Request for Lesson Plan in J.I.

Hi All,

I'm trying to find a lesson plan for teaching 7th & 8th graders the
basics of just intonation. Does anyone have something like that or
know where I might find it. I'm not a teacher and really don't know
where to start in writing one.

Thanks,

Robin

--- In tuning@yahoogroups.com, "Robin Perry" <jinto83@...> wrote:
> I'm trying to find a lesson plan for teaching 7th & 8th graders the
> basics of just intonation. Does anyone have something like that or
> know where I might find it. I'm not a teacher and really don't know
> where to start in writing one.

Well, a basic demonstration takes less than 30 minutes with a
harpsichord. Do this all directly in sound, and don't throw any
mathematical concepts at them until they have the sound firmly in their
ears.

Start from middle C. Tune a pure 4th 4:3 to the F above it, and a pure
5th 3:2 to the G. From the G tune a pure 4th to D and then from that D
a pure 5th up to A. From the A tune a pure 4th down to E and from E a
pure 5th up to B. Copy a C to C octave. Now you have the entire C
major scale, Pythagorean. Demonstrate that briefly.

Play some C, F, and G major triads, and the D minor and E minor triads.

Then, retune the E down so it's now a pure 5:4 from C, and remark (and
demonstrate) how much flatter this is than the other E we just had.
Demonstrate that the E-A is now rotten. Bring the A down so it's now
pure with both E and F...but now D-A is rotten. Bring the B down so
it's pure from both E and G. Now you have a just-intonation layout,
and since a break has to be present somewhere we've put it at D-A.

Replay the C, F, and G major triads, and the D minor and E minor
triads. Make some remarks about the differences.

(Even better, if you have a second set of strings available: leave the
first set in Pythagorean, and switch only the E/A/B of the second set
with these shifts of a comma downward. Then you can do quick and
direct comparisons, not only with the triads but also with comma-
shifted unisons.)

Then, demonstrate the two sizes of whole steps that are sitting there:
C-D is a 9:8, and D-E is a 10:9. Ask them if they can hear this
difference in size, melodically. Also demonstrate the F-B pure tritone.

As for sticking sharps and/or flats into the thing, it's merely a
matter of choosing what they're going to be pure to, and if that's done
by major 3rds, or by 4ths/5ths. Several possibilities present
themselves. All lead to various wolves....

If it's been going well so far, ask the students how they could get
around the D-A-E problem. Some bright student might suggest moving the
A a little bit, so it's only less bad from both of them. Play that,
with those two 1/2 comma intervals. Remark that we've just set up all
the naturals of Kirnberger's temperament....

Brad Lehman

Hi Robin;

Please make sure that you demonstrate beating, as you explain the integer frequency ratio theories;

and remember to point out the problems and limitations of JI as the basis of a practical musical tuning system.

Integer frequency ratios are the "intervals" that generate beating, yet not necessarily where the "musical harmonics" are to be found.

Try thinking beyond (2D) sinewaves;-)

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 15 Oct 2007, at 20:06, Robin Perry wrote:

> Hi All,
>
> I'm trying to find a lesson plan for teaching 7th & 8th graders the
> basics of just intonation. Does anyone have something like that or
> know where I might find it. I'm not a teacher and really don't know
> where to start in writing one.
>
> Thanks,
>
> Robin
>
>
>

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Robin Perry" <jinto83@> wrote:
> > I'm trying to find a lesson plan for teaching 7th & 8th graders the
> > basics of just intonation. Does anyone have something like that or
> > know where I might find it. I'm not a teacher and really don't know
> > where to start in writing one.
>
> Well, a basic demonstration takes less than 30 minutes with a
> harpsichord.

