RE: [tuning] G13#11 experiment, and egroups files

Joe Monzo wrote,

>Please post your analyses of this chord to your egroups folder.
>I'd love to see the graphs that go along with your explanations
>of the various rationaliztions of a complex chord like this.

Hmm . . . well it might be hard to make a 5 to 8 dimensional graph, but let
me show you all the concordant diads that are approximated in my solution:

G B c# d e f a
0 389 581 700 892 1016 1400

|---------2:3----------|----------2:3----------|

|---------3:4-----------|------3:4------|

|-------------3:5--------------|

|-4:5--| |------5:6------| |--4:5--|

|------5:6------|------5:6------|

|--------------5:8--------------|

|-----5:7------|----------7:9----------|

|----------------5:9-------------------|

|------------------5:9------------------|

|---------------------4:9----------------------|

> [Paul Erlich, message 11775]
>
> Joe Monzo wrote,
>
> >Please post your analyses of this chord to your egroups folder.
> >I'd love to see the graphs that go along with your explanations
> >of the various rationaliztions of a complex chord like this.
>
> Hmm . . . well it might be hard to make a 5 to 8 dimensional
> graph, but let me show you all the concordant diads that are
> approximated in my solution:
>
> <snip>

Hey Paul, thanks! If you would do the calculation for
MIDI pitch-bend instead of cents, I'll make a file of this
'rationalization'[*] too, and it will be more accurate than if
I simply use the cents-values from your post.

There are 4096 PBU (pitch-bend units) per 12-tET semitone, or
4096 * 12
= 2^14 * 3
= 49152 PBU per 'octave' (2/1).

So the formula is the same as for cents, but you substitute
'49152' for '1200':

PBU = INT((log(ratio) * (49152/log(2))) + .5)

So, for example, the PBU value for 3/2 is 28752.

Supply me with the raw figures and I'll translate it to MIDI.

-------------

[*] Of course, this version can only be considered a
'rationalization' in the sense that you demonstrate with your
chart; it's really a different tempering. (I only put this
note in because I figured you'd call me on that one! :)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

> [Paul Erlich]
> http://www.egroups.com/message/tuning/11775
>
> ... let me show you all the concordant diads that are
> approximated in my solution:
>
> G B c# d e f a
> 0 389 581 700 892 1016 1400
>
> |---------2:3----------|----------2:3----------|
>
> |---------3:4-----------|------3:4------|
>
> |-------------3:5--------------|
>
> |-4:5--| |------5:6------| |--4:5--|
>
> |------5:6------|------5:6------|
>
> |--------------5:8--------------|
>
> |-----5:7------|----------7:9----------|
>
> |----------------5:9-------------------|
>
> |------------------5:9------------------|
>
> |---------------------4:9----------------------|

I've made a webpage tying together various posts in this thread
and the MIDI-files I've made to illustrate them. You'll hear
Paul's rationalization of this chord automatically:

http://www.ixpres.com/interval/monzo/chords/13sharp11/erlich.htm

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

>
> MIDI pitch-bend instead of cents, I'll make a file of this
> 'rationalization'[*] too, and it will be more accurate than if
> I simply use the cents-values from your post.
>
>
> There are 4096 PBU (pitch-bend units) per 12-tET semitone, or
> 4096 * 12
> = 2^14 * 3
> = 49152 PBU per 'octave' (2/1).
>

I was curious as to why the manufacturers included such small units
in
pitch bends, when the ear's discrimination would be nowhere near
that... is there some reason??
_________ _______ ___ __ __ _ _
Joseph Pehrson

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>

>
> I've made a webpage tying together various posts in this thread
> and the MIDI-files I've made to illustrate them. You'll hear
> Paul's rationalization of this chord automatically:
>
> http://www.ixpres.com/interval/monzo/chords/13sharp11/erlich.htm

Why is it again that the original Monz files "moved around" a lot
more
than after they were processed with Paul's "total diadic harmonic
entropy minimizer..." (??)
________________ ______ ____ ___ _
Joseph Pehrson

[Monz:]
>> MIDI pitch-bend instead of cents, I'll make a file of this
>> 'rationalization'[*] too, and it will be more accurate than if
>> I simply use the cents-values from your post.
>>
>>
>> There are 4096 PBU (pitch-bend units) per 12-tET semitone, or
>> 4096 * 12
>> = 2^14 * 3
>> = 49152 PBU per 'octave' (2/1).

