Limitations of 72-tET

Joe, no one else has answered this (that I've seen): there _are_ in fact
only 128 pitches defined in MIDI (numbered 0 .. 127). But I would
recommend, as others have, that you go some other way than mapping
each MIDI note to a scale degree in 72-tET.

Ideally, you need a piece of software between your keyboard and the
module (internal or external) that produces the sound. You would
instruct the software in real-time (foot pedals? many means are
possible) what subset of 72-tET will be active at a given moment. It
apportions the target notes out to different channels, each tuned 17
cents from the others, as already described by others.

But let me ask you, Joe: are you satisfied with the limitations imposed
by 72-tET? I speak not of poorly tuned intervals (the ones I regularly
use are tuned quite well, IMO), but of the inability to distribute out
comma drift. Does your music not make use of C-A-D-G-C progressions?
Does it not matter if the music drifts? Or are you willing to correct
the drift in one sudden motion of a 72-tET microtone? To me, none of
these answers is satisfactory, but my view is heavily connected to the
kind of music I like and/or compose. Just curious...

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

/tuning/topicId_21686.html#21686

> Joe, no one else has answered this (that I've seen): there _are_ in
factonly 128 pitches defined in MIDI (numbered 0 .. 127). But I would
> recommend, as others have, that you go some other way than mapping
> each MIDI note to a scale degree in 72-tET.
>

Thanks, John... I believe that was the number I cited in my post as
well... So that really is "gobbled up" by 72-tET in a hurry... One
wouldn't want to use it that way, I agree...

> Ideally, you need a piece of software between your keyboard and the
> module (internal or external) that produces the sound. You would
> instruct the software in real-time (foot pedals? many means are
> possible) what subset of 72-tET will be active at a given moment.
It apportions the target notes out to different channels, each tuned
17 cents from the others, as already described by others.
>

I suppose if some foot pedal could provide the 6 "inflections" of 72-
tET from 12-tET, it could be quite useful. However, that could still
be quite "messy" if I wanted to "play" certain things into a
sequencer... and all the pitches would most probably have to have the
SAME inflections simultaneously... not such a good idea.

Of course, I can ENTER pitch bends into a "regular" 12-tET score...
which is something like what YOU do, I believe... but that also would
not be an effective "real time" process...and it would be much better
to have it done somehow "automatically" as YOU do...

> But let me ask you, Joe: are you satisfied with the limitations
imposed by 72-tET? I speak not of poorly tuned intervals (the ones I
regularly use are tuned quite well, IMO), but of the inability to
distribute out comma drift. Does your music not make use of C-A-D-G-
C progressions?

Not specifically... at least I HOPE not! :)

> Does it not matter if the music drifts? Or are you willing to
correct the drift in one sudden motion of a 72-tET microtone?

Well, perhaps I should be embarassed to state this... (but it works
well for me...) I compose almost entirely "by ear..."

So, I would be able to USE or CORRECT drift only in the context of
the particular place in a piece where it was occuring...

The CONTEXT would determine everything... NOT any systematic
foreplay...

_______ ___ _____ ____
Joseph Pehrson

[I wrote:]
>>Joe, no one else has answered this (that I've seen): there _are_ in
>>fact only 128 pitches defined in MIDI (numbered 0 .. 127). But I
>>would recommend, as others have, that you go some other way than
>>mapping each MIDI note to a scale degree in 72-tET.

[Joseph Pehrson:]
>Thanks, John... I believe that was the number I cited in my post as
>well... So that really is "gobbled up" by 72-tET in a hurry... One
>wouldn't want to use it that way, I agree...

Yes, you did surmise the correct number. The high bit in each byte is
reserved for "status" bytes, and so you get only 2^7 = 128.

[JdL:]
>>Ideally, you need a piece of software between your keyboard and the
>>module (internal or external) that produces the sound. You would
>>instruct the software in real-time (foot pedals? many means are
>>possible) what subset of 72-tET will be active at a given moment.
>>It apportions the target notes out to different channels, each tuned
>>17 cents from the others, as already described by others.

[Joe:]
>I suppose if some foot pedal could provide the 6 "inflections" of 72-
>tET from 12-tET, it could be quite useful. However, that could still
>be quite "messy" if I wanted to "play" certain things into a
>sequencer... and all the pitches would most probably have to have the
>SAME inflections simultaneously... not such a good idea.

Not what I'm thinking of at all! Consider a number of useful presets,
starting with a very basic just C major scale, with E, A, and B each one
notch below 12-tET. See what I mean?

[Joe:]
>Of course, I can ENTER pitch bends into a "regular" 12-tET score...
>which is something like what YOU do, I believe... but that also would
>not be an effective "real time" process...and it would be much better
>to have it done somehow "automatically" as YOU do...

