Yahoo Tuning Groups Ultimate Backup tuning How to teach microtonal music to students

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
>

🔗Carl Lumma <carl@...>

--- "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

🔗Mike Battaglia <battaglia01@...>

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

🔗bigAndrewM <bigandrewm@...>

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
> >
>

🔗bigAndrewM <bigandrewm@...>

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
>

🔗Carl Lumma <carl@...>

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@...m, "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
> >
>

🔗bigAndrewM <bigandrewm@...>

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
> > >
> >
>

🔗Mike Battaglia <battaglia01@...>

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

🔗bigAndrewM <bigandrewm@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗bigAndrewM <bigandrewm@...>

🔗piccolosandcheese <udderbot@...>

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 necessarya 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 canonan 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 ownscores, tuners, the necessary instrumentsmust 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
> >
>

🔗bigAndrewM <bigandrewm@...>

Thank you! I'll have to see if I can find the Maneri book, to see how he wrote it. And I know of Jon Fonville, although I haven't met him. I tried applying for grad school over at UCSD but, alas, they turned me down. This year.

Your songbook sounds like a fanastic idea - in my humble opinion, it's resources like that which should become extremely valuable for introducing microtonality to novices. I'm not really up-to-speed with Sagittal yet, but it definitely looks promising.

Speaking of Sagittal, one of the main reasons why I currently prefer Johnston notation to others is that he based his system on a 5-limit just major scale, instead of the pythagorean scale. I think that simply from an ear-recognition standpoint, that is a better starting point, and I know that lots of people prefer the other way. I suspect that the majority of people who prefer the latter are keyboard players, although that's only a guess. I think that time will be the arbiter of which is more popular. But - the other aspects of Sagittal look extremely interesting as far as I've been able to figure out. Maybe I'll end up using a hybrid.

Andrew

--- In tuning@yahoogroups.com, "piccolosandcheese" <udderbot@...> wrote:
>
> 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 necessarya 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 canonan 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 ownscores, tuners, the necessary instrumentsmust 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
>

🔗Carl Lumma <carl@...>

🔗Keenan Pepper <keenanpepper@...>

🔗bigAndrewM <bigandrewm@...>

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > There are some good reasons to use the pythagorean scale
> > (or some other MOS) for the nominals... The sagittal designers
> > actually see it as a bug in Johnston notation, and correcting
> > it was one of their goals for sagittal. In short, the more
> > regular the scale the nominals are based on, the less the
> > tendency for "accidental pileup".
> >
> > I would also argue that the pyagorean scale is better for
> > ear training, especially for beginners. It is easier to sing
> > this scale than the 5-limit JI diatonic, perhaps because it
> > only has two different sizes of step rather than three (and
> > this is true for every interval class, not just 2nds).
> > And the tendency in barbershop seems to be to keep the melody
> > in a MOS and apply comma adjustments to the harmony parts,
> > rather than the other way around.
>
> I couldn't agree more with this. Making the nominals "JI diatonic" seems
> nuts to me because one of the notated perfect fifths is not 3/2, but there's
> no indication which one. (Same with fourths, minor thirds, major sixths...)
> If G-D and D-A are not the same interval then you might as well make up
> totally new symbols, because the ones I know don't work like that.
>
> Keenan

Around 4 years ago Dave Keenan and I took a close look at the Johnston notation. In our discussion we referred to the explanation and specific examples in David Doty's Just Intonation Primer, available from: http://www.justintonation.net/primer1.html

Dave K. was in complete agreement with all of my observations, which I quote here in full, along with other comments I've added [in square brackets] for clarification:

<< Now that I've had a chance to look at it, I'm amazed at how many things I can find to fault, without even counting the false D-to-A fifth.

1) I don't know if it's just my Sagittal-arrow orientation, but I find it counter-intuitive that the 7 accidental (which not only seems to point *upward* but also sits *atop* the sharp and flat signs in Figures 5.1b and 5.2) actually *lowers* the pitch (by 32:35) and the inverted 7 (which not only seems to point *downward* but also sits *below* the sharp and flat signs in Figure 5.1b) actually *raises* the pitch.

[This is a matter of cosmetics rather than semantics and not a serious problem.]

2) In Figure 5.2 (the only diagram showing the symbols on a staff), the horizontal component of the +, -, 7, and inverted 7 signs tends to get lost when it gets too close to a staff line (see 32/27 on the 6th staff). The - sign is completely lost, and it's also rather difficult to distinguish an inverted 7 from a double-inverted 7 (see 8/7 vs. 64/49 and 12/7 vs. 64/49 on the bottom staff).

[Dave noted that this could be remedied by a properly designed font, e.g., something along the lines of our Sagittal-Wilson symbols could replace + - .]

3) Multiple accidentals make the size of the cumulative alteration difficult to estimate, particularly when they point in opposite directions. In Figure 5.1b, in the second plane down, the symbol in the upper right corner is:
A77++ (for 6615/4096)
Relative to C (taking into account the need to decrease five's exponent by 1, since the nominal is A) this translates to [ 3, 1, 2 >, which is
Ab'~|) and A'~~!! in Sagittal herculean & olympian, or
Ab/|~ and A||~ promethean, or
Ab(|( and A~||( athenian.
With Sagittal, the flags at least give you a general idea of the amount of alteration.

[The Sagittal symbols for JI in the higher-than-athenian levels are admittedly rather unusual and/or complicated, but this is to be expected if you want to distinguish a complicated ratio from a simpler one with a separate symbol. The herculean, promethean, and (especially) athenian levels of precision re-use symbols for simpler ratios to notate more complicated ratios, thereby allowing the composer to choose among several different levels of notational complexity. (Athenian-level symbols are guaranteed to get you within 5.4 cents of the desired pitch of a complex ratio, and in the overwhelming majority of cases within 2 cents. All reasonably simple 11-limit ratios are notated exactly.) The point I was making is that, unlike Sagittal symbols, laterally "stacked" Johnston symbols often require mental gymnastics to determine the total amount of alteration.]

4) The C-centric 5-comma breaks in the chain-of-fifths nominals increase the number of irregularities in interpreting ratios when one goes above the 5-limit; e.g., 7/4 of C is Bb7, whereas 7/4 of G is F7+, 7/4 of A is G7, and 7/4 of B is A7+. With Sagittal you can usually determine the prime factors in the ratio from the accidental, without taking the nominal into account. >>

[Those instances in which the nominal must be taken into account involve cases in which the same symbol is used for two different ratios differing by a very small amount, e.g., 35:36 (7-limit, 48.770 c) vs. 1024:1053 (13-limit, 48.348 c). In such cases, the intended ratio is easily determined by the musical context.]