Personally, I wouldn't use a harpsi, too hard to hear unless you are
used to that sound. I'd use a synthesizer with some fairly bright,
stable sound, something in the direction of Werckmeister's
recommendation: a good, stable regal. A basic sawtooth will do,
thought a slightly filtered one softening the highs is better. I use a
wave extracted from me singing a low Bb with a bright "a" as in hay or
bay, which is the favorite vowel sound of Corsican singers for their
nonsense syllables tuned utterly breatakingly rock solid pure. I
sampled myself, gave it a nice attack and short decay, and it sounds
every bit the regal.

The advantage of a synthesizer is that you can move fast among
different sounds, comparing things like our "normal" fifths and thirds
with pure versions. Also, you can bump up or down the relative
strengths of the harmonics, making the beats more or less obvious.
Finally, you can sustain intervals and chords indefinitely until
everybody cops to the beating. The problem with larger classes is that
many students will simple be sitting in a position where there are
nodes or reflective cancellations of one or the other of the critical
frequencies making it almost impossible to hear beats. For those who
can't hear, have them move around in the room or even just turn their
heads slowly. Seek a position yourself where the beats are readily
heard, and have the students stand there.

> Do this all directly in sound, and don't throw any
> mathematical concepts at them until they have the sound firmly in their
> ears.

Agree completely, though it won't hurt to tell them about the
harmonics of a single tone and how it is coincident harmonics between
tones which define pure intervals. This of course leads straight to
ratios, which also can't hurt if you demonstrate that those numbers
actually mean something you can hear.
>
> Start from middle C. Tune a pure 4th 4:3 to the F above it, and a pure
> 5th 3:2 to the G. From the G tune a pure 4th to D and then from that D
> a pure 5th up to A. From the A tune a pure 4th down to E and from E a
> pure 5th up to B. Copy a C to C octave. Now you have the entire C
> major scale, Pythagorean. Demonstrate that briefly.

I wouldn't. It's an unnatural construct foisted on western music by a
radical sectarian leader who refused to open his ears and mind enough
to admit a pure third. Luckily, he was ignored by a vast majority of
musicians world-wide, mostly because they didn't know about him. I
always use Corsicans, Mongolians, Indian Classics, etc, as the
starting point. Uncorrupted minds and ears. Lots of easy to find audio
examples to blast open the ears of those who suffer from Acquired
Intonation Deficiency Syndrome from having heard nothing but ET their
whole life. Even lots of Country Western uses pure thirds with the
almost pure fifths of ET. Check out the "Old Timey" stuff, lots of
good raw purity to be had there.

I'd start with a pure major triad, showing how it contains a pure
fifth and both types of pure third. Then make two more of 'em on the
dominant and subdominant, the second and third most important chords
in trad harmony. You not only have a diatonic scale in one possible
Just tuning (there are others), but you also have the three triads
which make up the sum total harmonic content of about 90% of pop
music. Now show where the booby trap is (supertonic minor triad).

Personally, I think that about wraps it up. No need to get into
Pythagorean and all that rot unless you want to start talking about
the commas, which is more advanced than needs be for an intro for kids
that young. My experience is that that more informatin you throw at
them, the more their eyes cross, and they forget to listen. They just
(bad pun) need to know that (a) there is a natural way to tune triads
dictated by the physics of sound, (b) it is very easy to hear it, but
(c) we don't do it 'cause it creates some conflicts, especially when
we think that each note can have only one fixed identity, which is
pretty damn primitive but hey that's where we're at at the moment. We
were much smarter until about 1800 or so...

> Remark that we've just set up all
> the naturals of Kirnberger's temperament....

Which 7th and 8th grader is gonna know who the f___Kirnberger was, or
even care? I never mention him, not even in the advanced class for 2nd
year conservatory students (general acoustics). It's enough getting
them to wrap their heads around meantones, mod meantones, and
circulating temps in one session, which is all we have time for.
Kirnberger is a complete waste of time. For the kids in the tuning
class, I do mention him, but only after they have enough real
temperaments under their belts to realize what a load of bunk K'berger
was/is. After they've been setting Rameau Mod Mean, Werckmeister
Continuo, and a couple of Neidhardt's, they laugh at K'berger's
plethora of Pythagorean thirds and his clumsy two-bit division of the
S. comma. Kunst des Reinen Satzes my a__! What a load of Dingo's
Kidneys!!! But that's for the really advanced kids. For junior high
kids, keep it simple!