Or under the control of the performer.

[JdL:]
>>But let me ask you, Joe: are you satisfied with the limitations
>>imposed by 72-tET? I speak not of poorly tuned intervals (the ones I
>>regularly use are tuned quite well, IMO), but of the inability to
>>distribute out comma drift. Does your music not make use of C-A-D-G-
>>C progressions?

[Joe:]
>Not specifically... at least I HOPE not! :)

Never?

[JdL:]
>>Does it not matter if the music drifts? Or are you willing to
>>correct the drift in one sudden motion of a 72-tET microtone?

[Joe:]
>Well, perhaps I should be embarassed to state this... (but it works
>well for me...) I compose almost entirely "by ear..."

Nothing wrong with that; quite the contrary, but are you aware of the
strait-jacket that 72-tET enforces?

[Joe:]
>So, I would be able to USE or CORRECT drift only in the context of
>the particular place in a piece where it was occuring...

In 72-tET, you can only correct by a full 17 cents at a time.

[Joe:]
>The CONTEXT would determine everything... NOT any systematic
>foreplay...

Well, that's my point. In most contexts, the ideal would seem to be
to let each successive note (and/or interval, as necessary) absorb a
small amount of the comma. The beauty of +/- cents notation is that
this is very easy to communicate. A more restrictive notation like
72-tET is unaccommodating in this regard, do you not think?

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

/tuning/topicId_21686.html#21688
>

>
> [Joe:]
> >I suppose if some foot pedal could provide the 6 "inflections" of
72- tET from 12-tET, it could be quite useful. However, that could
still be quite "messy" if I wanted to "play" certain things into a
> >sequencer... and all the pitches would most probably have to have
the SAME inflections simultaneously... not such a good idea.
>
> Not what I'm thinking of at all! Consider a number of useful
presets, starting with a very basic just C major scale, with E, A,
and B each one notch below 12-tET. See what I mean?
>

I see, John.... but it would be a somewhat "prescriptive" set up,
no?? In other words, a fair amount of the possible developing ideas
of the composition would ALREADY be determined by the set selection,
yes?? So, it would not be as "free" as it would sound if you had the
full 72-tET spectrum... Certainly, it wouldn't sound as "free" as
Joe Maneri and his beautiful women sound when they perform...

[They sound *VERY* free to me...)

> [JdL:]
> >>But let me ask you, Joe: are you satisfied with the limitations
> >>imposed by 72-tET? I speak not of poorly tuned intervals (the
ones I regularly use are tuned quite well, IMO), but of the inability
to distribute out comma drift. Does your music not make use of C-A-D-
G- C progressions?
>
> [Joe:]
> >Not specifically... at least I HOPE not! :)
>
> Never?
>

Well, possibly, John if there is something ELSE going on at the same
time in a "polytonal" context... Isn't it kind of difficult to
write "new, modern" music with a "naked" I-vi-ii-V-I (??!)

[Joe:]
> >Well, perhaps I should be embarassed to state this... (but it
works well for me...) I compose almost entirely "by ear..."
>

> Nothing wrong with that; quite the contrary, but are you aware of
the strait-jacket that 72-tET enforces?

Thanks for pointing this out to me... but what do the
other "advocates" of 72-tET on this list think of the "strait-jacket"
of 72-tET. I would be interested in further commentary...

Thanks!!!
________ _____ ____ __
Joseph Pehrson

[I wrote:]
>>Consider a number of useful presets, starting with a very basic just
>>C major scale, with E, A, and B each one notch below 12-tET. See what
>>I mean?

[Joseph Pehrson:]
>I see, John.... but it would be a somewhat "prescriptive" set up,
>no?? In other words, a fair amount of the possible developing ideas
>of the composition would ALREADY be determined by the set selection,
>yes?? So, it would not be as "free" as it would sound if you had the
>full 72-tET spectrum... Certainly, it wouldn't sound as "free" as
>Joe Maneri and his beautiful women sound when they perform...

>[They sound *VERY* free to me...)

Quite true. If you wanted, for example, the freedom to do microtonal
glissandos, it'd be tough (well, they could be preset, but...).

[Joe:]
>Well, possibly, John if there is something ELSE going on at the same
>time in a "polytonal" context... Isn't it kind of difficult to
>write "new, modern" music with a "naked" I-vi-ii-V-I (??!)

Well, perhaps you'll have no comma problems at all, and 72-tET will be
close to perfect.

JdL

--- In tuning@y..., jpehrson@r... wrote:
>
>
> Thanks for pointing this out to me... but what do the
> other "advocates" of 72-tET on this list think of the "strait-
jacket"
> of 72-tET. I would be interested in further commentary...
>
> Thanks!!!

