K2000/K2500 Intonation opinions requested

I am seeking input from tuning list subscribers on a new feature for the
Kurzweil K2000/K2500 synthesizer/samplers. The current operating systems for
these instruments does not change the pitch of currently sounding notes when
the intonation table is changed. A forthcoming operating system upgrade may
change this to instantaneously change the pitch of all sustaining and
released notes when the intonation table is changed. My questions are:

1. How many members would like all notes to instantaneouly change in pitch?
2. How many members would prefer to have the operating system remain as is
so that only new notes use the newly selected intonation table?

I have versed this as an either/or question because the K2000/K2500 User
Interface does not have space to select between the two options. A feature
to select between instantaneous/new note only tuning would have to be a
"hidden function" and will take more time to implement. In other words, if
the change IS implemented then current users who need the new notes only
version would not be able to upgrade their operating system. Also, since the
K2000 is ROM based, it is unlikely that more than one operating system
upgrade will be released. This is not an issue for the K2500 Flash ROM based
O.S. No other aspects of the intonation handling will be changed with the
next upgrade. It will still be limited to one system level intonation table
at a time.

I've used many intonation capable MIDI instruments, including the TX81Z,
DX7IIFD+E!, EPS, EPS-16 Plus and the K2500. I believe the K2000/K2500 to be
one of the most flexible in this regard, and hope to help it continue to
evolve in its intonation capabilities.

If you have other requests for Kurzweil intonation features, I can't really
process them at this time but hope to do so at a future date.

Important: If you send email directly to me, please use my Compuserve
account: 75023.2426@compuserve.com. I will be moving in a few weeks from
Kurzweil in Massachusetts to a new job in the southern U.S. and will not
receive any mail for the ycrdi.com address after that time. I could be
offline as long as 3 or 4 weeks but hopefully will not lose any messages. I
will still remain in contact with the Kurzweil group in regards to intonation
issues.

John Loffink
Senior Hardware Engineer
Young Chang Research & Development Institute
(Kurzweil Music Systems)
75023.2426@compuserve.com





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I am interested in Johnny Reinhard's remarks that cents notation is
helpful to performers. I can readily believe this, provided that fine
discriminations aren't necessary. I imagine that performers then identify
a sound or fingering with a cents designation. Would that be right?

I still don't like this for analytical purposes, however. I wonder
whether performers prefer this notation to others or just get used to it.

Paul Rapoport

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Before meaningfully playing a microtonal piece of music, pitch
discrimination must be heard in the mind's ear of the player; and at the
same time be written clearly regarding ideal theoretical pitch placement.

Interval relationship sensibilities are learned independently from exact
points of pitch, however.

The sense and the logic of the relationships of tones is apart from
their symbology. Using the method of notation I described is the most
accurate and straight forward approach I've yet discovered.

Johnny Reinhard
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com

On Thu, 24 Oct 1996, Paul Rapoport wrote:

> I am interested in Johnny Reinhard's remarks that cents notation is
> helpful to performers. I can readily believe this, provided that fine
> discriminations aren't necessary. I imagine that performers then identify
> a sound or fingering with a cents designation. Would that be right?
>
> I still don't like this for analytical purposes, however. I wonder
> whether performers prefer this notation to others or just get used to it.
>
> Paul Rapoport
>

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Thanks to Johnny Reinhard for his reply on using cents notation. It is
true that in using other signs as accidentals in front of notes you may
get notes with conflicting directions, e.g. an up arrow but a down comma
of some other sort, or two of one and three of another.

But I don't see this as a conflict. Nor would I see it as precipitating
working out cents values. In JI music that is truly harmonic, each pitch
may come from another, so that the signs in front of the notes show this
relationship, and therefore how to tune the note, including whom and what
to listen to most closely in the ensemble. Certainly Ben Johnston's
notation works this way, despite whatever problems it may have. It
suggests to performers that they are in a sense performing relationships.
Cents notations to me suggest performing fixed values out of context.