There's also some good Sacred Harp stuff to be found with pure triads,
but you have to search. Most of the stuff you can download is down by
modern social club choirs who don't know how to git down n raw when
raisin' yur voice in prayz untah the Lawd Awlmahtah (Hallelooyah
Bruther!) You need to find the old field recordings to get the rawl
thang! Worth the diggin'.

Ciao,

P

> > Remark that we've just set up all
> > the naturals of Kirnberger's temperament....
>
> Which 7th and 8th grader is gonna know who the f___Kirnberger was,
> or even care?

No, they're not going to care *who* Kirnberger was, or what he did.
The only reasons I brought up Kirnberger and his 1/2 comma division
of D-A-E:

- It's so easy, even an average 12-year-old could think it up: "Just
average them out, dude!" And then try it, hands on.

- It sounds grotesque, no matter who does it: a 12-year-old, or an
18th century theorist writing a whole book about it. It's not a
particularly good solution, musically, but it's *a* solution and easy
to deal with. Refinements can always come later.

- It illustrates, bluntly, that *something* must be done about that
comma to get rid of the wolf in those 5ths/4ths. And since this is
only an introduction, we wouldn't get too deeply beyond the
illustration that a blunt 1/2 comma division simply doesn't sound
very good.

- The 12-year-old gets to think of something creatively, first,
before being told that some 18th-century dude already discovered the
same thing and wrote a book about it. Children like to think up
creative solutions to problems, and then to hear that somebody
important was thinking the same way.

=====

My reasons to recommend harpsichord as the medium of the
demonstration?

- It demonstrates immediately the analog nature of tuning acoustical
instruments, sliding the pitch up or down smoothly until it's the
right spot. No digital twiddling of numbers on any dials anywhere,
or indeed expecting visible numbers to play any role in tuning, ears-
on.

- The tone is clear. Yes, I'd have them crowd around so they're near
enough to hear beats, and the beats vanishing when things are locking
into tune. A decent harpsichord has plenty of clear and bright
overtones.

- It's right there to see (the tuning lever in a circular motion on
the tuning pin) and hear (a nifty piece of ancient technology
going "ping").

- It demonstrates a day-to-day problem that real 18th century
musicians had to deal with: knowing how to keep their instrument in
tune regularly, and therefore developing a practical listening
skill. Not expecting some other dude, like a paid piano tuner, to
have the sole responsibility for the listening or the adjustments.

Brad Lehman

Near the bottom of this page is a very simplistic explanation and table of how 4 fifths + one third in JI (could/should/don't;-) equal an octave.

I hope this helps you

http://www.lucytune.com/tuning/just_intonation.html

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 16 Oct 2007, at 02:29, Brad Lehman wrote:

> > > Remark that we've just set up all
> > > the naturals of Kirnberger's temperament....
> >
> > Which 7th and 8th grader is gonna know who the f___Kirnberger was,
> > or even care?
>
> No, they're not going to care *who* Kirnberger was, or what he did.
> The only reasons I brought up Kirnberger and his 1/2 comma division
> of D-A-E:
>
> - It's so easy, even an average 12-year-old could think it up: "Just
> average them out, dude!" And then try it, hands on.
>
> - It sounds grotesque, no matter who does it: a 12-year-old, or an
> 18th century theorist writing a whole book about it. It's not a
> particularly good solution, musically, but it's *a* solution and easy
> to deal with. Refinements can always come later.
>
> - It illustrates, bluntly, that *something* must be done about that
> comma to get rid of the wolf in those 5ths/4ths. And since this is
> only an introduction, we wouldn't get too deeply beyond the
> illustration that a blunt 1/2 comma division simply doesn't sound
> very good.
>
> - The 12-year-old gets to think of something creatively, first,
> before being told that some 18th-century dude already discovered the
> same thing and wrote a book about it. Children like to think up
> creative solutions to problems, and then to hear that somebody
> important was thinking the same way.
>
> =====
>
> My reasons to recommend harpsichord as the medium of the
> demonstration?
>
> - It demonstrates immediately the analog nature of tuning acoustical
> instruments, sliding the pitch up or down smoothly until it's the
> right spot. No digital twiddling of numbers on any dials anywhere,
> or indeed expecting visible numbers to play any role in tuning, ears-
> on.
>
> - The tone is clear. Yes, I'd have them crowd around so they're near
> enough to hear beats, and the beats vanishing when things are locking
> into tune. A decent harpsichord has plenty of clear and bright
> overtones.
>
> - It's right there to see (the tuning lever in a circular motion on
> the tuning pin) and hear (a nifty piece of ancient technology
> going "ping").
>
> - It demonstrates a day-to-day problem that real 18th century
> musicians had to deal with: knowing how to keep their instrument in
> tune regularly, and therefore developing a practical listening
> skill. Not expecting some other dude, like a paid piano tuner, to
> have the sole responsibility for the listening or the adjustments.
>
> Brad Lehman
>
>
>

Robin Perry wrote:
> Hi All,
> > I'm trying to find a lesson plan for teaching 7th & 8th graders the > basics of just intonation. Does anyone have something like that or > know where I might find it. I'm not a teacher and really don't know > where to start in writing one.

I think I can decode "7th & 8th graders" as meaning 12 to 14 year olds. But there are other things you need to specify (or think about):

- How many students?

- How long is the lesson?

- Are they music specialists?

- Why are you doing it?

- What resources do you have?

- What do you want them to remember?

I'll suggest answers to the last question as: just intervals sound clean, you need to change the way you write music to use them properly, there are also strange JI intervals. The suggestions so far have been biased towards 5-limit traditional harmony. Perhaps you'd rather open their ears to modern microtonal music. It's really up to you.

Another question is whether you should focus on the mathematics. So far people have said "no". But tuning theory can be an interesting way of teaching an application of arithmetic with fractions. At that age they should know how to do it, and it'll be fresh in their minds, but I doubt they'll know it so well that it'll be trivial. So maybe that could be the focus of the lesson. If not, and especially for a short lesson, it's something you should avoid completely.

It's good for them to have something to listen to. That's why you have to know what the resources are. If it's a long lesson you could try getting some students to sing in JI. There are bound to be a few students in a choir of some kind so they'll have some experience of singing. As well as being fun and interesting, this will give them a chance to relax as their attention wanders mid-lesson.

Don't expect a ready-made lesson plan anyway. It'll never fit your exact circumstances. And play to your strengths! If you're a guest to the school (as seems likely) they'll be interested in what *you* do with it. Don't be afraid to talk about yourself.

Graham

Wow! It seems this topic struck a chord with a few people. Thank you
all for your suggestions. If I wind up having to write this myself,
I'll certainly incorporate your ideas on how to go about it. I'm
keeping all of your replies in a folder.

I am still looking for a ready made plan to use, however. I know there
must be an elementary school math or music teacher on this list???
Please!!!!

Thanks again,

Robin

--- In tuning@yahoogroups.com, "Robin Perry" <jinto83@...> wrote:
>
> Hi All,
>
> I'm trying to find a lesson plan for teaching 7th & 8th graders the
> basics of just intonation. Does anyone have something like that or
> know where I might find it. I'm not a teacher and really don't know
> where to start in writing one.
>
> Thanks,
>
> Robin
>

Might I suggest using a comparative monochord in class? Neither a harpsichord (due to gauge differences and built-in string-length differences) nor a synthesizer is going to have the immediate visual element of a monochord -- in which frequency ratios also correspond to string length ratios. Ideally, each student should have her own instrument, and one that she has built herself, but this is a matter of time and resources. (Lloyd Rodgers, Professor of Music at CSU Fullerton, now starts his theory classes with a trip to the hardware store to get materials for building monochords!).