[End of quote]

A further point to consider is that stacked Johnston symbols do not seem very suitable for notating temperaments. Dave & I gave issues such as these a lot of thought as we sought (over the course of several years!) to define a single set of symbols that could notate virtually any tuning.

Andrew, for these reasons I hope you will take the time to give the Sagittal system serious consideration.

--George

🔗bigAndrewM <bigandrewm@...>

🔗AWolf <wolftune@...>

Andrew,

I teach even beginning 7-year-old students that vibrations depend on the size of the vibrating object (string or air-column), and that sounds are made up of lots of mixed combinations of vibrations. It's a little easier to make sense of with strings, but I even teach young beginners that certain relationships are important, such as the half-way point of the string.

There is no reason to keep this sort of understanding from students. Some may be more interested than others, but I believe everyone ought to understand something about the basic nature of the thing they're doing. I see this lack as one of the biggest failings of many educators.

Also, there's no reason that brass players should just listen to brass music! You can play any music for them if it demonstrates an idea that is worthwhile. People need perspective, anyway.

Let us know how it all goes!

Best,
Aaron
http://wolftune.com

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> 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
> > >
> >
>

🔗bigAndrewM <bigandrewm@...>

Yeah, it is definitely much easier to show how sound physically works with strings, just because the vibrating medium isn't hidden behind a bunch of metal.

Which gives me some ideas for future lessons, too . . .

I agree that hesitance to teach how the instruments physically work is a failing, not of necessarily many educators, but of enough to make an unfortunate difference. With brass instruments, the way that the embouchure is hidden by the mouthpiece and how every person's distinct facial structure both make understanding how brass playing works can be extremely difficult to figure out. There aren't that many people out there who really understand it. But the mechanics of vibrating strings and equivalently vibrating airstreams (mostly) are much simpler. Mostly, anyway; certainly enough that any musician should have a pretty good understanding of the mechanisms.

Andrew

--- In tuning@yahoogroups.com, "AWolf" <wolftune@...> wrote:
>
> Andrew,
>
> I teach even beginning 7-year-old students that vibrations depend on the size of the vibrating object (string or air-column), and that sounds are made up of lots of mixed combinations of vibrations. It's a little easier to make sense of with strings, but I even teach young beginners that certain relationships are important, such as the half-way point of the string.
>
> There is no reason to keep this sort of understanding from students. Some may be more interested than others, but I believe everyone ought to understand something about the basic nature of the thing they're doing. I see this lack as one of the biggest failings of many educators.
>
> Also, there's no reason that brass players should just listen to brass music! You can play any music for them if it demonstrates an idea that is worthwhile. People need perspective, anyway.
>
> Let us know how it all goes!
>
> Best,
> Aaron
> http://wolftune.com
>

🔗AWolf <wolftune@...>

I use one of those spinny plastic tubes to show how vibrating air columns and the harmonic series works:

http://en.wikipedia.org/wiki/Whirly_tube
http://www.stevespanglerscience.com/experiment/sound-hose

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> Yeah, it is definitely much easier to show how sound physically works with strings, just because the vibrating medium isn't hidden behind a bunch of metal.
>
> Which gives me some ideas for future lessons, too . . .
>
> :D
>
> I agree that hesitance to teach how the instruments physically work is a failing, not of necessarily many educators, but of enough to make an unfortunate difference. With brass instruments, the way that the embouchure is hidden by the mouthpiece and how every person's distinct facial structure both make understanding how brass playing works can be extremely difficult to figure out. There aren't that many people out there who really understand it. But the mechanics of vibrating strings and equivalently vibrating airstreams (mostly) are much simpler. Mostly, anyway; certainly enough that any musician should have a pretty good understanding of the mechanisms.
>
> Andrew
>
>
>
> --- In tuning@yahoogroups.com, "AWolf" <wolftune@> wrote:
> >
> > Andrew,
> >
> > I teach even beginning 7-year-old students that vibrations depend on the size of the vibrating object (string or air-column), and that sounds are made up of lots of mixed combinations of vibrations. It's a little easier to make sense of with strings, but I even teach young beginners that certain relationships are important, such as the half-way point of the string.
> >
> > There is no reason to keep this sort of understanding from students. Some may be more interested than others, but I believe everyone ought to understand something about the basic nature of the thing they're doing. I see this lack as one of the biggest failings of many educators.
> >
> > Also, there's no reason that brass players should just listen to brass music! You can play any music for them if it demonstrates an idea that is worthwhile. People need perspective, anyway.
> >
> > Let us know how it all goes!
> >
> > Best,
> > Aaron
> > http://wolftune.com
> >
>

🔗bigAndrewM <bigandrewm@...>

Okay, having dijested Sagittal notation a bit (by no means do I really have it all figured out yet - not how it works, but why) this system seems to solve some issues that I had planned on solving myself regarding Johnston notation, anyway. The biggest problem for me was the manuscript, that the multiple accidentals simply can look ugly and would not be easy to read, and that parts of the symbols can sometimes become lost in the staff lines.

The point #4 (given in the previous post cited below) still has me a bit undecided. Yes, unless the base C major scale is Pythagorean, the chain of fifths is broken. But I'm not convinced that the fifths need to be pure for people to be able to read the music. I'm trying to approach this from the performer's point of view rather than the composer's.

Of course, I'm referring to Johnston's preference to use the 5-limit C major scale as the base scale. And Saggital looks like it will work in either case, either with the Pythagoream or the 5-limit C major scale.

Which is really cool. Great job in developing this, by the way. It definitely took a lot of work.

Someone who has never seen microtonal notation before (such someones would be the vast, vast majority of musicians) would want the initial presentation to be as simple as possible. This usually means 'how do I play a scale, and what does it look like?' With the 5-limit assumption of C major, the player would simply play the scale as it sounds in-tune to them at the moment, and there is no extra notation at all. With the Pythagorean assumption, there will be notation to account for the three syntonic commas that would be needed to play the scale in tune, which would have to be explained later. It's just a bit more cluttered at the start, and possibly unnecessarily.

To learn any just intonation system, that C major scale will have to be aurally memorized, so that the musician knows exactly where those notes are on their instrument or in their voice and how they sound in relation to the other notes of the same scale. They are going to learn the sound of the 5-limit scale no matter how it's actually notated. It just seems to me to be better to start the notation there as well simply because of how I expect people to learn it. Then, adding the accidentals only modifies exactly what the musician knows by ear from the beginning, not based on the Pythagorean scale which is more difficult to pinpoint aurally.

Obviously, I'm talking about playing on any instrument capable of very fine pitch-adjustment. Keyboards wouldn't matter; the key is pounded and a pitch comes out and it isn't up to the performer on those instruments how well in-tune those pitches are. It's all set up beforehand and they're stuck with what they got.