If Johnny finds that performers have to calculate cents, then I wonder
whether performers faced with a cents-notated score for JI have to
determine relationships, since no one performs numbers (i.e. cents
values) in an absolute sense.

In the only piece of JI I have had performed, the (amateur) performers
were indeed initially confused by the signs, wanting to know just how flat
or sharp certain notes were. But what does "a little sharp" or "quite
flat" mean when all you want is certain notes to be in tune? I taught them
to hear the harmonic structures, I suppose with some success, and kept the
cents values for the preface to the score, for those interested. This
turned out to be fairly close to 0% of the performing group, even
including a math teacher.

But I emphasize I have not had a lot of experience with performers in JI;
where I live there is little opportunity for this kind of thing.

Paul Rapoport


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If I read a notation that says 969 for this note and 840 for that, unless
I know the theory and have memorized arbitrary numbers, these two mean
rather little. But if I have a sign for the 7th harmonic and another for the
13th, then I know the relationships and can begin to hear and produce the
intervals.

On the other hand, I have produced music in which there is a variety of
signs going up and down, and performers don't generally have a clue where
the note is. Cents values would tell them.

These two problems are different sides of the issue, but I will vote for
the first every time. The reason is that although cents notations provide
descriptive adequacy, only something like the other one provides
explanatory adequacy. In other words, performers can learn cents
notation, but surely to provide the right notes they need to hear (and in
that sense understand) the interval structures. The structures provide
the explanation, the ability to generalize and therefore learn in the
classical sense. The cents values by themselves are a series of referents
without relation, rather like letters of an alphabet without words, or
perhaps words without syntax/semantics.

None of this means that performers can't learn from cents, but they must
go beyond the rather simple linear-looking (actually logarithmic)
relationships they express.

Johnny? Your turn. Maybe we're not even talking about the same thing.

Paul Rapoport

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Thanks Paul, we are talking about different things. The irony is that
the difficulty with which we try to express musical concepts on the internet
shows up the problems with computer notation we are presently reading.

> If I read a notation that says 969 for this note and 840 for that, unless
> I know the theory and have memorized arbitrary numbers, these two mean
> rather little. But if I have a sign for the 7th harmonic and another for the
> 13th, then I know the relationships and can begin to hear and produce the
> intervals.

Cents notation uses all the symbols of 24ET: this means that a 969 would
be notated as a B natural with a "-41" above the notehead (assuming C as
the fundamental). Hearing the basic essential intervals of consonance
(and perhaps dissonance) must be internalized by players independently by
players.

Perhaps we players are using cents the way Yamaha uses its 1024 points of
reference. Only our expansion to 1200 is more accurate.

Johnny Reinhard

Incidentally, does the list know that Johann Philipp Kirnberger, prize
student of J.S. Bach invented the notation of "i" before the very same B
natural to indicate that it was a 7/4 relationship (of 969 cents)?

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> I think Johnny's point is that if a note-head had, for example "-15" over it
> (meaning that it is to be played fifteen cents flat of 12TET), you can whip out
> a fingering variation that you have memorized to be roughly that much flat of
> that note. Once you know the 12TET fingerings, and any player of a given
> instrument would, it wouldn't take much more effort to augment that knowledge
> with a series of memorized cent variations.

If more than a few cents variations are put in front of a performer, I'd
guess that either it wouldn't make any difference, or it would be
difficult, unless you want only gross approximations.

I must say that the concept of modern woodwind instruments playing
microtonal music is one that does not interest me much. Not meant to upset
Johnny, who probably has more experience in this than anyone, but I don't
find the resultant timbres acceptable in many cases, and the awkward
fingerings work against all the developments of these instruments in the
past 200 years (possibly bassoon excepted).

Johnny, I'd be interested in your comments on this.

