Notation: cents make sense?

making a case for different notation systems that reflect the needs
of the instruments used:

jpehrson@rcn.com quoted from Johnny Reinhard:
>
> "Cents makes the most sense:
>
> 1200 divisions of the octave being the very threshold of human
> hearing for pitch differentiation. Additionally, cents allows for
> the total intellectualization of all pitch "points" on the line of
> frequency to be immediately apprehended. Most importantly, players
> always reference new pitches to constants -- like open strings and
> harmonics -- in order to find exotics. Microtonal notations that
> represent moving relationships can lose their constants in pitch
> drift, making it difficult to come up with the necessary hand
> positions or fingerings to produce the appropriate sounds. The
> solution is for all pitches to relate in a unified field in order to
> be fully prescriptive for players. Cents also anchors us to present
> music tradition -- no small feat.

In my little experience with microtonal music (29tet, quasi-random,
but actually ordered into u- and o-tonal regions involving the
factors 7, 11, and 13 (i.e., intervals which along with fourth and
fifth are represented fairly well by the temperament)) I was glad
about the alternatives.

Some of us wanted - and did - stick to "piano notation" with cent
deviations. They had discrete fingerings for each pitch figured out
and used the staff for a rough representation of the melody. They
had _no_ constants to refer to, each note was an entity by itself,
and I think that this is the reason the notation worked for them.

If I - on a trombone - do not play excessively high, I cannot
reference e.g. the 13th partial to a constant as postulated in the
quote above, and if I do (as with all the lower partials), it only
helps me playing very specific intervals that rarely occur in most
music. But I can play relative fourths, fifths, or major tones from
any starting pitch (gladly accepting overtones of Bb as constants if
any should occur), and I can make myself play pythagorean thirds,
too. The 29tet scale almost consists of major tones divided into
five parts, so the practical notation for me came close to
combinations of pythagorean whole tone scales with additional
accidentals (+1, +2, -1, -2). Actually, one of the tones has to be
minor and divided into 4 parts. Pythagorean notation singles out
this interval as a diminished third. The steps then are 48c instead
of 41c, which pitch drift may or may not iron out (as we didn't play
along the scale and switched whole tone scales on intervals wider
than a fifth, they never occurred).

I don't want to claim that I played this scale perfectly, but I
always had the feeling that I knew what I should be doing. "Play the
note 21 steps down" meant to go down a fifth (17 steps) and then 4
fifths of a major tone. In "piano notation" it would be "Go down
900c and up 31c". Am I to learn 100c steps (how?) on an instrument
where I will never use them?

I think different musics need different notations, and different
intruments need different notations. The composer might want to use
still another one. Why be more consistent than Partch?

klaus

> Of course, by using enharmonic
> quartertones, one need not use numbers larger than 25 to indicate
> cents distinctions (recently pointed out by Paul Erlich, a
> subscriber to the internet's busy Tuning List)."

In a message dated 4/23/01 7:18:38 PM, KSchmir@z.zgs.de writes:

<< > 1200 divisions of the octave being the very threshold of human

> hearing for pitch differentiation. >>

you're joking, right?
perception of JNDs changes with register. study your psychoacoustics.

In a message dated 4/23/01 8:39:58 PM Eastern Daylight Time,
Pitchcolor@aol.com writes:

> In a message dated 4/23/01 7:18:38 PM, KSchmir@z.zgs.de writes:
>
> << > 1200 divisions of the octave being the very threshold of human
>
> > hearing for pitch differentiation. >>
>
> you're joking, right?
> perception of JNDs changes with register. study your psychoacoustics.
>
>

Please enlighten: what are JNDs and how is this relevant to the ability to
differentiate finer than a single cent?

Johnny Reinhard

In a message dated 4/23/01 8:18:49 PM Eastern Daylight Time, KSchmir@z.zgs.de
writes:

> ". Am I to learn 100c steps (how?) on an instrument
> where I will never use them?