[Joseph Pehrson:]
>I was curious as to why the manufacturers included such small units in
>pitch bends, when the ear's discrimination would be nowhere near
>that... is there some reason??

In the MIDI format, data bytes each contain 7 usable bits (the high
bit signals a non-data, or "status" byte). The designers of the MIDI
format could have chosen to use only a single byte of resolution for
pitch bend messages, but that would be 3.125 cents/bend_unit (1/32 of a
semitone), not very good! So, they decided to prescribe an additional
data byte for each message. The result may be (certainly is!) overkill,
but better that than the reverse!

(Monzo's calcs assume the default condition, that the entire pitch bend
range is projected onto +/-2 semitones from the base note, or a total of
400 cents range. Thus, 400 cents / 2^7 = 400 cents / 128 = 3.125
cents).

JdL

--- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
>
> I was curious as to why the manufacturers included such small units
> in
> pitch bends, when the ear's discrimination would be nowhere near
> that... is there some reason??
> _________ _______ ___ __ __ _ _
> Joseph Pehrson

Joseph,

The reason I believe, is that you need this kind of fine resolution
when you move your pitch wheel for pitch bending - otherwise you'd
get this very coarse "stair-stepping" effect. With this fine
resolution it comes off like a gliss (or meend). And the really
unfortunate downside to the way midi works with pitch bend, is that
it sends the controller information "globally" - in other words, it
affects all pitches simultaneously on the same midi channel. So -
when folks are using this for microtonal demonstrations, they are
forced to put the different notes of chords on separate midi
channels. I personally prefer tuning tables in a synth to this
method, but the great and obvious advantage is that is allows us to
share midi files on our "General Midi" modules and sound cards. The
disadvantage is that you lose polyphony with the pitch bend
microtonal method - because each note of a chord must be treated as a
monophonic line - taking up more of your precious midi channels.

Hope this helps,

Jacky Ligon

--- In tuning@egroups.com, "John A. deLaubenfels" <jdl@a...> wrote:
So, they decided to prescribe an
additional data byte for each message. The result may be (certainly
is!)overkill,but better that than the reverse!

Thanks, John, for this answer!
__________ ____ __ __ __
Joseph Pehrson

>>>I was curious as to why the manufacturers included such small units
>>>in pitch bends, when the ear's discrimination would be nowhere near
>>>that... is there some reason??
>>
>>In the MIDI format, data bytes each contain 7 usable bits (the high
>>bit signals a non-data, or "status" byte). The designers of the MIDI
>>format could have chosen to use only a single byte of resolution for
>>pitch bend messages, but that would be 3.125 cents/bend_unit (1/32 of a
>>semitone), not very good! So, they decided to prescribe an additional
>>data byte for each message. The result may be (certainly is!) overkill,
>>but better that than the reverse!
>
>Thanks, John, for this answer!

Joe, I hope you saw Jacky's reply, because I believe it is correct. I
once read an excellent article on the MIDI standard, with a section on
pitch-bend that mentioned research on how many steps you need to fool the
ear into hearing a gliss. For most music, it's not much less than what's
provided in MIDI, IIRC (I wish I could remember where I read the article).
Now consider that 60 frames/sec can fool the eye into seeing smooth
motion, even for wagon wheels. Ever hear the saying, 'The ear is quicker
than the eye'?