> That is far easier than performing from a 7th or 13th harmonic sort of
> description, because with that you'd have think - in realtime, on the fly - "OK,
> what's the root of this chord (that in itself is especially tough since any
> realistic performance each performer will have PARTS, and not the whole
> conductor's score)? How does this note relate to that root? How much flat is a
> 13th harmonic from the closest 12TET pitch?" Or similarly, in 17TET say, "OK,
> what's the tonic now? Which scale step is this note relative to that tonic?
> How much sharp or flat is that 17TET note from the 12TET value that my
> instrument is designed to play?"

I don't think so. In JI in particular, the relationships are important,
and you may not have to have a score, although knowing where your note
"comes from" is significant. It may come from a previously sounding note.
And in a fair amount of JI, the number of different notes in a passage
(however defined) may not be high, so that memorizing a relationship sign
isn't difficult, and no more so than a cents value. I agree that it's not
easy, and in ETs it's still harder.

It won't take a sharp person to figure that I don't work with performers
very often in this material, partly because all the notations are a
problem, which reflects bigger problems in actually performing the music
with all but the most dedicated and experienced performers. In the
electronic case, the relationships in the score are paramount and then the
cents variations are not helpful unless you've memorized their
relationships--in which case why not use the relationships directly?

I wouldn't want, however, to teach people to hear and play the 13th
harmonic in relation to 12-tET. Gary, is that what you meant?

Paul R.

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> If I read a notation that says 969 for this note and 840 for that, unless
> I know the theory and have memorized arbitrary numbers, these two mean
> rather little. But if I have a sign for the 7th harmonic and another for the
> 13th, then I know the relationships and can begin to hear and produce the
> intervals.

I think Johnny's point is that if a note-head had, for example "-15" over it
(meaning that it is to be played fifteen cents flat of 12TET), you can whip out
a fingering variation that you have memorized to be roughly that much flat of
that note. Once you know the 12TET fingerings, and any player of a given
instrument would, it wouldn't take much more effort to augment that knowledge
with a series of memorized cent variations.

That is far easier than performing from a 7th or 13th harmonic sort of
description, because with that you'd have think - in realtime, on the fly - "OK,
what's the root of this chord (that in itself is especially tough since any
realistic performance each performer will have PARTS, and not the whole
conductor's score)? How does this note relate to that root? How much flat is a
13th harmonic from the closest 12TET pitch?" Or similarly, in 17TET say, "OK,
what's the tonic now? Which scale step is this note relative to that tonic?
How much sharp or flat is that 17TET note from the 12TET value that my
instrument is designed to play?"

The cent values, as Johnny so aptly pointed out, are ideal prescriptive
notation, whereas the harmonic numbers or whatever, are ideal descriptive
notation. Harmonic numbers on a JI conductor's score make it a whole lot easier
to figure out what effect is to be achieved, but they are very impractical to
work with in realtime on a performance basis.


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On Sun, 3 Nov 1996, Paul Rapoport wrote:

> If more than a few cents variations are put in front of a performer, I'd
> guess that either it wouldn't make any difference, or it would be
> difficult, unless you want only gross approximations.

Change to "if less than a few cents" and the above statement would be
accurate. Just relationships are heard on a different level...a separate
track form linear measurement by cents.

> I must say that the concept of modern woodwind instruments playing
> microtonal music is one that does not interest me much. Not meant to upset
> Johnny, who probably has more experience in this than anyone, but I don't
> find the resultant timbres acceptable in many cases, and the awkward
> fingerings work against all the developments of these instruments in the
> past 200 years (possibly bassoon excepted).
> Johnny, I'd be interested in your comments on this.

Today I learned a bit more about bagpipes than I would ever have before,
so I understand your lack of involvement with woodwinds. Contrary to
what you might think, microtones are rather easily invoked by
professional players. One would be hard pressed to tell whether a
microtone was played or a "normal" note. I once played the slow movement
melody of the Mozart Bassoon Concerto a quartertone low during a lecture
in York, England and asked if anyone heard any microtones. They answered
assuredly - not at all. I then told them that each and every note was a
microtone and they were aghast.