Essentially, I'm saying that I'm not sure if it even matters for performers if every fifth is perfect and every major second is exactly the same and so on in the notation. All they would want is how to adjust the pitch based on what they already know.

Andrew

>
> Around 4 years ago Dave Keenan and I took a close look at the Johnston notation. In our discussion we referred to the explanation and specific examples in David Doty's Just Intonation Primer, available from: http://www.justintonation.net/primer1.html
>
> Dave K. was in complete agreement with all of my observations, which I quote here in full, along with other comments I've added [in square brackets] for clarification:
>
> << Now that I've had a chance to look at it, I'm amazed at how many things I can find to fault, without even counting the false D-to-A fifth.
>
> 1) I don't know if it's just my Sagittal-arrow orientation, but I find it counter-intuitive that the 7 accidental (which not only seems to point *upward* but also sits *atop* the sharp and flat signs in Figures 5.1b and 5.2) actually *lowers* the pitch (by 32:35) and the inverted 7 (which not only seems to point *downward* but also sits *below* the sharp and flat signs in Figure 5.1b) actually *raises* the pitch.
>
> [This is a matter of cosmetics rather than semantics and not a serious problem.]
>
> 2) In Figure 5.2 (the only diagram showing the symbols on a staff), the horizontal component of the +, -, 7, and inverted 7 signs tends to get lost when it gets too close to a staff line (see 32/27 on the 6th staff). The - sign is completely lost, and it's also rather difficult to distinguish an inverted 7 from a double-inverted 7 (see 8/7 vs. 64/49 and 12/7 vs. 64/49 on the bottom staff).
>
> [Dave noted that this could be remedied by a properly designed font, e.g., something along the lines of our Sagittal-Wilson symbols could replace + - .]
>
> 3) Multiple accidentals make the size of the cumulative alteration difficult to estimate, particularly when they point in opposite directions. In Figure 5.1b, in the second plane down, the symbol in the upper right corner is:
> A77++ (for 6615/4096)
> Relative to C (taking into account the need to decrease five's exponent by 1, since the nominal is A) this translates to [ 3, 1, 2 >, which is
> Ab'~|) and A'~~!! in Sagittal herculean & olympian, or
> Ab/|~ and A||~ promethean, or
> Ab(|( and A~||( athenian.
> With Sagittal, the flags at least give you a general idea of the amount of alteration.
>
> [The Sagittal symbols for JI in the higher-than-athenian levels are admittedly rather unusual and/or complicated, but this is to be expected if you want to distinguish a complicated ratio from a simpler one with a separate symbol. The herculean, promethean, and (especially) athenian levels of precision re-use symbols for simpler ratios to notate more complicated ratios, thereby allowing the composer to choose among several different levels of notational complexity. (Athenian-level symbols are guaranteed to get you within 5.4 cents of the desired pitch of a complex ratio, and in the overwhelming majority of cases within 2 cents. All reasonably simple 11-limit ratios are notated exactly.) The point I was making is that, unlike Sagittal symbols, laterally "stacked" Johnston symbols often require mental gymnastics to determine the total amount of alteration.]
>
> 4) The C-centric 5-comma breaks in the chain-of-fifths nominals increase the number of irregularities in interpreting ratios when one goes above the 5-limit; e.g., 7/4 of C is Bb7, whereas 7/4 of G is F7+, 7/4 of A is G7, and 7/4 of B is A7+. With Sagittal you can usually determine the prime factors in the ratio from the accidental, without taking the nominal into account. >>
>
> [Those instances in which the nominal must be taken into account involve cases in which the same symbol is used for two different ratios differing by a very small amount, e.g., 35:36 (7-limit, 48.770 c) vs. 1024:1053 (13-limit, 48.348 c). In such cases, the intended ratio is easily determined by the musical context.]
>
> [End of quote]
>
> A further point to consider is that stacked Johnston symbols do not seem very suitable for notating temperaments. Dave & I gave issues such as these a lot of thought as we sought (over the course of several years!) to define a single set of symbols that could notate virtually any tuning.
>
> Andrew, for these reasons I hope you will take the time to give the Sagittal system serious consideration.
>
> --George
>

🔗bigAndrewM <bigandrewm@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
> Okay, having dijested Sagittal notation a bit (by no means do I really have it all figured out yet - not how it works, but why) this system seems to solve some issues that I had planned on solving myself regarding Johnston notation, anyway. The biggest problem for me was the manuscript, that the multiple accidentals simply can look ugly and would not be easy to read, and that parts of the symbols can sometimes become lost in the staff lines.
>
> The point #4 (given in the previous post cited below) still has me a bit undecided. Yes, unless the base C major scale is Pythagorean, the chain of fifths is broken. But I'm not convinced that the fifths need to be pure for people to be able to read the music. I'm trying to approach this from the performer's point of view rather than the composer's.
>
> Of course, I'm referring to Johnston's preference to use the 5-limit C major scale as the base scale. And Saggital looks like it will work in either case, either with the Pythagoream or the 5-limit C major scale.

Not sure what you mean by this. Sagittal is based on F-C-G-D-A-E-B being identical fifths. If you make that the Ptolemy 5-limit major scale instead, then you're not using Sagittal. (Sagittal gurus please correct me if I'm wrong.)

> Which is really cool. Great job in developing this, by the way. It definitely took a lot of work.
>
> Someone who has never seen microtonal notation before (such someones would be the vast, vast majority of musicians) would want the initial presentation to be as simple as possible. This usually means 'how do I play a scale, and what does it look like?' With the 5-limit assumption of C major, the player would simply play the scale as it sounds in-tune to them at the moment, and there is no extra notation at all. With the Pythagorean assumption, there will be notation to account for the three syntonic commas that would be needed to play the scale in tune, which would have to be explained later. It's just a bit more cluttered at the start, and possibly unnecessarily.

This reasoning is based on an incorrect assumption. If a musician is "playing the scale as it sounds in-tune to them at the moment", even in a C major context, they're going to play a D-A double stop as 3/2, never 40/27. In other words "playing the scale as it sounds in-tune to them at the moment" does not refer to any specific JI scale, but to an adaptive JI rendition based on a "smart" interpretation of the music.

If some particular musician *DID* already have the Ptolemy 5-limit major scale memorized and internalized, then what you're saying would make perfect sense, but I'm sure this is not true for the vast majority of musicians. "A major scale that sounds in-tune" is certainly not identical with "the Ptolemy 5-limit major scale".