Learning to hear different intervals is what it is all about. Having to use
100 cents as an interval is not necessary. Your reference can be 386 cents,
for example.

> I think different musics need different notations, and different
> intruments need different notations. The composer might want to use
> still another one. Why be more consistent than Partch?
>

Tablature is ancient and still works. I used to use tablature with the
bassoon (for Dune), but gave it up because it still leaves to much leeway on
a wind instrument. It is the mind that actually gets tuned up on a lot of
instruments. They are simply not able to deliver with mere "press and blow."

Johnny Reinhard

In a message dated 4/23/01 8:04:14 PM, Afmmjr@aol.com writes:

<< Please enlighten: what are JNDs and how is this relevant to the ability to
differentiate finer than a single cent? >>

JND = Just Noticable Difference

not suggesting that discrimination is finer than a "cent", rather, it is
usually worse, esp. in extreme registers or in extreme intensity. my main
point is that the cent isn't really very useful for discussing perception.
sorry I can't summarize the literature right for you, but that's the main
point

In a message dated 4/23/01 9:20:23 PM Eastern Daylight Time,
Pitchcolor@aol.com writes:

> not suggesting that discrimination is finer than a "cent", rather, it is
> usually worse, esp. in extreme registers or in extreme intensity. My main
> point is that the cent isn't really very useful for discussing perception.
>

This is rather my point, that musicians can hear "up to" a cent so that 1200
divisions of the octaves is the practical (or real world) threshold of what
we -- as musicians -- can make sense of. If I could hear better than the
system of notation, than it really would be doing me very much good.

Johnny Reinhard

--- In tuning@y..., Pitchcolor@a... wrote:
>
> In a message dated 4/23/01 8:04:14 PM, Afmmjr@a... writes:
>
> << Please enlighten: what are JNDs and how is this relevant to the
ability to
> differentiate finer than a single cent? >>
>
> JND = Just Noticable Difference
>
> not suggesting that discrimination is finer than a "cent", rather,
it is
> usually worse, esp. in extreme registers or in extreme intensity.
my main
> point is that the cent isn't really very useful for discussing
perception.
> sorry I can't summarize the literature right for you, but that's
the main
> point

Hi Pitchcolor -- well I've studied this, and while it is true that
the melodic JND is 5 cents in the best register and worse in lower
and very high registers, the harmonic JND is far finer. Piano tuners
achieve an accuracy within 1 cent for the generating intervals, and
with harmonic-series timbre instruments such as reeds, brass, or
bowed strings (or most synth sounds), you can achieve even greater
accuracy in JI intervals by tuning to eliminate beats. If you've ever
tried playing with JI on a digital synth with limited resolution
(usually in the 1-3 cent range), you'll know what I'm talking about.

--- In tuning@y..., Pitchcolor@a... wrote:
>
> In a message dated 4/23/01 8:04:14 PM, Afmmjr@a... writes:
>
> << Please enlighten: what are JNDs and how is this relevant to the
ability to
> differentiate finer than a single cent? >>
>
> JND = Just Noticable Difference
>
> not suggesting that discrimination is finer than a "cent", rather,
it is
> usually worse, esp. in extreme registers or in extreme intensity.
my main
> point is that the cent isn't really very useful for discussing
perception.
> sorry I can't summarize the literature right for you, but that's
the main
> point

Here's another point -- we don't hear intervals in terms of "number
of JNDs wide". We hear logarithmically. A musician who learns what
968 cents sounds like in the lower register will know what it sounds
like in the higher register. There are small distortions depending on
volume etc. but these are relatively unimportant.