> > That is far easier than performing from a 7th or 13th harmonic sort of
> > description, because with that you'd have think - in realtime, on the fly - "OK,
> > what's the root of this chord (that in itself is especially tough since any
> > realistic performance each performer will have PARTS, and not the whole
> > conductor's score)? How does this note relate to that root? How much flat is a
> > 13th harmonic from the closest 12TET pitch?" Or similarly, in 17TET say, "OK,
> > what's the tonic now? Which scale step is this note relative to that tonic?
> > How much sharp or flat is that 17TET note from the 12TET value that my
> > instrument is designed to play?"
>
> I don't think so. In JI in particular, the relationships are important,
> and you may not have to have a score, although knowing where your note
> "comes from" is significant. It may come from a previously sounding note.
> And in a fair amount of JI, the number of different notes in a passage
> (however defined) may not be high, so that memorizing a relationship sign
> isn't difficult, and no more so than a cents value. I agree that it's not
> easy, and in ETs it's still harder.
>
> It won't take a sharp person to figure that I don't work with performers
> very often in this material, partly because all the notations are a
> problem, which reflects bigger problems in actually performing the music
> with all but the most dedicated and experienced performers. In the
> electronic case, the relationships in the score are paramount and then the
> cents variations are not helpful unless you've memorized their
> relationships--in which case why not use the relationships directly?

Wherein an instrument can utilize tabliture, use it. Guitar chords or
Harry Partch Bass Marimba notation make sense because of the culture
surrounding those respective instruments. Cents notation as I've
described it puts the player in the "ball park" so that they can
appreciate the relative qualities of specific intervallic relationships.

For instance: if you want a player to play a 5/4 above a C,
notate it as an E -14 and
the player will IMMEDIATELY understand the the traditional E is to be
approached at a lower pitch level, thereby aiding in the understanding of
placing the pitch _in relation_ to another. If you want a player to play
a 5/4 above a C +10, then notate an E -4. Players would see that the E
-4 is not so different than a traditional E, just shaded in a low direction.

If one uses cents combined with a basic quartertone notation, then it
will not be necessary to "teach" players much at all, which will more
than likely make them happier about participating in a new sonic
adventure. I think it is incumbant upon a microtonal composer that is
writing for players to utilize the decades of learning that they have
invested in their careers. They will realize the justice of the new
intervals.

Johnny Reinhard

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> If more than a few cents variations are put in front of a performer, I'd
> guess that either it wouldn't make any difference, or it would be
> difficult, unless you want only gross approximations.

Actually you might be surprised, because there are patterns you can use to
derive, and more importantly to remember, them. One easy example is forked
fingerings on woodwinds. This is a little bit of an overgeneralization but it's
mostly true: The more toneholes you close below the highest opened tonehole the
flatter that note gets. Similarly on brasses, there are certain valve
combinations that are known to tend to be sharp or flat. So the problem is
essentially one of quantifying and memorizing.



> > ... Which scale step is this note relative to that tonic?
> > How much sharp or flat is that 17TET note from the 12TET value that my
> > instrument is designed to play?"
>
> I don't think so. In JI in particular, the relationships are important,
> and you may not have to have a score, ... so that memorizing a relationship
sign
> isn't difficult, and no more so than a cents value.

Not too difficult you think eh? Perhaps this isn't saying much, but I know
that I couldn't do it.

Let's assume that you have notation system that can augment each note-head
with information for both frequency-ratio relative to a tonic, and with the
choice of tonic itself (it would be pretty hopeless otherwise). Let's also
assume that tonics don't wander (without cent-based notation that would utterly
hopeless although pretty feasible with it).

The composition is notated in C Major. Two bars back you saw a notated
tonic-shift to A, and somehow the notation somehow prescribes that to be a 5:3 A
relative to the C of the key signature. You encounter a sequence of four
quarters in 4-4 time at 120bpm (a moderate pace of notes). The notes are:

C# with an 11 over it (meaning 11th harmonic of the A),
D with a 4 over it (meaning the usual 4:3 to A),
B with a 10 over it (meaning 10:9 to the A),
F# with a 5 over it (meaning 5:3 to the A).