> To learn any just intonation system, that C major scale will have to be aurally memorized, so that the musician knows exactly where those notes are on their instrument or in their voice and how they sound in relation to the other notes of the same scale. They are going to learn the sound of the 5-limit scale no matter how it's actually notated. It just seems to me to be better to start the notation there as well simply because of how I expect people to learn it. Then, adding the accidentals only modifies exactly what the musician knows by ear from the beginning, not based on the Pythagorean scale which is more difficult to pinpoint aurally.
>
> Obviously, I'm talking about playing on any instrument capable of very fine pitch-adjustment. Keyboards wouldn't matter; the key is pounded and a pitch comes out and it isn't up to the performer on those instruments how well in-tune those pitches are. It's all set up beforehand and they're stuck with what they got.
>
> Essentially, I'm saying that I'm not sure if it even matters for performers if every fifth is perfect and every major second is exactly the same and so on in the notation. All they would want is how to adjust the pitch based on what they already know.

All of this would make perfect sense, except that "what they already know" is almost guaranteed not to be the Ptolemy 5-limit major scale. In most cases, "what they already know" is somewhere in the spectrum between 12-equal and an adaptive JI rendition deviating from a base framework of meantone.

You're making it sound as if starting from the Ptolemy major scale is completely natural and intuitive, and starting from Pythagorean is unnatural or unnecessarily complicated. In reality they are simply different choices each with their own drawbacks. If you start from Pythagorean you have to teach people that C-E is not 5/4; if you start from Ptolemy on C you have to teach people that D-A is not 3/2 and D-F is not 6/5. Pythagorean has the drawback that all ratios of 5 must have accidentals; but Ptolemy has the (to me more serious) drawback of being inconsistent with the logical chain-of-fifths transposition structure that people already know.

Keenan

🔗bigAndrewM <bigandrewm@...>

I would absolutely love it if someone would convince me for good that I should abandon the Ptolemy scale. But, alas, it hasn't happened yet.

I guarantee that any professional wind musician can play any scale in-tune, 5-limit style. And what beginning students I have, if I play a drone, will naturally want to play whatever scale I'm meaning for them to learn with the 5-limit tunings as well. If they play it by themselves, they simply use fingerings and otherwise defer to the natural tendancies of their instrument, not otherwise gravitating toward any particular tuning. Those D-A and D-F artifacts simply don't come into play when kids learn the patterns. And when they get to music which does have ii chords, yes, they will tend to play the ii chord in-tune, outside of that 5-limit scale. But that is because of how music is taught with it's 12-ET assumptions. It doesn't have to be that way. Also, those D-A and D-F artifacts can't be explained away by using the chain-of-fifths Pythagorean major scale; there, they're just moved around so that every major third has them instead. It's a great accomodation for theorists, not so great for performers, IMHO.

>
> > To learn any just intonation system, that C major scale will have to be aurally memorized, so that the musician knows exactly where those notes are on their instrument or in their voice and how they sound in relation to the other notes of the same scale. They are going to learn the sound of the 5-limit scale no matter how it's actually notated. It just seems to me to be better to start the notation there as well simply because of how I expect people to learn it. Then, adding the accidentals only modifies exactly what the musician knows by ear from the beginning, not based on the Pythagorean scale which is more difficult to pinpoint aurally.
> >
> > Obviously, I'm talking about playing on any instrument capable of very fine pitch-adjustment. Keyboards wouldn't matter; the key is pounded and a pitch comes out and it isn't up to the performer on those instruments how well in-tune those pitches are. It's all set up beforehand and they're stuck with what they got.
> >
> > Essentially, I'm saying that I'm not sure if it even matters for performers if every fifth is perfect and every major second is exactly the same and so on in the notation. All they would want is how to adjust the pitch based on what they already know.
>
> All of this would make perfect sense, except that "what they already know" is almost guaranteed not to be the Ptolemy 5-limit major scale. In most cases, "what they already know" is somewhere in the spectrum between 12-equal and an adaptive JI rendition deviating from a base framework of meantone.
>
> You're making it sound as if starting from the Ptolemy major scale is completely natural and intuitive, and starting from Pythagorean is unnatural or unnecessarily complicated. In reality they are simply different choices each with their own drawbacks. If you start from Pythagorean you have to teach people that C-E is not 5/4; if you start from Ptolemy on C you have to teach people that D-A is not 3/2 and D-F is not 6/5. Pythagorean has the drawback that all ratios of 5 must have accidentals; but Ptolemy has the (to me more serious) drawback of being inconsistent with the logical chain-of-fifths transposition structure that people already know.
>
> Keenan
>

Yes, all true. I'm trying to approach this as if I want the most basic student possible to be able to learn it. A number of my beginning students learn from the O-so-loved basic band methods which start with fingerings and name-of-notes and this-is-a-half-note information. For band students, it is entirely the Bb major scale. No additional accidentals. No tuning instructions. They learn the notes, and they learn basic tunes that they can play with what notes they have learned. That's it. They don't care about whether or not an E is 6/5 or 81/64. They don't care about the difference between 10/9 and 9/8. They just learn patterns, and once they can get enough control over their instruments, they figure out how to bend pitches to get them in tune by ear. If that ever happens at all, given how impossible it can be to hear any kind of tuning in beginning band.

The question, is with which JI scale is it ultimately simpler to start students. Is it better to start them with the scale that is in-tune as they read it unaltered, or is it better to start them with the scale that, while it has the defective major and minor thirds, has the errors spread relatively evenly throughout it? I'm not sure.

I need to come up with some informal testing of this concept with what few students that I have. The problem is, how to pose the tests so I actually get useful information. I'm not sure how to do that.

If I play drones and ask students to play scales, this clearly is going to end up in 5-limit scales anyway. If I have them tune the fifths of the scale, forming it that way, they will end up with the Pythagorean version. Perhaps if I were to do one method with one subset of students and the other method with another subset, and wait and see over time which set picks up their scales faster, or which picks up tuning music in context faster?

🔗cityoftheasleep <igliashon@...>

Seems to me you're ultimately teaching them adaptive JI, rather than static JI, so the need for note names to correspond to single discrete pitches isn't there. In other words, you won't need separate accidentals for 27/16 and 5/3 (i.e. the two A's), because musical context and the student's ears will determine which pitch is to be played--thus obviating the need to notationally dictate it. So just use standard notation.

