Disappearing Commas

There have been various references to commas disappearing recently.

Could anyone tell me - is there a unique theoretical limit at which a
comma (of different kinds?) may be said to disappear? Are there
strict and not so strict definitions of which systems (or musical
sequences?) of which this can be said to pertain/occur? Is there a
single accepted definitive reference which defines the 'disappearance
of a comma'? (Helmholtz?) These are things I missed in my education.

Thanks.

> From: "Patrick Ozzard-Low"

> Will the Ensoniq extrapolate an arbitrary-number-division
> *non-equally- tempered* non-octave scale? That's interesting, I
> didn't realise it went that far - I thought it could only extraopolate
> *equally-tempered* non-octave scales? But you're saying the Ensoniq
> will allow a 23 note scale, with user specified non-equal divisions,
> which 'repeats' at intervals of 7/4 (and leaves specific keyboard
> keys within the 23 steps blank)? (for example).

Yes, but if you extrapolate from key A to key B and the desired interval is
not an exact integer cents division you might get some small error (1 cent
per range) in the extrapolation. Normally, you define a full octave and
extrapolate that.

> 1. Explain why high end resolution of 0.0061 cents would be useful?
> Otherwise manufacturers will assume craziness? Suggest other options
> and why?

That's the highest resolution of the MIDI Tuning Standard. It's not useful
for me, but is for some people doing drones. By high end I'm really
referring to computer synthesis type programs, not your everyday keyboard
synthesizer. This should be spelled out in the wishlist. MIDI response
isn't fast enough to make that pitch resolution usable due to phase
cancellations, as discussed previously in the list.

Manufacturers will think we're crazy asking for 0.1 cent resolution. I'll
probably rephrase the pitch resolutions as "to 0.1 cent or best possible
cents resolution" and add some exposition to the requests. In a wavetable
synthesizer the underlying samples would never be tuned to that accuracy.
Sorry, but it's true. Writing some new code is one thing, but
manufacturers are not going to order their sound development groups to tune
everything to 0.1 cent accuracy just for us microtonalist's benefit. That
would be a huge labor effort on their part. The idea is to keep this as
simple as possible, thereby raising the probability that these ideas will
be implemented.

> 3. I'm unclear how far the last line of your high-end spec addresses
> the question of adaptive tunings ("real-time updates of note
> pitches is selectable per note as instant pitch correction or new
> note only"). Could this be made clearer/ elaborated upon? An
> option to invoke built-in, user-configurable adaptivity should indeed
> be a requirement - at least in an ideal high-end machine. How best
> to provide *user configurability* for real-time adaptivit(ies) is not
> my area - but others might like to suggest?

I'm open to any ideas on this. I got the idea from the Justonic folks. I
use new note only updates myself. They were more inclined to real-time
updates, giving as an example barbershop quartets where a pitch swoop
wouldn't be out of place. The MIDI Tuning standard also requests real-time
updates. Do we really need both types available simultaneously?

> 5. Measurements in Cents and/or Hz and/or *Ratios*(?). To the
> What-Limit?

Again, we need to keep things simple for the manufacturers. Measurements
in cents is all we need to define any scale.

> As regards interface: here's an off-the-top-of ny-head sketch of the
> sort of thing I'd like to see:
>
> Click on a button called 'Tuning';
> Up comes a dialog box, which says:
> New or Load or Edit
> New is new, Load loads pre-defined tuning configuration; Edit edits
> one. Suppose we choose 'New' -
etc.

It's a good idea to give something like this as an example, but phrase them
as being options. It's important to break away the things that make
microtuning convenient from those that make it possible. Asking or
demanding too much work from the software engineers who write these
programs is likely to get us nothing in return. I'd really like to see any
possible simplifications to the wishlist.

John Loffink
jloffink@pdq.net

John Loffink wrote:

>I have posted my microtonal wishlist to my web site at
>http://freeweb.pdq.net/jloffink/architectures.html

Excellentissimo! Well, actually I only got time to look at it for
two minutes yesterday. But some quick thoughts below.

I wrote:

>> (3) Pitch assignation to a user definable keyboard zone - for
>> example - select a zone of 34 consecutive keyboard notes, and
>> assign each keyboard key a pitch value (ET or not) relative to 1/1
>> in that zone (normally in an ascending scale, but not necessarily).
>> Then tell the machine to automatically assign that 34 key tuning
>> scheme into the next octave either (for example) at the 35th key
>> above or at the 36th key above and below. (I don't suppose the
>> latter exists yet).

John Loffink replied:

>Most Ensoniq's have an "extrapolate" function that creates a scale in
>this manner and compiles it to the full keyboard tuning. I think
>that's the best way rather than having some third method of storing
>scales, if that's what you're suggesting.