OK, let's play it now. Here's what you think:

"The shift to the A tonic happened four seconds ago, you got that, right? It
was an A right, or was it D like the last time? Yeah, A. OK the first beat of
the is coming up measure; better get the first note out. A. Let's see that's
a comma-shift upward. No downward. Downward, right. Everything is shifted a
comma down from what the harmonics tell me. First note C# as 11th harmonic.
11the harmonic is pretty much right on a quarter tone. So does that mean that I
play a quartertone sharp or flat of a C#? Flat, right flat; that's our
convention. Wowwy, this half-second-long beat sure has gone by fast!

Whoah, that clarinet just played a real klinker on the half-beat there!
Should I adjust my pitch? No, that's OK, that's pretty much what it sounded
like in our one-and-only rehearsal. Never mind that; time's a-wastin'; I'd
better get back to get this C# out! OK so we've got a quartertone flat of a C#,
so that's this fingering. No wait, this is all relative to A, not C, so I have
to go down a comma from there. I guess that would be this fingering instead.
Right. OK ready to roll... Now where's the beat? Ooooookay, right ... NOW!
Switch fingerings.

How does it sound? Ooop, a little flat. Probably better lip it up a tad."

That's a pretty full half-second of your life! Those extra steps of
remembering how an 11th harmonic is tuned, and then offsetting that by how much
an A is tuned relative to a C sure would be great not to have to work out!


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Hi, does anybody on this list have a good system for notation of 19-ET and 31-ET
in a way where you maintain the relation to the 12-ET pentagram?

Jakob Draminsky Hojmark
101717.2145@compuserve.com



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From: PErlich@Acadian-Asset.com
Subject: RE: notation
PostedDate: 07-08-97 21:59:32
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I wouldn't know a 12-ET pentagram if it came up and bit
me on the nose. However, I find conventional staff
notation perfectly adequate for general meantones,
including 19 and 31tet.

It can be useful to have symbols (e.g. + and -) for
raising and lowering by a *quatertone* being the
difference between a diatonic and chromatic
semitone. This is 1 step in 19 and 31 tet, and is
also consistent with a quartertone being approx. half
of a 12TET semitone, and a neutral third specified
accordingly.

For this to make sense, 7/4 _has_ to be an augmented
sixth, not a minor seventh. It could, though, be a
subminor seventh, or a minor seventh minus a
quartertone.



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From: gbreed@cix.compulink.co.uk
Subject: Re: Natural Harmony
PostedDate: 11-08-97 20:46:10
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>Hi, does anybody on this list have a good system for notation of 19-ET and
>31-ET
>in a way where you maintain the relation to the 12-ET pentagram?

"Pentagram"?!

Anyway I think Paul Erlich reponded with the usual notation systems for
those two tunings.



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From: mr88cet@texas.net
Subject: Re: 13
PostedDate: 18-08-97 05:08:02
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>> What about a standard notation that can accurately capture any tuning?
>> (freqeuncy,volume,time)
>>
>> Two people to talk to along those lines are Ezra Simms and Johnny
>> Reinhard. Johnny is on the list, but I don't think Ezra is.

I have written an article about that--no conclusions, but it discusses the
pros and cons of what is out there. If anyone is interested, please let me
know and I'll wire or mail one to you.

Also, for those not on Newband's mailing list, I'll anounce a concert of
Dean Drummon's "The Last Laugh," for Newband accompanying silent film. It
is for large ensemble including all of Drummond's and 9 of Partch's
instruments:

3/5/98, 8pm: SUNY Purchase (914) 251-6200
3/11/98, 8pm: Library of Congress, Wash. DC (202) 432-SEAT
3/14/98, 8pm: The Kitchen, NYC (212) 255-5793

Adam B. Silverman
153 Cold Spring Street; A5
New Haven, CT 06511
adam.silverman@yale.edu