-Igs

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> I would absolutely love it if someone would convince me for good that I should abandon the Ptolemy scale. But, alas, it hasn't happened yet.
>
> > > Someone who has never seen microtonal notation before (such someones would be the vast, vast majority of musicians) would want the initial presentation to be as simple as possible. This usually means 'how do I play a scale, and what does it look like?' With the 5-limit assumption of C major, the player would simply play the scale as it sounds in-tune to them at the moment, and there is no extra notation at all. With the Pythagorean assumption, there will be notation to account for the three syntonic commas that would be needed to play the scale in tune, which would have to be explained later. It's just a bit more cluttered at the start, and possibly unnecessarily.
> >
> > This reasoning is based on an incorrect assumption. If a musician is "playing the scale as it sounds in-tune to them at the moment", even in a C major context, they're going to play a D-A double stop as 3/2, never 40/27. In other words "playing the scale as it sounds in-tune to them at the moment" does not refer to any specific JI scale, but to an adaptive JI rendition based on a "smart" interpretation of the music.
> >
> > If some particular musician *DID* already have the Ptolemy 5-limit major scale memorized and internalized, then what you're saying would make perfect sense, but I'm sure this is not true for the vast majority of musicians. "A major scale that sounds in-tune" is certainly not identical with "the Ptolemy 5-limit major scale".
>
> I guarantee that any professional wind musician can play any scale in-tune, 5-limit style. And what beginning students I have, if I play a drone, will naturally want to play whatever scale I'm meaning for them to learn with the 5-limit tunings as well. If they play it by themselves, they simply use fingerings and otherwise defer to the natural tendancies of their instrument, not otherwise gravitating toward any particular tuning. Those D-A and D-F artifacts simply don't come into play when kids learn the patterns. And when they get to music which does have ii chords, yes, they will tend to play the ii chord in-tune, outside of that 5-limit scale. But that is because of how music is taught with it's 12-ET assumptions. It doesn't have to be that way. Also, those D-A and D-F artifacts can't be explained away by using the chain-of-fifths Pythagorean major scale; there, they're just moved around so that every major third has them instead. It's a great accomodation for theorists, not so great for performers, IMHO.
>
>
> >
> > > To learn any just intonation system, that C major scale will have to be aurally memorized, so that the musician knows exactly where those notes are on their instrument or in their voice and how they sound in relation to the other notes of the same scale. They are going to learn the sound of the 5-limit scale no matter how it's actually notated. It just seems to me to be better to start the notation there as well simply because of how I expect people to learn it. Then, adding the accidentals only modifies exactly what the musician knows by ear from the beginning, not based on the Pythagorean scale which is more difficult to pinpoint aurally.
> > >
> > > Obviously, I'm talking about playing on any instrument capable of very fine pitch-adjustment. Keyboards wouldn't matter; the key is pounded and a pitch comes out and it isn't up to the performer on those instruments how well in-tune those pitches are. It's all set up beforehand and they're stuck with what they got.
> > >
> > > Essentially, I'm saying that I'm not sure if it even matters for performers if every fifth is perfect and every major second is exactly the same and so on in the notation. All they would want is how to adjust the pitch based on what they already know.
> >
> > All of this would make perfect sense, except that "what they already know" is almost guaranteed not to be the Ptolemy 5-limit major scale. In most cases, "what they already know" is somewhere in the spectrum between 12-equal and an adaptive JI rendition deviating from a base framework of meantone.
> >
> > You're making it sound as if starting from the Ptolemy major scale is completely natural and intuitive, and starting from Pythagorean is unnatural or unnecessarily complicated. In reality they are simply different choices each with their own drawbacks. If you start from Pythagorean you have to teach people that C-E is not 5/4; if you start from Ptolemy on C you have to teach people that D-A is not 3/2 and D-F is not 6/5. Pythagorean has the drawback that all ratios of 5 must have accidentals; but Ptolemy has the (to me more serious) drawback of being inconsistent with the logical chain-of-fifths transposition structure that people already know.
> >
> > Keenan
> >
>
> Yes, all true. I'm trying to approach this as if I want the most basic student possible to be able to learn it. A number of my beginning students learn from the O-so-loved basic band methods which start with fingerings and name-of-notes and this-is-a-half-note information. For band students, it is entirely the Bb major scale. No additional accidentals. No tuning instructions. They learn the notes, and they learn basic tunes that they can play with what notes they have learned. That's it. They don't care about whether or not an E is 6/5 or 81/64. They don't care about the difference between 10/9 and 9/8. They just learn patterns, and once they can get enough control over their instruments, they figure out how to bend pitches to get them in tune by ear. If that ever happens at all, given how impossible it can be to hear any kind of tuning in beginning band.
>
> The question, is with which JI scale is it ultimately simpler to start students. Is it better to start them with the scale that is in-tune as they read it unaltered, or is it better to start them with the scale that, while it has the defective major and minor thirds, has the errors spread relatively evenly throughout it? I'm not sure.
>
> I need to come up with some informal testing of this concept with what few students that I have. The problem is, how to pose the tests so I actually get useful information. I'm not sure how to do that.
>
> If I play drones and ask students to play scales, this clearly is going to end up in 5-limit scales anyway. If I have them tune the fifths of the scale, forming it that way, they will end up with the Pythagorean version. Perhaps if I were to do one method with one subset of students and the other method with another subset, and wait and see over time which set picks up their scales faster, or which picks up tuning music in context faster?
>

🔗Carl Lumma <carl@...>

Keenan wrote:

> Not sure what you mean by this. Sagittal is based on
> F-C-G-D-A-E-B being identical fifths. If you make that the
> Ptolemy 5-limit major scale instead, then you're not using
> Sagittal. (Sagittal gurus please correct me if I'm wrong.)

The gurus have stressed that the Sagittal accidentals can
be used with any nominals. Whether you are still "using
Sagittal" in that case is another matter.

> This reasoning is based on an incorrect assumption. If a
> musician is "playing the scale as it sounds in-tune to them at
> the moment", even in a C major context, they're going to play
> a D-A double stop as 3/2, never 40/27. In other words "playing
> the scale as it sounds in-tune to them at the moment" does not
> refer to any specific JI scale, but to an adaptive JI rendition
> based on a "smart" interpretation of the music.
> If some particular musician *DID* already have the Ptolemy
> 5-limit major scale memorized and internalized, then what
> you're saying would make perfect sense, but I'm sure this is
> not true for the vast majority of musicians. "A major scale
> that sounds in-tune" is certainly not identical with "the
> Ptolemy 5-limit major scale".

Absolutely right. The simplest way to teach an ensemble to
play JI is to drill the chords, like by having them play and
hold each chord in a piece in sequence. They'll take care of
the melody. Notation can assist in this process. One of the
simplest ways is probably local accidentals -- labels on the
notes that show their harmonic identity in the current chord
(e.g. "7", "11" etc). The musician just needs to know that 7
is a bit flatter than usual and sounds like a 7. I call this
"adaptive JI" notation on my notations page. Of course it's
no good when the basic scale is hard to notate in 12, but for
the diatonic scale it should work well. It won't give the
composer absolute control over microtonal pitch... for that
you'll need to either add root-change indications or go to
something like Sagittal. But to get adaptive, extended JI
going quickly I think it's ideal.