For the classroom purposes, the monochord need be nothing other than a strip of wood, ca 120x10 cm long. (Resting on a table or desk top, it can "borrow" the resonance of the furniture for amplification). You need two tuning pins (get from a local piano tuner along with a tuning hammer) turned into holes drilled in one end and two small nails on the other end to anchor the wires. Two small pieces of moulding with a sharp edge can serve as bridges and should be set one meter apart. A meter measuring tape (Ikea gives them out for free) can be mounted for easy measurement of string lengths. Finally, Bill Colvig had a very practical idea for an accurate moveable bridge -- a pair of tweezers, mounted on a block of wood so that the string can be stopped without pushing it downward and adding to the tension.

A typical lesson plan would include:

(1) tuning the strings to a unison

First consider simple ratios between an open string and a second, stopped string:

(2) locating the harmonic nodes of the strings and noting the proportions and musical intervals.

(3) locating the arithmetic divisions of the string and noting the proportions and musical intervals.

(4) When the strings are tuned low enough, simple ratios of the string vibrations should be visually observable, perhaps when translated into shadows projected on a wall.

(5) Ask the students: What is relationship between string length ratios and frequency ratios?

Then move on to compound intervals:

(6) Locate the octave of an octave and the octave of a fifth. What operations on string lengths and frequency ratios are being carried out?

(7) Locate the fifth of a fifth, and then the tone one octave lower. Again, describe this operation in terms of string lengths and ratios.

(8) Use this process to determine the notes of a familiar scale, marking the tones on the paper strip.

(9) Use the scale to play some simple tunes, perhaps with a pen or a glass as a slide.

******

For seventh or eighth graders, I would not even mention the word temperament. There is already a very rich set of information above, touching on maths (operations on fractions) and physics as well as music, capable of extension in each of the subject areas, and the issues involved in temperament really require a substantially larger bit of music theory and are, in practice, both contentious and culturally specific.

Daniel Wolf
Frnakfurt

Hi Robin,

--- In tuning@yahoogroups.com, "Robin Perry" <jinto83@...> wrote:
>
> Wow! It seems this topic struck a chord with a few
> people. Thank you all for your suggestions. If I wind
> up having to write this myself, I'll certainly incorporate
> your ideas on how to go about it. I'm keeping all of your
> replies in a folder.
>
> I am still looking for a ready made plan to use, however.
> I know there must be an elementary school math or music
> teacher on this list???
> Please!!!!

I have a lot of students taking individual piano lessons
who fall into this age range, and i always try my damnedest
to teach them as much as i can about tuning.

My experience is that most of the kids really like
learning about the physics and math, and i emphasize
that learning it from me will make those subjects easier
for them in school later. I've had many students who
tell me a couple of years down the road that their
teacher in school just taught something which they
already learned from me.

My approach is to ask the kids as many questions as
i can and make them think up the answers.

The beginning is to have them understand that sound
is produced by vibrations. Most kids this age know
that we have eardrums in our ears, and they know
how drums work, so it's easy enough to explain that
the source of the vibration causes the air to vibrate
in a wave pattern, which in turn causes the eardrums
to vibrate to the same pattern. I don't get into the
physiology beyond that, i simply say that the nerves
send that signal to the brain and the brain figures
out everything from that point.

With a piano, it's fairly easy to start out by having
them look at the keyboard, observe the repeating
patterns of the black keys, and then ask them why
the patterns repeat. After playing enough notes an
octave apart, the kids will come around to making the
link between the identical appearance and the
nearly-identical sound. It usually takes awhile,
because the kids aren't thinking about pitch-classes
right off the bat like we trained musicians, and it's
obvious to them that notes an octave apart are two
different notes, because one is quite a bit higher
than the other. But by making them listen to it enough
times, and compare the octave to the other intervals,
they eventually get it.

