questions about MIDI resolution

> ----- Original Message -----
> From: Orphon Soul, Inc. <tuning@orphonsoul.com>
> To: Tuning List <tuning@yahoogroups.com>
> Sent: Thursday, May 31, 2001 7:51 PM
> Subject: Re: [tuning] Re: defacto standard
>

> On 5/31/01 10:35 PM, "Dave Keenan" <D.KEENAN@UQ.NET.AU> wrote:
>
> Since 1024 = 665 + 359, 1024 has an extremely accurate fifth.
> But I doubt that factored into the binary-based standard.

Huh? I don't follow this at all.

1024 *does* have an extremely accurate approximation to the
3:2 ratio, but it's 2^(599/1024), which is only about
1/533-cent narrow than a 3:2.

But how do 665 and 359 figure into this? 2^(389/665)
and 2^(210/359) are both also pretty darn close to 3:2.
Is that what you meant?

>
> The QuickTime Musical Instruments resolution is actually 3072 though.
> Found that out the hard way... looking at the specs.
> It looks like it'll respond to the 14-bit resolution (49152-tET)
> but like a lot of pitch bend processing, ignores a few bits.

Yeah, but what seems really weird to me is that the QuickTime
spec ignores all but one bit from the first byte... strange.
The 7 bits of the second byte give a resolution to 128 units
per semitone, and QuickTime has 256, which means that it's using
only one bit more.

Can anyone explain this... Since the MIDI spec provides 14-bit
resolution, why do some manufacturers choose to recognize less
than that? What's the advantage?

-monz
http://www.monz.org
"All roads lead to n^0"

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On 6/1/01 4:23 AM, "monz" <joemonz@yahoo.com> wrote:

> But how do 665 and 359 figure into this? 2^(389/665)
> and 2^(210/359) are both also pretty darn close to 3:2.
> Is that what you meant?

Yup.
I just got used to the list of convergent temperaments;
for Pythagorean... after 53, 94, 147, 200, 253, 306, 359, 665.
It just threw me for a loop when I first found out
that 1024 was the sum of two of these.

>> The QuickTime Musical Instruments resolution is actually 3072 though.
>> Found that out the hard way... looking at the specs.
>> It looks like it'll respond to the 14-bit resolution (49152-tET)
>> but like a lot of pitch bend processing, ignores a few bits.
>
> Yeah, but what seems really weird to me is that the QuickTime
> spec ignores all but one bit from the first byte... strange.
> The 7 bits of the second byte give a resolution to 128 units
> per semitone, and QuickTime has 256, which means that it's using
> only one bit more.

Well David van Brink was fired from Apple.
He's the one that came up with the atomic structure
for QuickTime instruments apparently.
I have a copy of his Atomic Editor,
I'm working on a program to make microtonal patches.
It's such a complete pain...
It's kept me up many a night.
Actually it's only recently I discovered the 3072 resolution.

You would think having an onboard synth finally in this life,
they'd realize that musicians would want to EDIT the patches...
like they would with any edittable synth...?
Apparently in QuickTime 5, it's not even the same format as v2.5 - 4.1;
the Editor can't read it at all.
They seem to be hording.

> Can anyone explain this... Since the MIDI spec provides 14-bit
> resolution, why do some manufacturers choose to recognize less
> than that? What's the advantage?

Some of it goes back to what "era" the keyboard was from.
The problem with full 14 bit about 10 years ago,
was, well, consider the exponential growth of computer functionality.
Ten years ago, you try recording a pitch bend into a sequencer,
you wind up with SO much data because of the sensitivity,
it could easily crash the computer.

Bend up a whole tone, and you got about 32000 bytes!
That's considering a less-than-60-tick delta,
a byte for the channel command, and two byes for the pitch bend.
How fast can you bend a whole tone with a pitch wheel?
One second is a pretty slow bend.
32000 bytes into the 1989 version of Performer...?
"Sorry a system error occurred. Get a new computer."

There was also a kind of "twitching";
If you so much as bump a keyboard with a pitch wheel that's loose enough,
You get burbles. 0 -1 0 +1 0 -1 -2 -1 etc...
Also, you bump the keyboard and the pitch wheel can pick it up.

There were some other issues, but I don't remember well.
Possibly the storage of wavetables for every resolution?
I'm sorry I'll have to rummage for this one.