-Carl

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Absolutely right. The simplest way to teach an ensemble to
> play JI is to drill the chords, like by having them play and
> hold each chord in a piece in sequence. They'll take care of
> the melody. Notation can assist in this process. One of the
> simplest ways is probably local accidentals -- labels on the
> notes that show their harmonic identity in the current chord
> (e.g. "7", "11" etc). The musician just needs to know that 7
> is a bit flatter than usual and sounds like a 7. I call this
> "adaptive JI" notation on my notations page. Of course it's
> no good when the basic scale is hard to notate in 12, but for
> the diatonic scale it should work well. It won't give the
> composer absolute control over microtonal pitch... for that
> you'll need to either add root-change indications or go to
> something like Sagittal. But to get adaptive, extended JI
> going quickly I think it's ideal.

Combined with what Igs said, this makes for a very practical alternative to having the bare nominals represent either Pythagoren or Ptolemy major - have them represent both! What I mean is, simply don't represent 81/80 differences at all, leaving those slight adjustments up to the performers. Accidentals for higher-limit alterations could still be used. (Technically this means the notation would represent the codimension-1 temperament tempering out 81/80 exactly, and leave the position along the 81/80 axis up for interpretation.)

That way you could have your cake and eat it to. In the C major scale, CEG, FAC, and GBD would be 5-limit major triads, but DFA could also be 5-limit minor. G harmonic seventh could be distinguished from G dominant sevent with an accidental on the F: G B D Fv (where 'v' should be replaced by the correct Sagittal accidental for 64/63 down), and similarly for any higher primes you want to use.

Keenan

🔗Carl Lumma <carl@...>

"Keenan Pepper" <keenanpepper@...> wrote:

> > Absolutely right. The simplest way to teach an ensemble to
> > play JI is to drill the chords, like by having them play and
> > hold each chord in a piece in sequence. They'll take care of
> > the melody. Notation can assist in this process. One of the
> > simplest ways is probably local accidentals -- labels on the
> > notes that show their harmonic identity in the current chord
> > (e.g. "7", "11" etc). The musician just needs to know that 7
> > is a bit flatter than usual and sounds like a 7. I call this
> > "adaptive JI" notation on my notations page. Of course it's
> > no good when the basic scale is hard to notate in 12, but for
> > the diatonic scale it should work well. It won't give the
> > composer absolute control over microtonal pitch... for that
> > you'll need to either add root-change indications or go to
> > something like Sagittal. But to get adaptive, extended JI
> > going quickly I think it's ideal.
[snip]
> That way you could have your cake and eat it to. In the C major
> scale, CEG, FAC, and GBD would be 5-limit major triads, but DFA
> could also be 5-limit minor. G harmonic seventh could be
> distinguished from G dominant seventh with an accidental on
> the F: G B D Fv (where 'v' should be replaced by the correct
> Sagittal accidental for 64/63 down), and similarly for any
> higher primes you want to use.

That's still more complicated that what I'm suggesting, which
by to write 7F. Keep in mind the target here is monophonic
notation for monophonic instruments. Knowing which identity
they're supposed to play is valuable information, and learning
new accidentals and multiplying their commas is not the easiest
way to get it. -Carl

🔗kraiggrady <kraiggrady@...>

I tend to think dyads are a much easier way to teach JI than full chords. For one it is easier to hear the drop in volume along with the smoothing of beats.

....

If one uses the 5 limit major, one just uses the ii by what the ii does and say.
I have found the comma off fifth musically useful. i like to throw it up an octave to get it to beat even more. a good alternative to a dominant chord for tension.

...

As far as notation though to have to spell D-A as 3/2 with one of them with an accidental seems not a good idea. If one works also with a generalized keyboard, the cycle of fifths is the best way to go and accidentals make it clear where on the keyboard a not is.

On 15/03/12 5:15 AM, Keenan Pepper wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma"<carl@...> wrote:
>> Absolutely right. The simplest way to teach an ensemble to
>> play JI is to drill the chords, like by having them play and
>> hold each chord in a piece in sequence. They'll take care of
>> the melody. Notation can assist in this process. One of the
>> simplest ways is probably local accidentals -- labels on the
>> notes that show their harmonic identity in the current chord
>> (e.g. "7", "11" etc). The musician just needs to know that 7
>> is a bit flatter than usual and sounds like a 7. I call this
>> "adaptive JI" notation on my notations page. Of course it's
>> no good when the basic scale is hard to notate in 12, but for
>> the diatonic scale it should work well. It won't give the
>> composer absolute control over microtonal pitch... for that
>> you'll need to either add root-change indications or go to
>> something like Sagittal. But to get adaptive, extended JI
>> going quickly I think it's ideal.
> Combined with what Igs said, this makes for a very practical alternative to having the bare nominals represent either Pythagoren or Ptolemy major - have them represent both! What I mean is, simply don't represent 81/80 differences at all, leaving those slight adjustments up to the performers. Accidentals for higher-limit alterations could still be used. (Technically this means the notation would represent the codimension-1 temperament tempering out 81/80 exactly, and leave the position along the 81/80 axis up for interpretation.)
>
> That way you could have your cake and eat it to. In the C major scale, CEG, FAC, and GBD would be 5-limit major triads, but DFA could also be 5-limit minor. G harmonic seventh could be distinguished from G dominant sevent with an accidental on the F: G B D Fv (where 'v' should be replaced by the correct Sagittal accidental for 64/63 down), and similarly for any higher primes you want to use.
>
> Keenan
>
>
>
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/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

🔗Graham Breed <gbreed@...>

🔗Carl Lumma <carl@...>

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@> wrote:
> > Okay, having dijested Sagittal notation a bit (by no means do I really have it all figured out yet - not how it works, but why) this system seems to solve some issues that I had planned on solving myself regarding Johnston notation, anyway. The biggest problem for me was the manuscript, that the multiple accidentals simply can look ugly and would not be easy to read, and that parts of the symbols can sometimes become lost in the staff lines.

Okay, that's a start. You really don't have to become familiar with all of the Sagittal features and symbols to make effective use of it unless you're going to notate extremely complicated tunings or temperaments. The simpler tunings require far fewer symbols than the more complicated ones. Learn only the symbols that you need, and if you progress to more complicated tunings or higher harmonic limits, you can rest assured that the notation will be able to accommodate them.

> > The point #4 (given in the previous post cited below) still has me a bit undecided. Yes, unless the base C major scale is Pythagorean, the chain of fifths is broken. But I'm not convinced that the fifths need to be pure for people to be able to read the music. I'm trying to approach this from the performer's point of view rather than the composer's.
> >
> > Of course, I'm referring to Johnston's preference to use the 5-limit C major scale as the base scale. And Saggital looks like it will work in either case, either with the Pythagoream or the 5-limit C major scale.
>
> Not sure what you mean by this. Sagittal is based on F-C-G-D-A-E-B being identical fifths. If you make that the Ptolemy 5-limit major scale instead, then you're not using Sagittal. (Sagittal gurus please correct me if I'm wrong.)

