciate a lot of
music even when they struggle to play any consistent tuning. That said, teaching
JI and listening to beats and such is the best way to get them to be more
sensitive.

My first recommendation is to be transparent. Tell your own story, describe the
music you like and why. Share music with them without setting up an expectation
that they'll like it or not. Most students will just hear everything as just
more music. Unless they've been absolutely brain-washed in 12EDO, most students
don't see the big deal either way: they think all the different music just
sounds like interesting music but not remarkably different. I've been surprised
when some students seem to react strongly and others have no reaction or are
totally inconsistent about their feelings for different tunings.

All this led me to accept that music is a subjective experience and describing
the physical tunings out there in the world is the wrong approach. What's really
going on is subjective categorical perception and such.

So that said, you can teach more conceptually (like ratios and such) or more
experientially. Show students how to get a range of sounds, have them test their
own subjective JNDs melodically and harmonically... Have them make their own
scales, play over a drone, compose music... whatever.

I make use of the more user-friendly free software resources, like the TPXE
software version of the Tonal Plexus keyboard from H-Pi.com and the microtuning
capacities in Musescore
Listening to music from around the world is great too.

At the end of the day, it's just about exposing students to these things and
giving them perspective. If anyone is really excited to explore the details, you
can just go through that bit by bit...

Cheers,
Aaron Wolf
wolftune.com

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> I am a private music instructor, not a public-school music teacher, but
finding different ways of presenting basic musical information to students has
become a professional interest of mine. My particular preferred flavor of
microtonality is extended just intonation - I know that many people on this list
prefer various temperaments. It's all cool.
>
> My question is, has anyone experimented with presenting microtonal music to
their students, and if they show interest, how have you dished out the
information in a way that they can dijest and - most importantly - in a way that
enables them to believe that they can play it with practice?
>
> I don't currently have any students who are quite ready yet for extended just
intonation, but one thing that I do occasionally do is to play a drone (I'm a
trombonist) and have them play simple patterns and scales against it, to
practice their ear training and getting those standard intervals in tune. But I
think that more generally, the various flavors of microtonal music that are
possible will be much more successful if it can be presented in a way that
students, in particular children, can follow.
>
> Andrew
>

--- "bigAndrewM" <bigandrewm@...> wrote:

> Ummmmm, does this mean that no one on here can contribute to
> this topic?

Aside from Aaron Wolf, Paul Rubenstein is (or was) a member
here.  He teaches middle school kids how to make and play
microtonal guitars and in the past has had helpful comments
on the matter of music pedagogy

http://ubertar.com/

Denny Genovese used to participate here also.  During the
1990's, he had an ensemble of college kids performing on his
Partch- and Darreg-inspired instruments in extended JI.
I was one of his students, as were Darren Burgess &
Pat Pagano, who used to post here.

Bob Wendell is another former active member.  He is a choir
director who developed intonation training exercises for his
choir, which he later even tested in university studies.

Johnny Reinhard needs no introduction, having worked with
musicians in New York and from around the world for many
decades.  He advocates marking up traditional scores with
deviations from 12-ET to the nearest cent (+/- 1-50 cents).
One exercise he uses is to take an interval (octave,
semitone, etc) and practice singing equal divisions of it.

Joe Monzo ("monz") currently teaches piano and clarinet
privately in the San Diego area.

Aaron, Paul, Denny, Pat, Bob, Johnny, and monz all have
recordings available.  You might try reaching them offlist
for their comments.

Many others I'm forgetting, for sure, but that should give
you some leads.

-Carl

On Fri, Feb 24, 2012 at 4:18 PM, bigAndrewM <bigandrewm@...> wrote:
>
> Ummmmm, does this mean that no one on here can contribute to this topic?
>
> :/

I still haven't hit the magic bullet yet. Here are some insights that
I've found:

1) If your audience is more musically trained, they'll often be less
receptive to this stuff. They'll say stuff like "I still don't know
how to play in 12 yet, man." The people who are less trained and who
really don't know how to play in 12 will be more receptive.

