768edo de facto tuning standard?

hello all,

> From: <Pitchcolor@aol.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, July 06, 2003 3:48 PM
> Subject: [tuning] Fwd: [tuning-math] Mu explained
>
>
> What is the industry standard for pitch bend?
>
> There really is no industry standard for pitch bend.
> MIDI Tuning Standard (MTS) specifies 14 bit precision
> for pitch bend messages, which are to be sent in
> two bytes having 7 data bits and one data flag bit;
> however, the majority of manufacturers have not
> implemented 14 bit protocol in their MIDI equipment.
> Although some companies use fewer than 7 bits and
> some use a slightly greater number, the majority of units
> send pitch bend data in one byte having 7 data bits,
> so this is a good number to use as the industry default value.

and as i explained earlier today, the MIDI pitch-bend
convention is different from the MTS convention.

for the pitch-bend convention, which is what Aaron
is describing here and which is the only one which
applies for hardware MIDI instruments (AFAIK),
of those 7 data bits, one simply indicates the 12edo
MIDI-note at the pseudo-central data value of the total
pitch-bend range, and so therefore only 6 bits are used
for actual microtuning data.

Aaron's "mu" definitions are based on the total
bits of resolution, which spans a minimum of a
"whole-tone" at the finest pitch-bend setting;
he calls this particular one the "heptamu".

my "mu" definitions are all based on bits of resolution
per 12edo Semitone, and so i would call this the "hexamu",
6 bits per Semitone, which renders 768edo.

whichever method of defining "mus" is finally accepted
by the general tuning community, i propose recognizing
768edo as the _de facto_ hardware tuning standard.

any objections?

also, does anyone have any info on the true tuning
resolution of computer soundcards, by brand and model, etc.?

i'd like to get a good grasp of what tuning resolution
our hardware is actually producing.

-monz

Hi monz,

After reading the posts from you, Gene and Manuel the other day,
I finally realized that the language I was using was causing a lot
of the confusion. Wherever I had used the term MTS for MIDI
Tuning Standard, I assumed it was clear that I meant the MIDI
_pitch_bend Tuning Standard. Obviously, this was not clear at
all! In fact this was a poorly formed conflation which amounted to
an incorrect use of the phrase MTS. This morning I uploaded a
version of my pitch bend page which replaces the phrase 'MIDI
Tuning Standard' with 'MIDI pitch bend standard.' So to avoid
confusion there are now no direct references to MTS. I also
curbed the tone of emphatic finality present in the original text,
which was obviously a result of our heated debate. I plan to turn
this into a more useful page with more links, but for now it costs
me a long distance call to upload, so I do it only when I have to.

I hope this clears things up, and to all -- I thank you immensely
for your correction and your _patience!

On the topic of the 768 ED2 industry standard for MIDI, I think we
have to accept this until more manufacturers support 14 bit
precision.

Aaron

------
--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hello all,
>
>
>
> > From: <Pitchcolor@a...>
> > To: <tuning@yahoogroups.com>
> > Sent: Sunday, July 06, 2003 3:48 PM
> > Subject: [tuning] Fwd: [tuning-math] Mu explained
> >
> >
> > What is the industry standard for pitch bend?
> >
> > There really is no industry standard for pitch bend.
> > MIDI Tuning Standard (MTS) specifies 14 bit precision
> > for pitch bend messages, which are to be sent in
> > two bytes having 7 data bits and one data flag bit;
> > however, the majority of manufacturers have not
> > implemented 14 bit protocol in their MIDI equipment.
> > Although some companies use fewer than 7 bits and
> > some use a slightly greater number, the majority of units
> > send pitch bend data in one byte having 7 data bits,
> > so this is a good number to use as the industry default value.
>
>
> and as i explained earlier today, the MIDI pitch-bend
> convention is different from the MTS convention.
>
> for the pitch-bend convention, which is what Aaron
> is describing here and which is the only one which
> applies for hardware MIDI instruments (AFAIK),
> of those 7 data bits, one simply indicates the 12edo
> MIDI-note at the pseudo-central data value of the total
> pitch-bend range, and so therefore only 6 bits are used
> for actual microtuning data.
>
> Aaron's "mu" definitions are based on the total
> bits of resolution, which spans a minimum of a
> "whole-tone" at the finest pitch-bend setting;
> he calls this particular one the "heptamu".
>
> my "mu" definitions are all based on bits of resolution
> per 12edo Semitone, and so i would call this the "hexamu",
> 6 bits per Semitone, which renders 768edo.
>
> whichever method of defining "mus" is finally accepted
> by the general tuning community, i propose recognizing
> 768edo as the _de facto_ hardware tuning standard.
>
> any objections?
>
> also, does anyone have any info on the true tuning
> resolution of computer soundcards, by brand and model, etc.?
>
> i'd like to get a good grasp of what tuning resolution
> our hardware is actually producing.
>
>
>
> -monz