--- In tuning@y..., PERLICH@A... wrote:

/tuning/topicId_21466.html#21483

> --- In tuning@y..., Pitchcolor@a... wrote:
> >
> > In a message dated 4/23/01 8:04:14 PM, Afmmjr@a... writes:
> >
> > << Please enlighten: what are JNDs and how is this relevant to
the
> ability to
> > differentiate finer than a single cent? >>
> >
> > JND = Just Noticable Difference
> >
> > not suggesting that discrimination is finer than a "cent",
rather,
> it is
> > usually worse, esp. in extreme registers or in extreme
intensity.
> my main
> > point is that the cent isn't really very useful for discussing
> perception.
> > sorry I can't summarize the literature right for you, but that's
> the main
> > point
>
> Here's another point -- we don't hear intervals in terms of "number
> of JNDs wide". We hear logarithmically. A musician who learns what
> 968 cents sounds like in the lower register will know what it
sounds like in the higher register. There are small distortions
depending on volume etc. but these are relatively unimportant.

Wow... well this seems like an EXTREMELY IMPORTANT point if "cents
notation" is going to work at all!

_________ ______ ______
Joseph Pehrson

In a message dated 4/23/01 10:42:07 PM, PERLICH@ACADIAN-ASSET.COM writes:

<< Hi Pitchcolor -- well I've studied this, and while it is true that
the melodic JND is 5 cents in the best register and worse in lower
and very high registers, the harmonic JND is far finer. Piano tuners
achieve an accuracy within 1 cent for the generating intervals, and
with harmonic-series timbre instruments such as reeds, brass, or
bowed strings (or most synth sounds), you can achieve even greater
accuracy in JI intervals by tuning to eliminate beats. If you've ever
tried playing with JI on a digital synth with limited resolution
(usually in the 1-3 cent range), you'll know what I'm talking about. >>

Hi. Of course, with relatively steady state tones which do not change in
intensity, what you say is true. I think my point was in the context of
acoustic instruments, where a JND is a different sort of animal. Yes, I can
hear deviations of much less than a cent when I'm tuning a pipe on my pipe
organ, but our perception does not operate that way in "live performance,"
which was the context of the original post as I understood it.

In a message dated 4/23/01 10:43:24 PM, PERLICH@ACADIAN-ASSET.COM writes:

<< We hear logarithmically. A musician who learns what
968 cents sounds like in the lower register will know what it sounds
like in the higher register. There are small distortions depending on
volume etc. but these are relatively unimportant. >>

right, except that these small distortions are usually not small and can be
highly significant to our perception. You know that there are more variables
thrown into the perceptual equation than we can count, and at this point in
view of known research, we know clearly that we cannot equate our perception
of an interval with any single "cent value". What we know is that perception
cannot be and should not be quantified this way.

In a message dated 4/23/01 11:18:53 PM, Pitchcolor writes:

<< I can hear deviations of much less than a cent >>

I mean JND = 5 cents

In a message dated 4/23/01 9:49:12 PM, Afmmjr@aol.com writes:

<< This is rather my point, that musicians can hear "up to" a cent so that
1200
divisions of the octaves is the practical (or real world) threshold of what
we -- as musicians -- can make sense of. >>

Fair enough, but the implications of this point are suspect, because making
sense of what we hear in terms of cents is an intellectual construct - not a
real world threshold. I think we probably agree on this... anyway, you and I
have better things to do.

best,
Aaron

In a message dated 4/24/01 12:25:52 AM, jpehrson@rcn.com writes:

<< A musician who learns what
968 cents sounds like in the lower register will know what it
sounds like in the higher register. >>

we only think we know the same interval in all registers. Perception of
intervals changes alot with register; the same intervals in higher register
will sound narrower than in low regster - largely a result of the changes in
intensity.

Johnny Reinhard wrote:
> Learning to hear different intervals is what it is all about.
> Having to use 100 cents as an interval is not necessary. Your
> reference can be 386 cents, for example.

Sorry!
I thought you were advocating equal tempered notation with cent
deviations. This would probably work for run-of-the-mill guitars,
modern woodwinds, and certainly synthesizers with editable tuning
maps, where 100c steps are "built in" as a reference, whereas
singers (no reference at all), brass players (different reference
intervals from each harmonic) and, to a lesser extent, players of
unfretted string instruments (the tuning intervals as reference) may
want the quality (5-, 7-, 11-ish) of their melodic intervals
indicated in a more direct way.
Tempered notation with the licence to deviate (common practice, in
other words) is fine whenever the performers understand the harmonic
idiom.