2) You have to know a bit about the personality of the person you're
trying to sell this to. What's the best way to push it - does this
approach represent "freedom from the constraints of 12?" Is it
"xenharmonic music," meaning "strange yet familiar?" Is it just that
you're exploring "music in exotic tuning systems?" Is it "purer
harmony than 12" you're after? These different views of the same thing
target different people, and you mismatch them at your peril. (A
professional jazz musician, for instance, may not feel like music
represented by a strange-sounding greek word promoting "strange" (yet
familiar) music that provides "purer harmony than 12" is anything he
cares about, but he might like "music in exotic tuning systems.")

3) There's always this balance to strike between theory and practice.
If you tell people too much theory at first, they're going to run away
(and even talking about ratios at all is "too much theory" for a lot
of people). can be good, but stay away from the heavier stuff at
first. But, if you just hand people 31-EDO and don't give them any
guidance at all, they might feel overwhelmed. Andrew and Jacob might
have some better ideas on how to tackle this. I always thought that
certain tunings might be better for this than others but I don't know
which ones people will respond to best in general. There's
7-EDO/14-EDO as a one trick pony, or you could try 15-EDO to have them
mess with blackwood, or you could do some JI, or 11-EDO for relatively
good 4:7:9:11, or 9-EDO or 16-EDO for mavila, or 17-EDO or maybe
19-EDO. I dunno what people tend to respond to best, and it also
depends on what they can play without needing much guidance if you're
trying to do hands-on stuff.

I do note that people tend to think that harmonic series stuff is
really cool. Maybe you could load up harmonics 16-32 and let them go
nuts at first. You should also make sure they understand that that's
only one of the cool things you can do in novel tuning systems and not
the whole point of it though. Things like 7-EDO aren't very accurate
but are still pretty awesome and interesting, especially if you're
just starting out.

4) When you do end up moving to theory, if you do at all, I always
thought 19-EDO might be a good choice to start things off. 19-EDO
supports meantone, but instead of saying C# and Db are the same, you
say that the distance between C and C# is the same as the distance
between C# and Db. It's still very logical and makes easy conceptual
sense, but you can then show how it leads to completely new enharmonic
modulations and some slightly different properties (three major thirds
no longer equals an octave, for example). Once they get their head
wrapped around that, which is a significant undertaking in and of
itself, maybe then they're ready to mess with theory in some other
tuning systems, like 22 or whatever.

-Mike

Ah, interesting. All of my current students happen to be middle-schoolers (by
chance), so getting into technical details of how to tune simply doesn't apply
right now. I don't specifically mention microtonality or just intonation by name
at all; if the course of a lesson takes the right turn (most of them are still
working on just getting the instrument to respons consistently, learning how to
read music, things like that, although a couple of them are ahead of the
learning curve) I will simply suggest something like "try tuning this note this
way and see what you hear."

I haven't been bringing in recordings for them to check out. For starters, there
really isn't that much out there for brass players that uses anything beyond
what is implied for the classical performance practice of getting chords in tune
and the occasional melodic pitch-bending of jazz. Although, I have been thinking
of throwing a short recording of the Kepler Quartet at a couple of them. But
even then, I feel that it would be most beneficial for them to listen to stuff
that they are working on already, so they can do the immediate
listen-and-imitate thing. One of my students (the most advanced) has recordings
of Miles Davis and a book of Miles transcriptions, for example. My time with
each student is limited, so I try to make the most of it.