Then i explain frequency and wavelength, and the 2/1
ratio, and that the reason why those notes sound so
similar is because those are the two smallest numbers
that can be compared, so they're the closest relationship.

Then continue similarly for 3/2, 4/3, 5/4, etc.

Once i get them used to how the ratios relate to what
they hear, then i play a low note on the piano and
have them listen very carefully until they can hear
the overtones, usually helping out by also playing the
higher notes which come close to overtones while
holding down the low note. This leads to an explanation
of the harmonic series.

I'm always careful to explain that the overtones are
slightly different in pitch from what the piano keys
are tuned to. This becomes very easy if the piano has
a note which produces a clear 7th or 11th harmonic,
because the difference between the harmonic and the
piano key is readily heard.

From there, it's a fairly simple matter to explain
how a whole tuning system can be built out of notes
like that, hence, JI.

For some students, i've even been able to go thru the
whole process of building a 12-tone scale out of 4ths
and 5ths, and then explaining how the piano closes the
cycle, but how the slight difference in the JI pitches
results in the pythagorean-comma. This requires an
explanation of cents, which is fairly easy to grasp.

First i tell them that the pythagorean-comma is
about 1/4 of a semitone (i.e., 25 cents) because that's
something that they can relate to the piano a little
easier. Then i get a little more accurate and explain
that it's closer to 24 cents.

They usually get pretty confused intially by the
explanation of the comma, but when i explain the
process of tempering each 4th or 5th by 2 cents,
they can see that by the time the 13th note in the
cycle is reached, the previous 12 notes have eliminated
that 24 cents, so the 13th note is the same as the first.

If they're interested in it beyond that point, it's
time to get Tonescape downloaded and running on their
computer! ;-)

-monz
http://tonalsoft.com
Tonescape microtonal music software

I thought one of the points of JI was to go beyond 12 pitches in the
octave. That is its natural habitat. So it doesn't make all that much
sense to use a 12-note-per-octave keyboard instrument as your main
resource - unless you are willing to use strongly nonstandard tunings,
for example setting the D key to 10/9 and the Eb to 9/8. Then you have
the ingredients for 'My country tis of thee' or 'God save the Queen'
in JI.

Practically, if one has a good, loud harpsichord with a sustained,
harmonic-rich tone, it could work. Expecting 30 children to cluster
round anything is a bit impractical though. With a mediocre or
short-toned harpsichord, which alas is rather more likely, it is not
worth even starting.

Basically keyboard music and keyboard tunings are a misleading
distraction from the subject. (Perhaps that's a reason why there is no
standard JI lesson plan for the standard piano-bashing music teacher!)
The best one could do in this direction would be an old harmonium or
reed-organ (19th century descendent of the regal) where you can adjust
the reeds in real time.

But really: it *strongly* depends on what resources you have at hand.