Klaus

Wow, I guess I hadn't realized that there is such a gulf between "hearing" an
interval in the head and "producing" it. Keyboard players might be able to
skirt the issue, but most every other musical instrument must be heard in the
mind before attempting to produce it, as with the voice. Frankly, 12-tET is
more difficult to learn to hear than 5-limit JI which is contained in the
timbre of your voice.

In teaching bassoon, I teach a distinctive "resonant pocket" of distinctive
harmonic relationship timbre, unique to each fingering. This translates to a
distinctive inner shape and embouchure and wind velocity for each note.
Rounding out pitch to cents is the only humane thing to do.

Johnny Reinhard

--- In tuning@y..., Pitchcolor@a... wrote:
>
> In a message dated 4/24/01 12:25:52 AM, jpehrson@r... writes:
>
> << A musician who learns what
> 968 cents sounds like in the lower register will know what it
> sounds like in the higher register. >>
>
> we only think we know the same interval in all registers.
Perception of
> intervals changes alot with register; the same intervals in higher
register
> will sound narrower than in low regster - largely a result of the
changes in
> intensity.

Hello there, Aaron (?), and I think you may be basing a lot of your
information on psychoacoustic experiments with sine waves (where true
2:1 octaves sound flat, especially in the lower and higher
registers). Our intervallic acumen is far greater with normal
instrument timbres with harmonic series overtones -- these are more
important than the fundamental in producing the sensation we
call "pitch". I recommend you look over the research you've been
citing and make sure sine waves aren't being used (I'll bet they
are) -- I'd completely agree with you that giving 968 cents to 1 cent
accuracy is pretty meaningless for sine waves -- but it certainly is
not meaningless for some of the very slow, beautiful JI music with
harmonic timbres that some of our list members create.

In a message dated 4/24/01 4:10:21 PM, PERLICH@ACADIAN-ASSET.COM writes:

<< I think you may be basing a lot of your
information on psychoacoustic experiments with sine waves >>

Thanks; this is a good point. A lot of the research does deal with sine wave
experiments, and a lot of the percieved effects detailed in many studies are
fascinating but have little to do with perception of complex timbres, as you
note. However, I also try to pay close attention to what I hear with my own
ears, and I try not to cite a claim from some research that I have not
confirmed by my own experience. Some of this experience is: I've worked as
a pipe organ tuner and I own a pipe organ which I tune myself; I tune pianos;
I'm a percussionist, I play viola, guitar, piano; I've sung in many choirs
(some incredible and some not so good); I've taught voice; I've studied
trumpet, horn, etc. though I don't play them. I've played in orchestras as a
percussionist and as a violist, I've performed on a lot of recordings; I
write a lot of music and I listen to a lot of music both live and recorded.
It's not that I think this is all that unique; I say all of this to give you
some idea of where I'm coming from - that I have learned about the practical
aspects of tuning and the physical and psychological problems involved with
tuning in practice first hand. The effects I've mentioned actually exist in
my own experience, and I try to speak from that.
Aaron

In a message dated 4/24/01 4:10:21 PM, PERLICH@ACADIAN-ASSET.COM writes:

<< I'd completely agree with you that giving 968 cents to 1 cent
accuracy is pretty meaningless for sine waves -- but it certainly is
not meaningless for some of the very slow, beautiful JI music with
harmonic timbres that some of our list members create. >>

with computers and synthesis, every cent counts when the "patch" isn't a
bandwidth sound like a "string orchestra" (i.e. I noticed that mclaren uses
synth string sounds to cover up some tuning characteristics for demonstration
purposes). Computers and synths experienced through headphones have their
own pitch phenomena, though. But I think this discussion generally leads to
an abyss, and I'm content to leave it at that.
Aaron