Will the Ensoniq extrapolate an arbitrary-number-division
*non-equally- tempered* non-octave scale? That's interesting, I
didn't realise it went that far - I thought it could only extraopolate
*equally-tempered* non-octave scales? But you're saying the Ensoniq
will allow a 23 note scale, with user specified non-equal divisions,
which 'repeats' at intervals of 7/4 (and leaves specific keyboard
keys within the 23 steps blank)? (for example).

Not sure if I'm suggesting a 'third method', I may just have been
suggesting something I didn't think could currently be done
quasi-automatically. (Of course you can do anything like this
manually on existing samplers, but you run out of 'key-groups' (and
patience)).

Immediate reactions to wishlist page (John, if any of this appeals,
feel free to use/modify however you please):

1. Explain why high end resolution of 0.0061 cents would be useful?
Otherwise manufacturers will assume craziness? Suggest other options
and why?

2. Add idea of 'on-board absolute pitch meter' for sample based
modules? (I totally agree that the machines ought to show _actual_
resolution.)

3. I'm unclear how far the last line of your high-end spec addresses
the question of adaptive tunings ("real-time updates of note
pitches is selectable per note as instant pitch correction or new
note only"). Could this be made clearer/ elaborated upon? An
option to invoke built-in, user-configurable adaptivity should indeed
be a requirement - at least in an ideal high-end machine. How best
to provide *user configurability* for real-time adaptivit(ies) is not
my area - but others might like to suggest?

4. The function definitions could be augmented by adding some ideas
about the interface - ie., how the user wants the 'logic' of tuning
options to be presented and controlled. (Perhaps this is
controversial?) (see below)

5. Measurements in Cents and/or Hz and/or *Ratios*(?). To the
What-Limit?

As regards interface: here's an off-the-top-of ny-head sketch of the
sort of thing I'd like to see:

Click on a button called 'Tuning';
Up comes a dialog box, which says:
New or Load or Edit
New is new, Load loads pre-defined tuning configuration; Edit edits
one. Suppose we choose 'New' -
Up comes a dynamic dialog box:
Global or Instrument or Instrument-Element or MIDI Channel
As you click different options, radio buttons/check boxes become
avaialble or not etc:
Define '1/1' to keyboard : key and pitch (conventional
name plus or minus cents, and in Hz)
Choose Equal-Tempered or Non-Equal-Tempered;
Depending on what you choose, dialogue box changes etc:
Define terms: Cents or Hz or Ratios;
Choose cyclic interval (1200=default, or XXXX, or none);
If ET - choose number of scale steps;
If non-ET - choose number of scale steps and exact sequence
of intervals;
Assign synth sound(s) - synth deals automatically;
Assign sampler sounds - user chooses from a list of samples,
(each of which contains the original sampled pitch in Name +/-
cents/Hz as part of the sample field. Module assigns program or
samples accordingly, to nearest acurate pitch etc. User is then
offered opportunity to test and override sample mapping if
necessary).

Obviously no one wants to do this for every instrument - so once
a template is saved it can be recalled etc.

Patrick O-L

Patrick Ozzard-Low wrote:
>5. Measurements in Cents and/or Hz and/or *Ratios*(?). To the
>What-Limit?

Measurement in ratios would likely be difficult to implement unless the tuning
were set up by ratio, and really not necessary for non-rational tunings.
Though it would be interesting, it's really not the purpose of a synth tuning
table. There are probably programs available to do the calculations for those
who want to know that information. Actually, I think the Hypercard JICalc,
downloadable for free from the Mills site, can do that; only for Mac, though.
(BTW, if you have access to a Mac and haven't yet gotten the JICalc, do it
now!)

What might be nice is the ability to enter tunings into a synth table via
ratios of up to a certain limit - 4095? (one less than 2^12). Heck, most
software today is 32-bit, why not ask for 4,294,967,295? Maybe that's
overkill - OK, a 16-bit calculation would yield 65,535-limit ratios; that'd do
for me. :-)

>Will the Ensoniq extrapolate an arbitrary-number-division
>*non-equally- tempered* non-octave scale?

Yes. You describe any sequence of intervals between any group of keys,
and it will duplicate that sequence of intervals across successive keys.

This probably isn't a particularly useful example, but you can, for
example set up this sequence of pitch relationships:

C4
50c
C#4
40c
D4
30c
D#4

And then tell it to extrapolate from C4 to D#4, and you'll end up with:
..
A3
50c
A#3
40c
B3
30c
C4
50c
C#4
40c
D4
30c
D#4
50c
E4
40c
F4
30c
F#4
..