I agree completely with John deLaubenfels that 72-tET is not a
suitable way to play DIATONIC music with better harmonies than 12-
tET. But this is exactly the same situation we have in strict JI.
It's that annoying comma problem.

As we went over this situation over and over again, Joseph, but you
still wanted to go with strict JI, it didn't seem that bringing it up
again in the context of 72-tET was going to be very fruitful.

We should let John deLaubenfels know that your music (that I've
heard) has absolutely nothing to do (as far as I can tell) with
common-practice Western tonal diatonic harmony . . . but it's still
important to know which commas will vanish and which won't in any
particular tuning. In 72-tET, the 81:80 won't vanish, but the 224:225
will . . . making possible some other (more bizarre, non-
diatonic) "pump" progressions that would drift in JI.

Actually, I think you'll find a lot of 72-tET subsets in the
archives . . . look for Dave Keenan's messages from a couple of years
ago (?) . . .

--- In tuning@y..., PERLICH@A... wrote:

/tuning/topicId_21686.html#21694

> I agree completely with John deLaubenfels that 72-tET is not a
> suitable way to play DIATONIC music with better harmonies than 12-
> tET. But this is exactly the same situation we have in strict JI.
> It's that annoying comma problem.
>
> As we went over this situation over and over again, Joseph, but you
> still wanted to go with strict JI, it didn't seem that bringing it
up again in the context of 72-tET was going to be very fruitful.
>

Gee... I feel I'm "improving." It only took THREE "overs" this
time... generally I go for at least four...

> We should let John deLaubenfels know that your music (that I've
> heard) has absolutely nothing to do (as far as I can tell) with
> common-practice Western tonal diatonic harmony . . . but it's still
> important to know which commas will vanish and which won't in any
> particular tuning. In 72-tET, the 81:80 won't vanish, but the
224:225 will . . . making possible some other (more bizarre, non-
> diatonic) "pump" progressions that would drift in JI.
>

Well, of course there are some times that I might actually want to
USE a comma... Look at that great recent piece by David Beardsley...
I forget the name of it... that used a great "comma pump" in the
melodic line...

Of course, I was rather doubting that this was really a "comma"... it
seemed like too many cents difference for that!

> Actually, I think you'll find a lot of 72-tET subsets in the
> archives . . . look for Dave Keenan's messages from a couple of
years ago (?) . . .

OK... I'll look into this. Seems like everybody with a real "tuning
head" has been well over 72.... good sign I'm on the right track...

_________ ______ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> Well, of course there are some times that I might actually want to
> USE a comma... Look at that great recent piece by David
Beardsley...
> I forget the name of it... that used a great "comma pump" in the
> melodic line...

That wasn't a comma pump at all . . . it was just a comma or small
interval, used melodically. A comma pump is a progression around a
series of chords that results in a net pitch drift in JI but not in
some temperament.

--- In tuning@y..., jpehrson@r... wrote:
>
> Well, of course there are some times that I might actually want to
> USE a comma... Look at that great recent piece by David
Beardsley...
> I forget the name of it... that used a great "comma []" in the
> melodic line...

That's a good sign you might like 72-tET. In 72-tET all sorts of
commas come out to 1 step (1/6 of a semitone, or 1/12 tone).

For example, if you hold down the note C as a drone, and play a
melody which forms the following consonant intervals above C:

12/11
11/10
10/9
9/8
8/7

you'll be moving by the following steps:

JI 72-tET
121:120 1
100:99 1
81:80 1
64:63 2

Just because the first three steps are equal increments in 72-tET
doesn't mean the sound will be completely different in 72-tET than in
JI. Each of the consonant intervals formed with C will be quite
recognizable in 72-tET if you already know what they sound like in
JI, all of them being less than 4 cents off. And in a live
performance by string or wind players, the harmonic intervals are
likely to be adjusted anyway.

So lots of Beardsley-style comma-movements will be possible in 72-tET.

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_21686.html#21709

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Well, of course there are some times that I might actually want
to
> > USE a comma... Look at that great recent piece by David
> Beardsley...
> > I forget the name of it... that used a great "comma pump" in the
> > melodic line...
>
> That wasn't a comma pump at all . . . it was just a comma or small
> interval, used melodically. A comma pump is a progression around a
> series of chords that results in a net pitch drift in JI but not in
> some temperament.

So, you're saying that *technically* a _comma pump_ ALWAYS has to
refer back to the original beginning chord...

So, actually you can never have a "pump" if you never hear the
beginning chord again??