hi Aaron,

> From: "pitchcolor" <Pitchcolor@aol.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, July 08, 2003 9:48 AM
> Subject: [tuning] Re: 768edo de facto tuning standard? + pitchbend webpage
updated!
>
>
> Hi monz,
>
> After reading the posts from you, Gene and Manuel the other day,
> I finally realized that the language I was using was causing a lot
> of the confusion. Wherever I had used the term MTS for MIDI
> Tuning Standard, I assumed it was clear that I meant the MIDI
> _pitch_bend Tuning Standard. Obviously, this was not clear at
> all! In fact this was a poorly formed conflation which amounted to
> an incorrect use of the phrase MTS. This morning I uploaded a
> version of my pitch bend page which replaces the phrase 'MIDI
> Tuning Standard' with 'MIDI pitch bend standard.' So to avoid
> confusion there are now no direct references to MTS. I also
> curbed the tone of emphatic finality present in the original text,
> which was obviously a result of our heated debate. I plan to turn
> this into a more useful page with more links, but for now it costs
> me a long distance call to upload, so I do it only when I have to.

i think we finally all got it straight now. but
don't feel that you have to accept most of the
blame, even if you did make an error or two, because
as i've said and as Gene agreed, the official MIDI
documentation on tuning is really terrible.

i suppose it just reflects the fact that there
was so little general interest in tuning back
in 1983, when MIDI was first published.

i'd like to link to your page from my webpage
on MIDI tuning and from all the "mu" Dictionary
pages too. i'm still editing all of those.

> On the topic of the 768 ED2 industry standard for MIDI,
> I think we have to accept this until more manufacturers
> support 14 bit precision.

i did a listening test on my computer with Cakewalk,
using hexamus (my definition, 768edo) and all the
finer resolutions down to dodekamus (49152edo,
the Cakewalk limit).

i can hear that there is a difference with the
hexamu but not the heptamu or any smaller mu.
therefore, i know for sure now that my soundcard
has hexamu resolution and no better.

(i'm not even exactly sure of the make and model of
my soundcard: it looks like my hardware is Crystal
4281 Legacy Audio Device.)

so the bottom line is: all the microtonal music
i've been creating on my computer for all these years
has been in 768edo, first with Texture sequencer
software and my Yamaha instruments (DX7-II and TG-77),
and then with Cakewalk software and my PC soundcards.

the exception to this was the few years in between
when i used Cakewalk in conjunction with the Yamaha
instruments, which would have been around 1992-1996.
the Yamaha instruments have a resolution of 1024edo
(i.e., 10 bits per 8ve).

so, it's good to finally know what tuning i've
been using all these years! (... having thought
that it was 49152edo.)

this is the information i'm interested in knowing.
exactly what resolution do various soundcards have?

i'm not really using MIDI instruments anymore,
doing all of my musical work entirely on the computer
these days, so this info is more valuable to me than
the the data on resolutions of instruments that's
available at the Microtonal Synthesis website.

Gabor posted a few details. any more forthcoming?

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> whichever method of defining "mus" is finally accepted
> by the general tuning community, i propose recognizing
> 768edo as the _de facto_ hardware tuning standard.
>
> any objections?

my ensoniq vfx-sd keyboard, after pressing ensoniq hard enough, was
revealed to have 512edo resolution. so 768 isn't "de facto" for me,
anyway.