Yes, that's correct. Although you would be using Sagittal symbols, you wouldn't be using them in the way they were intended to be used. The Sagittal system was designed to notate JI so that (on a conventional staff) there would be a correlation between the prime factors in a ratio and the Sagittal accidental used to notate that ratio. Thus a 5-comma-down symbol \! indicates that there's a 5-factor (and no other prime <5) in the ratio, and a 7-comma-down symbol !) that there's a 7-factor (and no other prime <5) in the ratio, etc. (There are also symbols for combinations of primes >3 that can be memorized fairly easily.)

Now let's notate a "just" G major scale in this manner:
G A B\! C D E\! F!!\ G
It's immediately evident that the fifth A to E\! is a comma narrower than just and the minor 3rd A to C is pythagorean (i.e., a comma narrower than just), so replacing the A (9/8 of G) with A\! (10/9 of G) will give you a just minor triad A\! C E\! -- and this is valid in all keys!

> > Which is really cool. Great job in developing this, by the way. It definitely took a lot of work.

It was more work than you could ever imagine! Dave Keenan & I were both sticklers for details and didn't always agree on things, but we were determined to keep at it until we had reached an agreement that we had gotten it right.

> > Someone who has never seen microtonal notation before (such someones would be the vast, vast majority of musicians) would want the initial presentation to be as simple as possible. This usually means 'how do I play a scale, and what does it look like?' With the 5-limit assumption of C major, the player would simply play the scale as it sounds in-tune to them at the moment, and there is no extra notation at all. With the Pythagorean assumption, there will be notation to account for the three syntonic commas that would be needed to play the scale in tune, which would have to be explained later. It's just a bit more cluttered at the start, and possibly unnecessarily.
>
> This reasoning is based on an incorrect assumption. If a musician is "playing the scale as it sounds in-tune to them at the moment", even in a C major context, they're going to play a D-A double stop as 3/2, never 40/27. In other words "playing the scale as it sounds in-tune to them at the moment" does not refer to any specific JI scale, but to an adaptive JI rendition based on a "smart" interpretation of the music.
>
> If some particular musician *DID* already have the Ptolemy 5-limit major scale memorized and internalized, then what you're saying would make perfect sense, but I'm sure this is not true for the vast majority of musicians. "A major scale that sounds in-tune" is certainly not identical with "the Ptolemy 5-limit major scale".
>
> > To learn any just intonation system, that C major scale will have to be aurally memorized, so that the musician knows exactly where those notes are on their instrument or in their voice and how they sound in relation to the other notes of the same scale. They are going to learn the sound of the 5-limit scale no matter how it's actually notated. It just seems to me to be better to start the notation there as well simply because of how I expect people to learn it. Then, adding the accidentals only modifies exactly what the musician knows by ear from the beginning, not based on the Pythagorean scale which is more difficult to pinpoint aurally.

You're not really doing anyone a favor by making something simpler in the short run if it results in its being much more complicated in the long run. If you want to make it simple at the very first, then leave off the microtonal accidentals at first until the supertonic false fifth is encountered, at which point the student will understand the need for the comma-accidental.

> > Obviously, I'm talking about playing on any instrument capable of very fine pitch-adjustment. Keyboards wouldn't matter; the key is pounded and a pitch comes out and it isn't up to the performer on those instruments how well in-tune those pitches are. It's all set up beforehand and they're stuck with what they got.
> >
> > Essentially, I'm saying that I'm not sure if it even matters for performers if every fifth is perfect and every major second is exactly the same and so on in the notation. All they would want is how to adjust the pitch based on what they already know.

> All of this would make perfect sense, except that "what they already know" is almost guaranteed not to be the Ptolemy 5-limit major scale. In most cases, "what they already know" is somewhere in the spectrum between 12-equal and an adaptive JI rendition deviating from a base framework of meantone.
>
> You're making it sound as if starting from the Ptolemy major scale is completely natural and intuitive, and starting from Pythagorean is unnatural or unnecessarily complicated. In reality they are simply different choices each with their own drawbacks. If you start from Pythagorean you have to teach people that C-E is not 5/4; if you start from Ptolemy on C you have to teach people that D-A is not 3/2 and D-F is not 6/5. Pythagorean has the drawback that all ratios of 5 must have accidentals; but Ptolemy has the (to me more serious) drawback of being inconsistent with the logical chain-of-fifths transposition structure that people already know.

There's an additional thing to consider if you try to use the Johnston principle to notate temperaments and tempered tunings. For meantone temperament (or tunings such as 19-equal or 31-equal, where the comma is distributed equally over the chain of fifths) there's no need for the 5-comma symbol, since the 5-comma (80:81) vanishes, so there's no problem. But what about 72-equal? With the Johnston method, 2/3 of the tones in the 12-equal circle would get microtonal accidentals, whereas with Sagittal the nominals (plus sharps or flats) notates the circle of 12 fifths without any microtonal accidentals (and the next lower circle of 12 fifths is notated by adding the \! Symbol).

Sure, Johnston notation was intended only for JI, but that's just my point. Why use a notation limited only to JI when you can have one that will do it all (and, for that matter, do it better!) in a consistent manner?

Andrew, since the way you've described introducing the scale to your students sounds very much like adaptive JI, you may want to consider presenting the pitches as two circles of 12 fifths a comma apart (i.e., as a subset of 72-equal), using the 5-comma-down symbol to indicate the tones that need to be adjusted downward in pitch to get closer to pure thirds & sixths. Another advantage is that the \! alteration in 72-equal is only about 3/4 of what's required in strict JI.

--George

🔗kraiggrady@...

🔗bigAndrewM <bigandrewm@...>

George, thank you wonderfully for your responses thus far!

I have more dijestion to do.

And thanks to everyone else who has commented, too. Good constructive criticism is good for the soul.