Andrew



--- In tuning@yahoogroups.com, "AWolf" <wolftune@...> wrote:
>
> Wow, surprised to see the not-so-helpful comments otherwise, I thought lots of
people would have ideas...
>
> I'm a private music teacher, and I teach JI and other tuning issues to my
students.
>
> In my experience, teaching has been extremely valuable in showing *me* that
tuning isn't really so fundamental all the time. It's easy as a connoisseur to
get all wrapped up in the tuning details. However, students appreciate a lot of
music even when they struggle to play any consistent tuning. That said, teaching
JI and listening to beats and such is the best way to get them to be more
sensitive.
>
> My first recommendation is to be transparent. Tell your own story, describe
the music you like and why. Share music with them without setting up an
expectation that they'll like it or not. Most students will just hear everything
as just more music. Unless they've been absolutely brain-washed in 12EDO, most
students don't see the big deal either way: they think all the different music
just sounds like interesting music but not remarkably different. I've been
surprised when some students seem to react strongly and others have no reaction
or are totally inconsistent about their feelings for different tunings.
>
> All this led me to accept that music is a subjective experience and describing
the physical tunings out there in the world is the wrong approach. What's really
going on is subjective categorical perception and such.
>
> So that said, you can teach more conceptually (like ratios and such) or more
experientially. Show students how to get a range of sounds, have them test their
own subjective JNDs melodically and harmonically... Have them make their own
scales, play over a drone, compose music... whatever.
>
> I make use of the more user-friendly free software resources, like the TPXE
software version of the Tonal Plexus keyboard from H-Pi.com and the microtuning
capacities in Musescore
> Listening to music from around the world is great too.
>
> At the end of the day, it's just about exposing students to these things and
giving them perspective. If anyone is really excited to explore the details, you
can just go through that bit by bit...
>
> Cheers,
> Aaron Wolf
> wolftune.com
>
> --- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@> wrote:
> >
> > I am a private music instructor, not a public-school music teacher, but
finding different ways of presenting basic musical information to students has
become a professional interest of mine. My particular preferred flavor of
microtonality is extended just intonation - I know that many people on this list
prefer various temperaments. It's all cool.
> >
> > My question is, has anyone experimented with presenting microtonal music to
their students, and if they show interest, how have you dished out the
information in a way that they can dijest and - most importantly - in a way that
enables them to believe that they can play it with practice?
> >
> > I don't currently have any students who are quite ready yet for extended
just intonation, but one thing that I do occasionally do is to play a drone (I'm
a trombonist) and have them play simple patterns and scales against it, to
practice their ear training and getting those standard intervals in tune. But I
think that more generally, the various flavors of microtonal music that are
possible will be much more successful if it can be presented in a way that
students, in particular children, can follow.
> >
> > Andrew
> >
>

Actually, yes, that might help a bit. Thanks.

Andrew

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- "bigAndrewM" <bigandrewm@> wrote:
>
> > Ummmmm, does this mean that no one on here can contribute to
> > this topic?
>
> Aside from Aaron Wolf, Paul Rubenstein is (or was) a member
> here.  He teaches middle school kids how to make and play
> microtonal guitars and in the past has had helpful comments
> on the matter of music pedagogy
>
> http://ubertar.com/
>
> Denny Genovese used to participate here also.  During the
> 1990's, he had an ensemble of college kids performing on his
> Partch- and Darreg-inspired instruments in extended JI.
> I was one of his students, as were Darren Burgess &
> Pat Pagano, who used to post here.
>
> Bob Wendell is another former active member.  He is a choir
> director who developed intonation training exercises for his
> choir, which he later even tested in university studies.
>
> Johnny Reinhard needs no introduction, having worked with
> musicians in New York and from around the world for many
> decades.  He advocates marking up traditional scores with
> deviations from 12-ET to the nearest cent (+/- 1-50 cents).
> One exercise he uses is to take an interval (octave,
> semitone, etc) and practice singing equal divisions of it.
>
> Joe Monzo ("monz") currently teaches piano and clarinet
> privately in the San Diego area.
>
> Aaron, Paul, Denny, Pat, Bob, Johnny, and monz all have
> recordings available.  You might try reaching them offlist
> for their comments.
>
> Many others I'm forgetting, for sure, but that should give
> you some leads.
>
> -Carl
>

I agree - harmonic series stuff is pretty cool, and it's possible with that to
lock the notes in by ear, rather than depending on the "balanced points of
instability" that virtually any temperament will have which typically requires a
keyboard or something similar.