John Loffink wrote:

>Sorry, but it's true. Writing some new code is one thing, but
>manufacturers are not going to order their sound development groups to
tune
>everything to 0.1 cent accuracy just for us microtonalist's benefit.
That
>would be a huge labor effort on their part. The idea is to keep this as
>simple as possible, thereby raising the probability that these ideas
will
>be implemented.

What difference does it make how the samples are tuned? So long as you
correct for mistuning, there shouldn't be problem. That is, record a
sample as being Eb, 0.32 cents sharp of equal temperament, or whatever.
It's really easy to work out the pitch of a sample: count the number of
bytes in the loop. Anyway, give us a sampler and we can tune the samples
ourselves. And a lot of voices will use square or sawtooth waves which
can be tuned accurately. This isn't a good argument for poor tuning
precision, even if it is the argument they give.

Drew Skyfyre wrote:

> Hate to be a wet blanket, but how many commercial synth co.s do you
> think are actually ever going to implement realistic microtuning
> capabilities ?

Well, we can but ask. Most manufacturers seem to be ignorant that we
_want_ higher precision. I prefer to focus my efforts on encouraging
people to use the tuning capability they already have. Hence my website
-- now with an equal temperament page!

There we are, had to get the plug in.

> Ensoniqs do 0.4 [cents]

Do they? Have you tested the accuracy, or is this merely the precision
of the tuning table?


Graham Breed
gbreed@cix.co.uk www.cix.co.uk/~gbreed

>Wouldn't it be preferable for any synth that incorporates decent
>microtuning to
>not be sample based ,but rather generate its sounds using an actual
>synthesis technique,
>like Physical Modelling,FM,etc. ?

Because ...?

> From: mr88cet@texas.net (Gary Morrison)
> John (Loffink), that might be a useful column to add to your web page.
> A fair number of synthesizers are not multitimbral, and I suspect that
> people would like to know that.

I've recently added a synth help page with links that (sometimes) have this
information. I'd like to keep the information on my charts to a manageable
level.

> From: Drew Skyfyre
> Hokay , reality check.
>
> Hate to be a wet blanket, but how many commercial synth co.s do you
> think are actually ever going to implement realistic microtuning
> capabilities ? All this wish list stuff brings out the kid in me ,but
> I've seen
> synth models com and go, and "the more things change,the more they stay
> the same".
> >From the responses I've gotten from co.s (except Ensoniq!)after
enquiring
> about microtuning,
> I'd say fat chance. It isn't up there on their list of "shiny new
> features that will
> dazzle music store visitors and seperate them from their money."

I've watched synth models come and go since 1979. Back then, I couldn't
buy anything except a Buchla or Serge Modular or Korg PS series that could
do just intonation. Actually, I couldn't buy them because I couldn't
afford their multiple thousands of $ price ranges. By 1989 there were a
handful of models to choose from. Today there are dozens of current models
supporting tuning tables, including several portable keyboards (the kind
with builtin speakers) from Yamaha, normally the bastion of lowest common
denominator consumerism. So progress has definitely been made. Nobody
expects the wishlist to be implemented overnight, but manufacturers
certainly can't do it unless they hear our input.

The microtuning wish list should also be useful for software synthesizers,
a market that is still in its formative stages and much more adaptable than
commercial synths.

Microtonalism will be raised on the priority list when there's more
commonly available music out there to be heard like Robert Rich. That's
not up to the companies, that's up to us. The more instruments that have
microtuning features, no matter how primitive they may be, the greater
chance we have of this happening.

> From:
>
> There is a paper in the Journal of the Acoustical Society of America Vol.
24
> No. 6 published in November 1952 by J. Donald Harris entitled: "Pitch
> Discrimination".

The paper you cited is one of the reasons why we don't get better than 1
cent resolution from our synthesizers. Is there a citeable reference that
gives pitch discrimination in terms of harmonic context? I know list
members have done these experiments, but have the results ever been
published anywhere that carries the weight of a JASA paper?

John Loffink
jloffink@pdq.net

Another thing :

Wouldn't it be preferable for any synth that incorporates decent
microtuning to
not be sample based ,but rather generate its sounds using an actual
synthesis technique,
like Physical Modelling,FM,etc. ?

I've read a number of warnings about the tendency of E-mu thingies to not
transpose
samples properly. But natural, unless a sample is retuned only within +/-
@ 4 whole-tones.

I'm for the better informed among you to make a nice neat wish list with
2 levels
of implementation and then we should send it over to Ensoniq.

Cheers,
Drew

"It irritates me that neither Lycurgus nor Plato had any knowledge of
them,...
How remote from such perfection would Plato find that Republic which he
thought up
'viri a diis recentes' (men fresh from the gods)."
-Michel de Montaigne (1533-1592), "On the Cannibals",an essay.