Hey I got you the QY links pretty quick though huh? ;)

Marc

In-Reply-To: <B73CCFF5.2D3A%tuning@orphonsoul.com>
Marc wrote:

> Some of it goes back to what "era" the keyboard was from.
> The problem with full 14 bit about 10 years ago,
> was, well, consider the exponential growth of computer functionality.
> Ten years ago, you try recording a pitch bend into a sequencer,
> you wind up with SO much data because of the sensitivity,
> it could easily crash the computer.
>
> Bend up a whole tone, and you got about 32000 bytes!
> That's considering a less-than-60-tick delta,
> a byte for the channel command, and two byes for the pitch bend.
> How fast can you bend a whole tone with a pitch wheel?
> One second is a pretty slow bend.
> 32000 bytes into the 1989 version of Performer...?
> "Sorry a system error occurred. Get a new computer."

It's worse than that. You'd saturate the MIDI stream. You get 3125
instructions per second, a pitch bend is 3 instructions.

But this is only on transmitting. All the soundcards I've tested (not a
statistically significant sample :) respond to all bits, but then truncate
it to their internal resolution (usually around a cent).

One Ensoniq I heard seemed to be interpolating to give smooth pitch bends,
which unfortunately sounded a real mess for pitch bend tuning.

Note also that internal MIDI streams in a PC don't have the speed
restrictions mentioned above. Check the MIDI Yoke documentation on
feedback. This can be a problem in other ways. I found that MIDI Relay
sent (N)RPN messages so fast they arrived out of order in the sequencer,
so I had to slow them down (or maybe I forgot ;).

Modern keyboards have a "to host" cable that can plug straight into the
PC. I don't know whether or not this observes the old MIDI bit rate.

Graham

On 6/1/01 5:00 AM, "graham@microtonal.co.uk" <graham@microtonal.co.uk>
wrote:

> It's worse than that. You'd saturate the MIDI stream. You get 3125
> instructions per second, a pitch bend is 3 instructions.

That's right. Thank you.
That was definitely one of the issues.
I forgot about that particular speed limit.

> ----- Original Message -----
> From: Orphon Soul, Inc. <tuning@orphonsoul.com>
> To: Tuning List <tuning@yahoogroups.com>
> Sent: Friday, June 01, 2001 1:52 AM
> Subject: Re: [tuning] questions about MIDI resolution
>

> I just got used to the list of convergent temperaments;
> for Pythagorean... after 53, 94, 147, 200, 253, 306, 359, 665.
> It just threw me for a loop when I first found out
> that 1024 was the sum of two of these.

Hmmm... I don't know if you've already mentioned
these numbers games and I missed it... but I got
interested in this and started calculating.

12 + 41 = 53
53 + 41 = 94
94 + 53 = 147
147 + 53 = 200
200 + 53 = 253
253 + 53 = 306
306 + 53 = 359
359 + 306 = 665
665 + 359 = 1024

So now what's the significance of these numbers?

I see that some of the ones in the second column
designate temperaments that are especially good
approximations of Pythagorean and 5-limit JI systems.

...?

-monz
http://www.monz.org
"All roads lead to n^0"

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Hi Monz,

You may be unaware of the "relative error theorem", which Paul Hahn
and I discussed some years ago, and Marc recently brought up.

Here's an example of how you can use the theorem.

The 5:4 in 15-tET is sharp by 0.1711 of a 15-tET degree
The 5:4 in 19-tET is flat by 0.1166 of a 19-tET degree

15 + 19 = 34 . . . and . . . +0.1711 + -0.1166 = +0.0545

The theorem then tells you that

The 5:4 in 34-tET is sharp by 0.0545 of a 34-tET degree.

So . . . very crudely stated . . . a good ET plus a good ET equals
another good ET.

Examples:

12+19=31
12+22=34
19+22=41
31+22=53
31+41=72

etc.

On 6/1/01 4:29 PM, "monz" <joemonz@yahoo.com> wrote:

> 12 + 41 = 53
> 53 + 41 = 94
> 94 + 53 = 147
> 147 + 53 = 200
> 200 + 53 = 253
> 253 + 53 = 306
> 306 + 53 = 359
> 359 + 306 = 665
> 665 + 359 = 1024
>
>
> So now what's the significance of these numbers?

It's the series you get when you run only 2:1 and 3:2
through the Brun algorithm for convergent temperaments.
1024 isn't actually *on* the list, which is why I was surprised
to find out it was the sum of two of them,
as 359 and 665 are on it.
Not every day you see a power of two hanging around.

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> > On 5/31/01 10:35 PM, "Dave Keenan" <D.KEENAN@U...> wrote:
> >
> > Since 1024 = 665 + 359, 1024 has an extremely accurate fifth.
> > But I doubt that factored into the binary-based standard.

Monz, I didn't write that at all. It was Marc (Orphon Soul).

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_24167.html#24258

> Monz, I didn't write that at all. It was Marc (Orphon Soul).

Oops, my bad!... sorry, Dave. I knew it was Marc... I never
noticed that it was inadvertently attributed to you.

shantih,

monz
http://www.monz.org
"All roads lead to n^0"