That said, has anyone tried to write method books for teaching 19-ET on a
retuned piano? Simply taking one of Aaron Hunt's Tuning Boxes and plugging it
into a keyboard and telling a student to jam on it can be cool, but so much of
modern pedagogy depends on combining aural with written instruction. Plus, for a
lot of people, it's not just about jamming. They want to play songs.

Andrew



--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Feb 24, 2012 at 4:18 PM, bigAndrewM <bigandrewm@...> wrote:
> >
> > Ummmmm, does this mean that no one on here can contribute to this topic?
> >
> > :/
>
> I still haven't hit the magic bullet yet. Here are some insights that
> I've found:
>
> 1) If your audience is more musically trained, they'll often be less
> receptive to this stuff. They'll say stuff like "I still don't know
> how to play in 12 yet, man." The people who are less trained and who
> really don't know how to play in 12 will be more receptive.
>
> 2) You have to know a bit about the personality of the person you're
> trying to sell this to. What's the best way to push it - does this
> approach represent "freedom from the constraints of 12?" Is it
> "xenharmonic music," meaning "strange yet familiar?" Is it just that
> you're exploring "music in exotic tuning systems?" Is it "purer
> harmony than 12" you're after? These different views of the same thing
> target different people, and you mismatch them at your peril. (A
> professional jazz musician, for instance, may not feel like music
> represented by a strange-sounding greek word promoting "strange" (yet
> familiar) music that provides "purer harmony than 12" is anything he
> cares about, but he might like "music in exotic tuning systems.")
>
> 3) There's always this balance to strike between theory and practice.
> If you tell people too much theory at first, they're going to run away
> (and even talking about ratios at all is "too much theory" for a lot
> of people). can be good, but stay away from the heavier stuff at
> first. But, if you just hand people 31-EDO and don't give them any
> guidance at all, they might feel overwhelmed. Andrew and Jacob might
> have some better ideas on how to tackle this. I always thought that
> certain tunings might be better for this than others but I don't know
> which ones people will respond to best in general. There's
> 7-EDO/14-EDO as a one trick pony, or you could try 15-EDO to have them
> mess with blackwood, or you could do some JI, or 11-EDO for relatively
> good 4:7:9:11, or 9-EDO or 16-EDO for mavila, or 17-EDO or maybe
> 19-EDO. I dunno what people tend to respond to best, and it also
> depends on what they can play without needing much guidance if you're
> trying to do hands-on stuff.
>
> I do note that people tend to think that harmonic series stuff is
> really cool. Maybe you could load up harmonics 16-32 and let them go
> nuts at first. You should also make sure they understand that that's
> only one of the cool things you can do in novel tuning systems and not
> the whole point of it though. Things like 7-EDO aren't very accurate
> but are still pretty awesome and interesting, especially if you're
> just starting out.
>
> 4) When you do end up moving to theory, if you do at all, I always
> thought 19-EDO might be a good choice to start things off. 19-EDO
> supports meantone, but instead of saying C# and Db are the same, you
> say that the distance between C and C# is the same as the distance
> between C# and Db. It's still very logical and makes easy conceptual
> sense, but you can then show how it leads to completely new enharmonic
> modulations and some slightly different properties (three major thirds
> no longer equals an octave, for example). Once they get their head
> wrapped around that, which is a significant undertaking in and of
> itself, maybe then they're ready to mess with theory in some other
> tuning systems, like 22 or whatever.
>
> -Mike
>

Hi Andrew,

You've just mentioned that your students are middle-schoolers.
Did you also let it slip that they are brass instrumentalists?
Why not tell us something about what you're up to?