Andrew

--- In tuning@yahoogroups.com, "gdsecor" <gdsecor@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> >
> > --- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@> wrote:
> > > Okay, having dijested Sagittal notation a bit (by no means do I really have it all figured out yet - not how it works, but why) this system seems to solve some issues that I had planned on solving myself regarding Johnston notation, anyway. The biggest problem for me was the manuscript, that the multiple accidentals simply can look ugly and would not be easy to read, and that parts of the symbols can sometimes become lost in the staff lines.
>
> Okay, that's a start. You really don't have to become familiar with all of the Sagittal features and symbols to make effective use of it unless you're going to notate extremely complicated tunings or temperaments. The simpler tunings require far fewer symbols than the more complicated ones. Learn only the symbols that you need, and if you progress to more complicated tunings or higher harmonic limits, you can rest assured that the notation will be able to accommodate them.
>
> > > The point #4 (given in the previous post cited below) still has me a bit undecided. Yes, unless the base C major scale is Pythagorean, the chain of fifths is broken. But I'm not convinced that the fifths need to be pure for people to be able to read the music. I'm trying to approach this from the performer's point of view rather than the composer's.
> > >
> > > Of course, I'm referring to Johnston's preference to use the 5-limit C major scale as the base scale. And Saggital looks like it will work in either case, either with the Pythagoream or the 5-limit C major scale.
> >
> > Not sure what you mean by this. Sagittal is based on F-C-G-D-A-E-B being identical fifths. If you make that the Ptolemy 5-limit major scale instead, then you're not using Sagittal. (Sagittal gurus please correct me if I'm wrong.)
>
> Yes, that's correct. Although you would be using Sagittal symbols, you wouldn't be using them in the way they were intended to be used. The Sagittal system was designed to notate JI so that (on a conventional staff) there would be a correlation between the prime factors in a ratio and the Sagittal accidental used to notate that ratio. Thus a 5-comma-down symbol \! indicates that there's a 5-factor (and no other prime <5) in the ratio, and a 7-comma-down symbol !) that there's a 7-factor (and no other prime <5) in the ratio, etc. (There are also symbols for combinations of primes >3 that can be memorized fairly easily.)
>
> Now let's notate a "just" G major scale in this manner:
> G A B\! C D E\! F!!\ G
> It's immediately evident that the fifth A to E\! is a comma narrower than just and the minor 3rd A to C is pythagorean (i.e., a comma narrower than just), so replacing the A (9/8 of G) with A\! (10/9 of G) will give you a just minor triad A\! C E\! -- and this is valid in all keys!
>
> > > Which is really cool. Great job in developing this, by the way. It definitely took a lot of work.
>
> It was more work than you could ever imagine! Dave Keenan & I were both sticklers for details and didn't always agree on things, but we were determined to keep at it until we had reached an agreement that we had gotten it right.
>
> > > Someone who has never seen microtonal notation before (such someones would be the vast, vast majority of musicians) would want the initial presentation to be as simple as possible. This usually means 'how do I play a scale, and what does it look like?' With the 5-limit assumption of C major, the player would simply play the scale as it sounds in-tune to them at the moment, and there is no extra notation at all. With the Pythagorean assumption, there will be notation to account for the three syntonic commas that would be needed to play the scale in tune, which would have to be explained later. It's just a bit more cluttered at the start, and possibly unnecessarily.
> >
> > This reasoning is based on an incorrect assumption. If a musician is "playing the scale as it sounds in-tune to them at the moment", even in a C major context, they're going to play a D-A double stop as 3/2, never 40/27. In other words "playing the scale as it sounds in-tune to them at the moment" does not refer to any specific JI scale, but to an adaptive JI rendition based on a "smart" interpretation of the music.
> >
> > If some particular musician *DID* already have the Ptolemy 5-limit major scale memorized and internalized, then what you're saying would make perfect sense, but I'm sure this is not true for the vast majority of musicians. "A major scale that sounds in-tune" is certainly not identical with "the Ptolemy 5-limit major scale".
> >
> > > To learn any just intonation system, that C major scale will have to be aurally memorized, so that the musician knows exactly where those notes are on their instrument or in their voice and how they sound in relation to the other notes of the same scale. They are going to learn the sound of the 5-limit scale no matter how it's actually notated. It just seems to me to be better to start the notation there as well simply because of how I expect people to learn it. Then, adding the accidentals only modifies exactly what the musician knows by ear from the beginning, not based on the Pythagorean scale which is more difficult to pinpoint aurally.
>
> You're not really doing anyone a favor by making something simpler in the short run if it results in its being much more complicated in the long run. If you want to make it simple at the very first, then leave off the microtonal accidentals at first until the supertonic false fifth is encountered, at which point the student will understand the need for the comma-accidental.
>
> > > Obviously, I'm talking about playing on any instrument capable of very fine pitch-adjustment. Keyboards wouldn't matter; the key is pounded and a pitch comes out and it isn't up to the performer on those instruments how well in-tune those pitches are. It's all set up beforehand and they're stuck with what they got.
> > >
> > > Essentially, I'm saying that I'm not sure if it even matters for performers if every fifth is perfect and every major second is exactly the same and so on in the notation. All they would want is how to adjust the pitch based on what they already know.
>
> > All of this would make perfect sense, except that "what they already know" is almost guaranteed not to be the Ptolemy 5-limit major scale. In most cases, "what they already know" is somewhere in the spectrum between 12-equal and an adaptive JI rendition deviating from a base framework of meantone.
> >
> > You're making it sound as if starting from the Ptolemy major scale is completely natural and intuitive, and starting from Pythagorean is unnatural or unnecessarily complicated. In reality they are simply different choices each with their own drawbacks. If you start from Pythagorean you have to teach people that C-E is not 5/4; if you start from Ptolemy on C you have to teach people that D-A is not 3/2 and D-F is not 6/5. Pythagorean has the drawback that all ratios of 5 must have accidentals; but Ptolemy has the (to me more serious) drawback of being inconsistent with the logical chain-of-fifths transposition structure that people already know.
>
> There's an additional thing to consider if you try to use the Johnston principle to notate temperaments and tempered tunings. For meantone temperament (or tunings such as 19-equal or 31-equal, where the comma is distributed equally over the chain of fifths) there's no need for the 5-comma symbol, since the 5-comma (80:81) vanishes, so there's no problem. But what about 72-equal? With the Johnston method, 2/3 of the tones in the 12-equal circle would get microtonal accidentals, whereas with Sagittal the nominals (plus sharps or flats) notates the circle of 12 fifths without any microtonal accidentals (and the next lower circle of 12 fifths is notated by adding the \! Symbol).
>
> Sure, Johnston notation was intended only for JI, but that's just my point. Why use a notation limited only to JI when you can have one that will do it all (and, for that matter, do it better!) in a consistent manner?
>
> Andrew, since the way you've described introducing the scale to your students sounds very much like adaptive JI, you may want to consider presenting the pitches as two circles of 12 fifths a comma apart (i.e., as a subset of 72-equal), using the 5-comma-down symbol to indicate the tones that need to be adjusted downward in pitch to get closer to pure thirds & sixths. Another advantage is that the \! alteration in 72-equal is only about 3/4 of what's required in strict JI.
>
> --George
>

How to teach microtonal music to students

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