In the absence of resources, building three- or four-string monochords
is a good start - assuming that you can get them to function.

~~~T~~~

In addition to the harpsichord presentations I've already mentioned,
I did a JI demonstration once in a public lecture using a $20 "Lap
Harp" from Wal-Mart. The thing is a trapezoid with two octaves of
strings, having the diatonic scale only. It's played with either a
guitar pick (included) or fingers. I set it up with a just scale,
and it was nice not only to strum the entire scale at once for its
ringing effect, but also to play major/minor triads and some 7th
chords. The major-major 7th chord of C-E-G-B sounds spectacular, and
with the D 9th added as well...even on a lousy little $20 instrument.

C 0, D 0, E -1, F 0, G 0, A -1, B -1.

One could buy two of these and have them tuned differently from one
another, for some comma-shifted unisons. Or have the second
instrument supply some sharps or flats against the first one.

Most of the time I leave this "Lap Harp" in regular 1/6 comma, which
also makes it sound like a much more than $20 instrument.

Brad Lehman

My sincerest thanks, once again, everyone! I will reply to each of
you eventually. My time for pursuing this development is very
limited right now, so please have patience. I do appreciate the
suggestions very much.

Regards,

Robin

--- In tuning@yahoogroups.com, "Robin Perry" <jinto83@...> wrote:
>
> Wow! It seems this topic struck a chord with a few people. Thank
you
> all for your suggestions. If I wind up having to write this
myself,
> I'll certainly incorporate your ideas on how to go about it. I'm
> keeping all of your replies in a folder.
>
> I am still looking for a ready made plan to use, however. I know
there
> must be an elementary school math or music teacher on this list???
> Please!!!!
>
> Thanks again,
>
> Robin
>
>
>
>
>
> --- In tuning@yahoogroups.com, "Robin Perry" <jinto83@> wrote:
> >
> > Hi All,
> >
> > I'm trying to find a lesson plan for teaching 7th & 8th graders
the
> > basics of just intonation. Does anyone have something like that
or
> > know where I might find it. I'm not a teacher and really don't
know
> > where to start in writing one.
> >
> > Thanks,
> >
> > Robin
> >
>

Hi Joe,

I've tried to send you a personal note off-list but it seems to be
getting bounced by your ISP. Anyone else having that problem?

All the best,

Robin

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Robin,
>
>
> --- In tuning@yahoogroups.com, "Robin Perry" <jinto83@> wrote:
> >
> > Wow! It seems this topic struck a chord with a few
> > people. Thank you all for your suggestions. If I wind
> > up having to write this myself, I'll certainly incorporate
> > your ideas on how to go about it. I'm keeping all of your
> > replies in a folder.
> >
> > I am still looking for a ready made plan to use, however.
> > I know there must be an elementary school math or music
> > teacher on this list???
> > Please!!!!
>
>
> I have a lot of students taking individual piano lessons
> who fall into this age range, and i always try my damnedest
> to teach them as much as i can about tuning.
>
> My experience is that most of the kids really like
> learning about the physics and math, and i emphasize
> that learning it from me will make those subjects easier
> for them in school later. I've had many students who
> tell me a couple of years down the road that their
> teacher in school just taught something which they
> already learned from me.
>
> My approach is to ask the kids as many questions as
> i can and make them think up the answers.
>
>
> The beginning is to have them understand that sound
> is produced by vibrations. Most kids this age know
> that we have eardrums in our ears, and they know
> how drums work, so it's easy enough to explain that
> the source of the vibration causes the air to vibrate
> in a wave pattern, which in turn causes the eardrums
> to vibrate to the same pattern. I don't get into the
> physiology beyond that, i simply say that the nerves
> send that signal to the brain and the brain figures
> out everything from that point.
>
> With a piano, it's fairly easy to start out by having
> them look at the keyboard, observe the repeating
> patterns of the black keys, and then ask them why
> the patterns repeat. After playing enough notes an
> octave apart, the kids will come around to making the
> link between the identical appearance and the
> nearly-identical sound. It usually takes awhile,
> because the kids aren't thinking about pitch-classes
> right off the bat like we trained musicians, and it's
> obvious to them that notes an octave apart are two
> different notes, because one is quite a bit higher