-Carl

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> Actually, yes, that might help a bit. Thanks.
>
> Andrew
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > --- "bigAndrewM" <bigandrewm@> wrote:
> >
> > > Ummmmm, does this mean that no one on here can contribute to
> > > this topic?
> >
> > Aside from Aaron Wolf, Paul Rubenstein is (or was) a member
> > here.  He teaches middle school kids how to make and play
> > microtonal guitars and in the past has had helpful comments
> > on the matter of music pedagogy
> >
> > http://ubertar.com/
> >
> > Denny Genovese used to participate here also.  During the
> > 1990's, he had an ensemble of college kids performing on his
> > Partch- and Darreg-inspired instruments in extended JI.
> > I was one of his students, as were Darren Burgess &
> > Pat Pagano, who used to post here.
> >
> > Bob Wendell is another former active member.  He is a choir
> > director who developed intonation training exercises for his
> > choir, which he later even tested in university studies.
> >
> > Johnny Reinhard needs no introduction, having worked with
> > musicians in New York and from around the world for many
> > decades.  He advocates marking up traditional scores with
> > deviations from 12-ET to the nearest cent (+/- 1-50 cents).
> > One exercise he uses is to take an interval (octave,
> > semitone, etc) and practice singing equal divisions of it.
> >
> > Joe Monzo ("monz") currently teaches piano and clarinet
> > privately in the San Diego area.
> >
> > Aaron, Paul, Denny, Pat, Bob, Johnny, and monz all have
> > recordings available.  You might try reaching them offlist
> > for their comments.
> >
> > Many others I'm forgetting, for sure, but that should give
> > you some leads.
> >
> > -Carl
> >
>

lol

I think I did let it slip.

I'm not talking specifically about brass instruction, but more generalized.

I do, in fact, have a couple of projects that I'm working on - group tuning
drills and chorales. But it's also a matter of interest as a composer: if we can
get more people to play interesting microtonal music of lots of flavors, the
more non-musicians will become interested and check it out as well.

I'm planning on writing two slightly different approaches, and I think they both
will be decent depending on what goals the students have.

One is a drill book of very basic chord progressions with some specific
instructions on how to tune the notes, given in normal 12-ET-speak via cent
adjustments and being specific about what part of a chord each voice is playing
per note. The goal there is not microtonality specifically, but ear training.
Teaching students how to really get chords in tune. How to recognize by ear to
what part of a chord their note belongs. To recognize by ear the basic chord
progressions.

The second is a set of 4-part chorales using Ben Johnston's notation system,
starting with very basic 5-limit harmony and adding higher harmonics as the
chorales get more advanced. I chose Johnston's system, not just because I like
it, but because it was the most simple of the JI notation systems that I've seen
to introduce for the first, most basic chorales.

The first is almost done; the second is, as you might imagine, a bit more work,
and is a work slowly in progress. Both are intended for high-school age students
and above; essentially, once the students have gained basic control of their
instruments and understand how music notation works.

Andrew


--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Andrew,
>
> You've just mentioned that your students are middle-schoolers.
> Did you also let it slip that they are brass instrumentalists?
> Why not tell us something about what you're up to?
>
> -Carl
>
> --- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@> wrote:
> >
> > Actually, yes, that might help a bit. Thanks.
> >
> > Andrew
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > >
> > > --- "bigAndrewM" <bigandrewm@> wrote:
> > >
> > > > Ummmmm, does this mean that no one on here can contribute to
> > > > this topic?
> > >
> > > Aside from Aaron Wolf, Paul Rubenstein is (or was) a member
> > > here.  He teaches middle school kids how to make and play
> > > microtonal guitars and in the past has had helpful comments
> > > on the matter of music pedagogy
> > >
> > > http://ubertar.com/
> > >
> > > Denny Genovese used to participate here also.  During the
> > > 1990's, he had an ensemble of college kids performing on his
> > > Partch- and Darreg-inspired instruments in extended JI.
> > > I was one of his students, as were Darren Burgess &
> > > Pat Pagano, who used to post here.
> > >
> > > Bob Wendell is another former active member.  He is a choir
> > > director who developed intonation training exercises for his
> > > choir, which he later even tested in university studies.
> > >
> > > Johnny Reinhard needs no introduction, having worked with
> > > musicians in New York and from around the world for many
> > > decades.  He advocates marking up traditional scores with
> > > deviations from 12-ET to the nearest cent (+/- 1-50 cents).
> > > One exercise he uses is to take an interval (octave,
> > > semitone, etc) and practice singing equal divisions of it.
> > >
> > > Joe Monzo ("monz") currently teaches piano and clarinet
> > > privately in the San Diego area.
> > >
> > > Aaron, Paul, Denny, Pat, Bob, Johnny, and monz all have
> > > recordings available.  You might try reaching them offlist
> > > for their comments.
> > >
> > > Many others I'm forgetting, for sure, but that should give
> > > you some leads.
> > >
> > > -Carl
> > >
> >
>