----- Original Message -----
From: "Paul Erlich" <perlich@aya.yale.edu>
To: <tuning@yahoogroups.com>
Sent: Tuesday, July 08, 2003 12:33 PM
Subject: [tuning] Re: 768edo de facto tuning standard?

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > whichever method of defining "mus" is finally accepted
> > by the general tuning community, i propose recognizing
> > 768edo as the _de facto_ hardware tuning standard.
> >
> > any objections?
>
> my ensoniq vfx-sd keyboard, after pressing ensoniq hard enough, was
> revealed to have 512edo resolution. so 768 isn't "de facto" for me,
> anyway.

of course there are some exceptions. some
hardware will have less resolution, as does
your ensoniq, and a very few will have better
resolution, as the Turtle Beach soundcard i
mentioned in another post.

but in general, the vast majority of hardware
seems to have a maximum resolution of 768edo.

now, let's support that vague statement with
some hard facts!

... meantime, since i calculated that the hexamu

>> "... is an irrational number, but is extremely close
>> to the ratio 2217:2215 ( 3^1 5^-1 443^-1 739^1 ) :
>> the difference is ~ 1/70,000 of a cent, which makes
>> them for all intents and purposes identical"

then can we say that those vast legions of us who
*do* effectively have 768edo have also been using
3/5/443/739-prime-limit JI? ;-)

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> ... meantime, since i calculated that the hexamu
>
> >> "... is an irrational number, but is extremely close
> >> to the ratio 2217:2215 ( 3^1 5^-1 443^-1 739^1 ) :
> >> the difference is ~ 1/70,000 of a cent, which makes
> >> them for all intents and purposes identical"
>
> then can we say that those vast legions of us who
> *do* effectively have 768edo have also been using
> 3/5/443/739-prime-limit JI? ;-)

i know you're joking, but if one were to take this seriously, one
could counter that the interval of 181 hexamus is at least as common
in practice as the interval of 1 hexamu, and either can generate
768edo equally easily, and 181 hexamus is extremely close to the
ratio 2382:2023 ( 2^1 3^1 7^-1 17^-2 397^1) : the difference is less
than 1/80,000 of a cent, which means that the scale generated by 767
repetitions of this interval is a bit closer to 768edo than the scale
generated by 767 repetitions of the interval you mention above.

hi paul,

> From: "Paul Erlich" <perlich@aya.yale.edu>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, July 08, 2003 1:02 PM
> Subject: [tuning] Re: 768edo de facto tuning standard?
>
>
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > ... meantime, since i calculated that the hexamu
> >
> > >> "... is an irrational number, but is extremely close
> > >> to the ratio 2217:2215 ( 3^1 5^-1 443^-1 739^1 ) :
> > >> the difference is ~ 1/70,000 of a cent, which makes
> > >> them for all intents and purposes identical"
> >
> > then can we say that those vast legions of us who
> > *do* effectively have 768edo have also been using
> > 3/5/443/739-prime-limit JI? ;-)
>
> i know you're joking, but if one were to take this
> seriously, one could counter that the interval of
> 181 hexamus is at least as common in practice as the
> interval of 1 hexamu, and either can generate 768edo
> equally easily, and 181 hexamus is extremely close
> to the ratio 2382:2023 ( 2^1 3^1 7^-1 17^-2 397^1) :
> the difference is less than 1/80,000 of a cent, which
> means that the scale generated by 767 repetitions of
> this interval is a bit closer to 768edo than the scale
> generated by 767 repetitions of the interval you mention
> above.

whew, thanks for setting me straight! ;-)

so then it doesn't really make a difference whether
we call our microtonal music 397-limit or 739-limit.

;-) ;-)

-monz

better yet, 207 hexamus can also generate 768edo, it's approximated
by 1825:1514 ( 2^-1 5^2 73^1 757^-1 ), and the difference is only ~
1/96,000 of a cent.

and best of all, 381 hexamus can generate 768edo, it's approximated
by 543:385 ( 3^1 5^-1 7^-1 11^-1 181^1 ), and the difference is only
~ 1/375,000 of a cent! this is clearly a simpler and more accurate
rational generator for approximating 768edo . . . ok, enough of this
silly game!