_______ _____ _ _____
Joseph Pehrson

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_21686.html#21710

> Just because the first three steps are equal increments in 72-tET
> doesn't mean the sound will be completely different in 72-tET than
in JI. Each of the consonant intervals formed with C will be quite
> recognizable in 72-tET if you already know what they sound like in
> JI, all of them being less than 4 cents off. And in a live
> performance by string or wind players, the harmonic intervals are
> likely to be adjusted anyway.

This is excellent... and it is true that I am now getting excited
about composing in 72-tET.

I figure one octave on a standard Halberstadt could possibly be about
3.5 feet long... I figure I would need a standard 7 octaves, so my
keyboard should, most probably, be 24.5 feet long...

I'm hoping it will *fold* so I can take it to the gig...

________ ______ ___ _
Joseph Pehrson

Hi Joseph,

Just to mention, you can go over the 128 Midi note limit by using
multiple midi In channels.

That gives up to 15*12 = 180 notes per octave.

So, would be perfectly possible to design a midi keyboard with up to
that many notes per octave, totally standard in all other ways, supporting
pedals, pitch bend wheels, modulation wheels, etc etc, and
send it through either software or hardware capable of retuning
according to the midi in channel as well as the note number.

Actually, I plan at some point in future to add option to FTS to
tune according to midi in channnel.

Would be very useful for 24 note two keyboard scales. (Of course
will need to get a second keyboard to try it out).

With 72 notes per octave, perhaps one needs a purpose made keyboard,
but if one happens to have 6 midi keyboards around, in a music
department or something, one could stack them on top of each other
like an organ, and see what happens.

The shallower the depth of the case for the keyboard the better
of course - with six keyboards of normal depth, one would perhaps require
about the maximum span of the hand just to get from the bottom
keyboard to the top one.

Robert

Of course, it's max of

16*12 = 192 notes per octave

for multiple midi in channel keyboards.

Sorry - used to subtracting 1 for the non melodic perc. chann.
for calculations involving midi out channels.

Robert

--- In tuning@y..., jpehrson@r... wrote:

>
> So, you're saying that *technically* a _comma pump_ ALWAYS has to
> refer back to the original beginning chord...
>
> So, actually you can never have a "pump" if you never hear the
> beginning chord again??
>
I guess what makes it a "pump" is that it's a chord progression that goes around and around,
over and over, and the pitch level changes my a small, fixed amound each time you get back to
the first chord . . .

--- In tuning@y..., "Robert Walker" <robert_walker@r...> wrote:

/tuning/topicId_21686.html#21759

> Hi Joseph,
>
> Just to mention, you can go over the 128 Midi note limit by using
> multiple midi In channels.
>
> That gives up to 15*12 = 180 notes per octave.

Thanks so much, Robert... That would, of course, help a little bit.

[combining keyboards for 72-tET]

> The shallower the depth of the case for the keyboard the better
> of course - with six keyboards of normal depth, one would perhaps
require about the maximum span of the hand just to get from the bottom
> keyboard to the top one.
>

Yes... I am wondering how close together Rick Tagawa's are...

________ ______ _____
Joseph Pehrson

From the top of top keyboard to the top of the bottom keyboard it is 24". The average distance
between keyboards is 5". I can almost play two keyboard with one hand. Each has it's own wire
rack (Home Depot) secured between two pieces of plywood.

The plywood frame is 4 sided. It has a bottom and a back for stability. The sides have tiered
cutouts so that the synths tilt slightly forward with about an 1" of the black keys exposed . . .
like a normal racked synth stand.

I built this because the stand I hobbled together from one I ordered from Musicians Friend made it
almost imossible to access the controls & therefore the tuning.

Each keyboard can slide out so I can change settings.

I used to have this balancing act which actually gave me more playability but I was tired of the
casio always turning itself off (it has an automatic turnoff.)

RT

jpehrson@rcn.com wrote:

> --- In tuning@y..., "Robert Walker" <robert_walker@r...> wrote:
>
>
> > The shallower the depth of the case for the keyboard the better
> > of course - with six keyboards of normal depth, one would perhaps
> require about the maximum span of the hand just to get from the bottom
> > keyboard to the top one.
> >
>
> Yes... I am wondering how close together Rick Tagawa's are...
>
> ________ ______ _____
> Joseph Pehrson
>
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--- In tuning@y..., Rick Tagawa <ricktagawa@e...> wrote:

/tuning/topicId_21686.html#21811

> From the top of top keyboard to the top of the bottom keyboard it
is 24". The average distance between keyboards is 5". I can almost
play two keyboard with one hand. Each has it's own wire
> rack (Home Depot) secured between two pieces of plywood.

Thanks, Rick...

It would be great to get a "feeling" for 72-tET with this "hands on"
approach!

_______ ______ _____ ____
Joseph Pehrson