Have you thought about using 72-EDO? Makes life incredibly simple:
1/6th of a semitone turns a 12-EDO major third into an almost perfect
5/4, 1/3 of a semitone turns a 12-EDO minor 7th into an almost perfect
7/4, 1/2 of a semitone turns a 12-EDO tritone into an almost perfect
11/8. Can't get more conceptually simple than that.

-Mike


On Sun, Feb 26, 2012 at 4:01 PM, bigAndrewM <bigandrewm@...> wrote:
>
>
>
> lol
>
> I think I did let it slip.
>
> I'm not talking specifically about brass instruction, but more
> generalized.
>
> I do, in fact, have a couple of projects that I'm working on - group
> tuning drills and chorales. But it's also a matter of interest as a
> composer: if we can get more people to play interesting microtonal music of
> lots of flavors, the more non-musicians will become interested and check it
> out as well.
>
> I'm planning on writing two slightly different approaches, and I think
> they both will be decent depending on what goals the students have.
>
> One is a drill book of very basic chord progressions with some specific
> instructions on how to tune the notes, given in normal 12-ET-speak via cent
> adjustments and being specific about what part of a chord each voice is
> playing per note. The goal there is not microtonality specifically, but ear
> training. Teaching students how to really get chords in tune. How to
> recognize by ear to what part of a chord their note belongs. To recognize by
> ear the basic chord progressions.
>
> The second is a set of 4-part chorales using Ben Johnston's notation
> system, starting with very basic 5-limit harmony and adding higher harmonics
> as the chorales get more advanced. I chose Johnston's system, not just
> because I like it, but because it was the most simple of the JI notation
> systems that I've seen to introduce for the first, most basic chorales.
>
> The first is almost done; the second is, as you might imagine, a bit more
> work, and is a work slowly in progress. Both are intended for high-school
> age students and above; essentially, once the students have gained basic
> control of their instruments and understand how music notation works.
>
> Andrew

From what I understand, 72-EDO is great for notation, and is it a possibility.
And it has the advantage of being based on the common notation system that
everyone who reads music knows. I still prefer my Johnston notation, which has
it's own advantages with being based on common notation in a slightly different
way. But, yes, I can see how it would be useful for this purpose. Do you know of
any practical teaching methods specifically in 72-EDO?

Andrew


--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Have you thought about using 72-EDO? Makes life incredibly simple:
> 1/6th of a semitone turns a 12-EDO major third into an almost perfect
> 5/4, 1/3 of a semitone turns a 12-EDO minor 7th into an almost perfect
> 7/4, 1/2 of a semitone turns a 12-EDO tritone into an almost perfect
> 11/8. Can't get more conceptually simple than that.
>
> -Mike
>

Can you elaborate a bit on what constitutes a practical teaching method?

-Mike


On Sun, Feb 26, 2012 at 6:33 PM, bigAndrewM <bigandrewm@...> wrote:
>
> From what I understand, 72-EDO is great for notation, and is it a
> possibility. And it has the advantage of being based on the common notation
> system that everyone who reads music knows. I still prefer my Johnston
> notation, which has it's own advantages with being based on common notation
> in a slightly different way. But, yes, I can see how it would be useful for
> this purpose. Do you know of any practical teaching methods specifically in
> 72-EDO?