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > ... meantime, since i calculated that the hexamu
> >
> > >> "... is an irrational number, but is extremely close
> > >> to the ratio 2217:2215 ( 3^1 5^-1 443^-1 739^1 ) :
> > >> the difference is ~ 1/70,000 of a cent, which makes
> > >> them for all intents and purposes identical"
> >
> > then can we say that those vast legions of us who
> > *do* effectively have 768edo have also been using
> > 3/5/443/739-prime-limit JI? ;-)
>
> i know you're joking, but if one were to take this seriously, one
> could counter that the interval of 181 hexamus is at least as
common
> in practice as the interval of 1 hexamu, and either can generate
> 768edo equally easily, and 181 hexamus is extremely close to the
> ratio 2382:2023 ( 2^1 3^1 7^-1 17^-2 397^1) : the difference is
less
> than 1/80,000 of a cent, which means that the scale generated by
767
> repetitions of this interval is a bit closer to 768edo than the
scale
> generated by 767 repetitions of the interval you mention above.

> From: "Paul Erlich" <perlich@aya.yale.edu>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, July 08, 2003 1:18 PM
> Subject: [tuning] Re: 768edo de facto tuning standard?
>
>
> better yet, 207 hexamus can also generate 768edo,
> it's approximated by 1825:1514 ( 2^-1 5^2 73^1 757^-1 ),
> and the difference is only ~ 1/96,000 of a cent.
>
> and best of all, 381 hexamus can generate 768edo, it's
> approximated by 543:385 ( 3^1 5^-1 7^-1 11^-1 181^1 ),
> and the difference is only ~ 1/375,000 of a cent!
> this is clearly a simpler and more accurate rational
> generator for approximating 768edo . . . ok, enough
> of this silly game!

but it was fun for a while, wasn't it? ;-)

seriously tho, this is exactly the kind of thing
McLaren goes on about, to prove that "we don't
prefer low-prime JI", etc, by composing music which
has ratios with ridiculously high prime-factors which
are extremely close to more familiar ones like 3:2
and 5:4. and of course, the music sounds like
regular JI.

numbers, numbers, numbers ...

i'm just glad that now i finally know what i'm
really hearing.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > From: "Paul Erlich" <perlich@a...>
> > To: <tuning@yahoogroups.com>
> > Sent: Tuesday, July 08, 2003 1:18 PM
> > Subject: [tuning] Re: 768edo de facto tuning standard?
> >
> >
> > better yet, 207 hexamus can also generate 768edo,
> > it's approximated by 1825:1514 ( 2^-1 5^2 73^1 757^-1 ),
> > and the difference is only ~ 1/96,000 of a cent.
> >
> > and best of all, 381 hexamus can generate 768edo, it's
> > approximated by 543:385 ( 3^1 5^-1 7^-1 11^-1 181^1 ),
> > and the difference is only ~ 1/375,000 of a cent!
> > this is clearly a simpler and more accurate rational
> > generator for approximating 768edo . . . ok, enough
> > of this silly game!
>
>
>
> but it was fun for a while, wasn't it? ;-)
>
> seriously tho, this is exactly the kind of thing

exactly? i don't see much similarity here.

> McLaren goes on about, to prove that "we don't
> prefer low-prime JI", etc, by composing music which
> has ratios with ridiculously high prime-factors which
> are extremely close to more familiar ones like 3:2
> and 5:4. and of course, the music sounds like
> regular JI.

in fact, i've used the argument that 30000001:20000001 sounds just
like 3:2 dozens of times around here and don't think it's silly at
all. however, what it shows is that we have a certain tolerance for
tuning errors when it comes to low-number ratios, and that high-
number ratios will simply be interpreted in terms of (possibly
several) nearby low-number ratios. if mclaren is specifically
choosing intervals extremely close to 3:2 and 5:4, then he's
undermining his own argument, since he himself is clearly preferring
intervals in the immediate vicinity of low-number ratios over all
others!