> than the other. But by making them listen to it enough
> times, and compare the octave to the other intervals,
> they eventually get it.
>
> Then i explain frequency and wavelength, and the 2/1
> ratio, and that the reason why those notes sound so
> similar is because those are the two smallest numbers
> that can be compared, so they're the closest relationship.
>
> Then continue similarly for 3/2, 4/3, 5/4, etc.
>
> Once i get them used to how the ratios relate to what
> they hear, then i play a low note on the piano and
> have them listen very carefully until they can hear
> the overtones, usually helping out by also playing the
> higher notes which come close to overtones while
> holding down the low note. This leads to an explanation
> of the harmonic series.
>
> I'm always careful to explain that the overtones are
> slightly different in pitch from what the piano keys
> are tuned to. This becomes very easy if the piano has
> a note which produces a clear 7th or 11th harmonic,
> because the difference between the harmonic and the
> piano key is readily heard.
>
> From there, it's a fairly simple matter to explain
> how a whole tuning system can be built out of notes
> like that, hence, JI.
>
>
> For some students, i've even been able to go thru the
> whole process of building a 12-tone scale out of 4ths
> and 5ths, and then explaining how the piano closes the
> cycle, but how the slight difference in the JI pitches
> results in the pythagorean-comma. This requires an
> explanation of cents, which is fairly easy to grasp.
>
> First i tell them that the pythagorean-comma is
> about 1/4 of a semitone (i.e., 25 cents) because that's
> something that they can relate to the piano a little
> easier. Then i get a little more accurate and explain
> that it's closer to 24 cents.
>
> They usually get pretty confused intially by the
> explanation of the comma, but when i explain the
> process of tempering each 4th or 5th by 2 cents,
> they can see that by the time the 13th note in the
> cycle is reached, the previous 12 notes have eliminated
> that 24 cents, so the 13th note is the same as the first.
>
> If they're interested in it beyond that point, it's
> time to get Tonescape downloaded and running on their
> computer! ;-)
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

Yep. I've been trying to email Monz for weeks. 5 days wait then bounce.

At 06:34 PM 18/10/2007, you wrote:
>Hi Joe,
>
>I've tried to send you a personal note off-list but it seems to be
>getting bounced by your ISP. Anyone else having that problem?
>
>All the best,
>
>Robin

Hi Robin and Dave,

--- In tuning@yahoogroups.com, "Robin Perry" <jinto83@...> wrote:
>
> Hi Joe,
>
> I've tried to send you a personal note off-list
> but it seems to be getting bounced by your ISP.
> Anyone else having that problem?

I mentioned here just about a week ago: we had to
kill all of the tonalsoft.com email addresses because
they were all getting so inundated with spam that
it was messing up our server.

It really sucks, because i had intended my tonalsoft
address to permanently be the one that i use for
correspondence concerning music and tuning.

Fucking spammers really piss me off.

Use either one of these from now on:

joemonz(AT)yahoo.com

monz(AT)juno.com

-monz
http://tonalsoft.com
Tonescape microtonal music software

Ahh.. ok... thanks... sorry to hear about the artery clogging..

Robin

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Robin and Dave,
>
>
> --- In tuning@yahoogroups.com, "Robin Perry" <jinto83@> wrote:
> >
> > Hi Joe,
> >
> > I've tried to send you a personal note off-list
> > but it seems to be getting bounced by your ISP.
> > Anyone else having that problem?
>
>
> I mentioned here just about a week ago: we had to
> kill all of the tonalsoft.com email addresses because
> they were all getting so inundated with spam that
> it was messing up our server.
>
> It really sucks, because i had intended my tonalsoft
> address to permanently be the one that i use for
> correspondence concerning music and tuning.
>
> Fucking spammers really piss me off.
>
>
> Use either one of these from now on:
>
> joemonz(AT)yahoo.com
>
> monz(AT)juno.com
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> Hi Robin and Dave,
>
> --- In tuning@yahoogroups.com, "Robin Perry" <jinto83@> wrote:
> > Hi Joe,
> >
> > I've tried to send you a personal note off-list
> > but it seems to be getting bounced by your ISP.
> > Anyone else having that problem?
>
> I mentioned here just about a week ago: we had to
> kill all of the tonalsoft.com email addresses because
> they were all getting so inundated with spam that
> it was messing up our server.

It shouldn't do. Have you tried

http://bogofilter.sourceforge.net

?

-Carl