Random comments:

* Do you know about Sagittal, a recent attempt to generalize
Johnston notation?
http://sagittal.org

* The biggest schools I know of to teach 72 are that of
Joe Maneri and the Boston Microtonal Society (both in Boston).
Maybe someone can clarify the relationship (if any) between
between them.  Maneri passed away in 2009 and his official
site seems to be down.
http://bostonmicrotonalsociety.org

* Regarding notation generally, this page may be of interest
http://lumma.org/music/theory/notation/

-Carl

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> From what I understand, 72-EDO is great for notation, and is
> it a possibility. And it has the advantage of being based on
> the common notation system that everyone who reads music knows.
> I still prefer my Johnston notation, which has it's own
> advantages with being based on common notation in a slightly
> different way. But, yes, I can see how it would be useful for
> this purpose. Do you know of any practical teaching methods
> specifically in 72-EDO?
>
> Andrew
>

Something you can teach to high schoolers on commonly used instruments.

Andrew


--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Can you elaborate a bit on what constitutes a practical teaching method?
>
> -Mike
>

I know of it, but that's about it. I'm dijesting it now.

Andrew


--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Random comments:
>
> * Do you know about Sagittal, a recent attempt to generalize
> Johnston notation?
> http://sagittal.org
>
>

There is a 72-EDO ear training book by Joe Maneri called "Preliminary Exercises
in the Virtual Pitch Continuum". I have no personal experience with it, but it
and things like it are still used at New England Conservatory. And Jon Fonville
at UCSD is doing ear-training type things with grad students using Johnston's
notation.

I am working on a songbook which will illustrate the use of Sagittal in the
notation of fifty or so songs in JI and EDO's 11,12,17,22,31, and 41. I hope I
am able to finish soon, so that it be input to the conversation.

A long time ago, I envisioned a collaborative hub for microtonal pedagogy:
http://xenharmonic.wikispaces.com/MicroPedagogyCollective

The invitation to collect ideas, experiences, materials here still stands. This
is what xenharmonic wiki was made for.

In my experience of attempting to teach this stuff (mostly to college-age
musicians and non-musicians), an idea of Praxis (theory and practice) has been
most useful. A frequent shifting of format, from arithmetic to singing and back
again, seems to be a key to keeping things unfolding for everyone. Often, an
understanding of the math behind something is an entirely different thing than
being able to reproduce it sonically (and both are necessary).

In 2005 I started work on a 31-tone method book of solos/duos/quartets/octets
for bass clef instruments (bassoon, trombone, cello, contrabass, etc.). It
seemed like a fruitful direction, and I hope to finish it someday. I think that
method books addressing the issues of playing specific tunings on specific
instruments are a crucial part of a new & needed musical infrastructure. I am
beginning to suspect that a "start anywhere" approach is desirable or even
necessary—a constellation of concepts, as opposed to some definitive
hierarchy/sequence of fundamental ideas. This is consistent with how I absorbed
a microtonal understanding--I realized I needed to understand a bunch of new
things at once, which were consistent with each other but not necessarily with
what I already knew, and it all eventually became part of a larger inquiry about
knowledge and radical change.

Another crucial part of a xenharmonic infrastructure might be a living canon—an
open group of composers composing accessible music that's fun to play and
rewarding on a bunch of levels at once. By accessible, I don't mean an aesthetic
constraint, but that the means to reproduce the music on one's own—scores,
tuners, the necessary instruments—must be widely available. I hope that the
songbook I'm working on might seed such a canon.

...and I think that a 19-edo scordatura keyboard method book could be a
fantastic contribution!

Jacob

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> From what I understand, 72-EDO is great for notation, and is it a possibility.
And it has the advantage of being based on the common notation system that
everyone who reads music knows. I still prefer my Johnston notation, which has
it's own advantages with being based on common notation in a slightly different
way. But, yes, I can see how it would be useful for this purpose. Do you know of
any practical teaching methods specifically in 72-EDO?
>
> Andrew
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > Have you thought about using 72-EDO? Makes life incredibly simple:
> > 1/6th of a semitone turns a 12-EDO major third into an almost perfect
> > 5/4, 1/3 of a semitone turns a 12-EDO minor 7th into an almost perfect
> > 7/4, 1/2 of a semitone turns a 12-EDO tritone into an almost perfect
> > 11/8. Can't get more conceptually simple than that.
> >
> > -Mike
> >
>