--- In tuning@yahoogroups.com, "pitchcolor" <Pitchcolor@a...> wrote:
> Hi monz,
>
> After reading the posts from you, Gene and Manuel the other day,
> I finally realized that the language I was using was causing a lot
> of the confusion. Wherever I had used the term MTS for MIDI
> Tuning Standard, I assumed it was clear that I meant the MIDI
> _pitch_bend Tuning Standard. Obviously, this was not clear at
> all!

I think it's taken all of us a while to sort this out. Let's put the
blame on the midi guys.

In fact this was a poorly formed conflation which amounted to
> an incorrect use of the phrase MTS. This morning I uploaded a
> version of my pitch bend page which replaces the phrase 'MIDI
> Tuning Standard' with 'MIDI pitch bend standard.'

Great!

> On the topic of the 768 ED2 industry standard for MIDI, I think we
> have to accept this until more manufacturers support 14 bit
> precision.

I think I'll take a look at the commas and temperaments
characteristic of 768-rt.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> then can we say that those vast legions of us who
> *do* effectively have 768edo have also been using
> 3/5/443/739-prime-limit JI? ;-)

Why are the vast legions stuck on sound cards?

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_45368.html#45377

>
> of course there are some exceptions. some
> hardware will have less resolution, as does
> your ensoniq, and a very few will have better
> resolution, as the Turtle Beach soundcard i
> mentioned in another post.
>
> but in general, the vast majority of hardware
> seems to have a maximum resolution of 768edo.
>

***Hi Monz,

Yes, this is the 1.56 cents definition I was just talking about
regarding the TX81Zs.

Certainly, this is good enough for Blackjack, since most of
the "crucial" and noticable consonances deviate in about the 2 to 3
cent range, as I understand it...

It seems John Lofflink's _microtonal synthesis_ site is now down, and
it looks like more than a *temporary* development. I just e-mailed
John to find out more about this...

J. Pehrson

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

/tuning/topicId_45368.html#45383

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > > From: "Paul Erlich" <perlich@a...>
> > > To: <tuning@yahoogroups.com>
> > > Sent: Tuesday, July 08, 2003 1:18 PM
> > > Subject: [tuning] Re: 768edo de facto tuning standard?
> > >
> > >
> > > better yet, 207 hexamus can also generate 768edo,
> > > it's approximated by 1825:1514 ( 2^-1 5^2 73^1 757^-1 ),
> > > and the difference is only ~ 1/96,000 of a cent.
> > >
> > > and best of all, 381 hexamus can generate 768edo, it's
> > > approximated by 543:385 ( 3^1 5^-1 7^-1 11^-1 181^1 ),
> > > and the difference is only ~ 1/375,000 of a cent!
> > > this is clearly a simpler and more accurate rational
> > > generator for approximating 768edo . . . ok, enough
> > > of this silly game!
> >
> >
> >
> > but it was fun for a while, wasn't it? ;-)
> >
> > seriously tho, this is exactly the kind of thing
>
> exactly? i don't see much similarity here.
>
> > McLaren goes on about, to prove that "we don't
> > prefer low-prime JI", etc, by composing music which
> > has ratios with ridiculously high prime-factors which
> > are extremely close to more familiar ones like 3:2
> > and 5:4. and of course, the music sounds like
> > regular JI.
>
> in fact, i've used the argument that 30000001:20000001 sounds just
> like 3:2 dozens of times around here and don't think it's silly at
> all. however, what it shows is that we have a certain tolerance for
> tuning errors when it comes to low-number ratios, and that high-
> number ratios will simply be interpreted in terms of (possibly
> several) nearby low-number ratios. if mclaren is specifically
> choosing intervals extremely close to 3:2 and 5:4, then he's
> undermining his own argument, since he himself is clearly
preferring
> intervals in the immediate vicinity of low-number ratios over all
> others!

***I thought Johnny Reinhard's term for this kind of thing was kind
of cute: "slight of hand" JI. Of course, since these are ratios it,
supposedly *is* JI, but the "slight of hand" element (tromp
l'oreille?) remains...

J. Pehrson