-Carl

--- In tuning@egroups.com, Carl Lumma <CLUMMA@N...> wrote:
>
> Joe, I hope you saw Jacky's reply, because I believe it is correct.
I once read an excellent article on the MIDI standard, with a
section
on pitch-bend that mentioned research on how many steps you need to
fool the ear into hearing a gliss. For most music, it's not much
less
than what's provided in MIDI, IIRC (I wish I could remember where I
read the article).
> Now consider that 60 frames/sec can fool the eye into seeing smooth
> motion, even for wagon wheels. Ever hear the saying, 'The ear is
quicker than the eye'?
>
> -Carl

Thanks so much, Jacky (she's my CD-burner consultant!) and Carl for
the info. Yes, I did see Jacky's post... and thank you! That is
VERY
interesting, and the ear "pitch bend" resolution would make a
wonderful experiment...

Of course, John's comment of only getting 3 cents resolution from a
one-byte system would also be a powerful limitation....

Thanks, all!!

____________ _____ __ __ _
Joseph Pehrson

[Joseph Pehrson:]
>>I was curious as to why the manufacturers included such small units in
>>pitch bends, when the ear's discrimination would be nowhere near
>>that... is there some reason??

[Jacky Ligon, TD 758.11 (archive 11842):]
>The reason I believe, is that you need this kind of fine resolution
>when you move your pitch wheel for pitch bending - otherwise you'd
>get this very coarse "stair-stepping" effect. With this fine
>resolution it comes off like a gliss (or meend).

(To which Carl Lumma responds, below...)

[Jacky:]
>And the really
>unfortunate downside to the way midi works with pitch bend, is that
>it sends the controller information "globally" - in other words, it
>affects all pitches simultaneously on the same midi channel. So -
>when folks are using this for microtonal demonstrations, they are
>forced to put the different notes of chords on separate midi
>channels. I personally prefer tuning tables in a synth to this
>method, but the great and obvious advantage is that is allows us to
>share midi files on our "General Midi" modules and sound cards. The
>disadvantage is that you lose polyphony with the pitch bend
>microtonal method - because each note of a chord must be treated as a
>monophonic line - taking up more of your precious midi channels.

Quite right, and it's a pain! It be nice if there were a universal
sysex that'd retune every synth on the fly without hogging precious
MIDI channels (it'd have to be compact, though!). If retuning gains
enough popularity, I expect that something of this sort will evolve; we
shall see.

Does anybody know about the post-MIDI interface that's out there
somewhere?

[Carl Lumma, TD 759.9 (archive 11865):]
>Joe, I hope you saw Jacky's reply, because I believe it is correct. I
>once read an excellent article on the MIDI standard, with a section on
>pitch-bend that mentioned research on how many steps you need to fool
>the ear into hearing a gliss. For most music, it's not much less than
>what's provided in MIDI, IIRC (I wish I could remember where I read the
>article).

Dang, I wish you could, too! Anybody out there have this? My initial
reaction is skepticism, Carl. How many pitch bend messages are you
going to send per second? Say one every 16 msec, about 64/sec. Much
closer than that and you'll clog the MIDI stream badly. How fast does
the gliss move? Say 100 cents in 1/2 sec, just to grab a number out of
the air. Then each successive MIDI pitch bend message will jump by
more than 3 cents! The MIDI resolution is 40.96 bend units per cent;
that seems like WAY more than would be needed for such a game.

If anything, I'd expect the fine resolution to be useful for long,
sustained pairs of notes. Then, of course, in real life it's usually
the playing synth that is limited.

In my own retuning glisses I typically used 64 msec spacing and was
well content with the results. Other ears may vary, of course!

[Carl:]
>Now consider that 60 frames/sec can fool the eye into seeing smooth
>motion, even for wagon wheels. Ever hear the saying, 'The ear is
>quicker than the eye'?

I wonder! It'd be easy to create MIDI files with different
granularities. I'm piled pretty high with obligations right now, but
mebbie I'll try to gen some files for comparison. Carl, would you
provide some guess for what resolution range would be useful?

JdL