No doubt about Lehman's Bach scale

Hi all,

I've just recently found out how to *manually* re-tune my
Roland keyboard to any different 12-note tuning; yes, I
found the manual! But it doesn't seem there's any way to
download a tuning to it, or have it remember a tuning I've
set (except for a toggle between the current non-standard
tuning and standard 12EDO).

So it was opportune that I just now read the following two
old messages, from Bradley Lehman answering George
Secor, and from George Secor answering Carl Lumma.

I decided to make my own little (non-Bach) experiment.
Having retuned the keyboard (to the nearest cent), I then
proceeded to improvise in all major and minor keys for about
30 minutes. I then switched back to standard for 5 minutes,
then again to Brad's tuning for another 5 minutes.

Verdict: Brad's tuning is decidedly smoother in A major,
and keys near to it in the cycle of fiths, than 12 EDO.
There's a more singing tone, less roughness, slower beating.
For contrast, I went to the other extreme, playing in Ab
major and minor and also in Db. I was pleased to find how
smooth these keys were.

Of course, this has absolutely no bearing on what tunings
Bach used! But I do like the sound of this tuning, both with
the sampled piano and harpsichord sounds on this keyboard.
Because it's late at night, I didn't let fly with the pipe organ
:-) tho I must try that tomorrow.

Regards,
Yahya

_______________________________________________
Date: Thu, 25 Aug 2005
From: Bradley P Lehman
Subject: re: Further doubts about Lehman's 'Bach' scale

> (...) While you might get some interesting results playing
> some of Bach's music in it, I would not expect anything in the key of
> A major (its worst triad) to fare particularly "well" (pun intended.
>

Rather than "expecting" some, or speculating, how about tuning a
harpsichord and an organ this way and playing some? From more than a year
of doing so, A major has become one of my favorite keys to play in and
listen to, with its melodic smoothness and the brightness of those sharps.
The note C#, as it turns out, is exactly midway between A and F. One
could turn your observations right around and say them the other way: in
other temperaments, the interval Db-F is so much worse than A-C# that the
music played using it (such as quite a bit of Bach's in F minor) "doesn't
fare particularly well".

... [snipt]

Bradley Lehman
http://www.larips.com

and:
________________________________________________________________________

Date: Thu, 25 Aug 2005
From: "George D. Secor"
Subject: Re: scala file for Lehman's Bach tuning

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> Could somebody post it?
>
> -C.

! lehman-bach.scl
!
Brad Lehman's Bach keyboard temperament
12
!
98.04500
196.09000
298.04500
392.18000
501.95500
596.09000
698.04500
798.04500
894.13500
998.04500
1094.13500
2/1

________________________________________________________________________

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.11.10/120 - Release Date: 5/10/05

That sounds very doubtful to me. The objective facts are these.

In Lehman's D major the intervals D-A, G-D, A-C#, A-E beat *faster*
than in ET; D-F# is the same as ET; only G-B is purer (i.e. beats
less) or E-B if you count the II chord as important.

In A major almost every interval of the basic I-IV-V cycle is less
pure than ET, except E-B, so almost every interval beats faster than ET.

In E major the only degrees of the scale that beat slower than ET in
their harmonic context are B and F#.

So I don't know why anyone would hear *less* beats than ET in these
keys, particularly if the main source of beating is the thirds.

Perhaps it is due to the phenomenon of 'intermittent beating' noted
for example by Lindley. This means that the most objectionable beats
are not the fastest, but those at a frequency of about 10 per second.
So at a certain point, it makes the sound 'smoother' to have *more*
frequent beats.

Perhaps Yahya just likes near-Pythagorean tuning?

Anyway, I have tried the tuning on a real instrument (harpsichord).
While I expected that E major would be the worst, in the event it
wasn't objectionable; but I didn't like the sound of a full A major
chord at all. In total 3 noticeable faults: E too low, C# too high, F
too high.

~~~T~~~

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> Hi all,
>
> I've just recently found out how to *manually* re-tune my
> Roland keyboard to any different 12-note tuning; yes, I
> found the manual! But it doesn't seem there's any way to
> download a tuning to it, or have it remember a tuning I've
> set (except for a toggle between the current non-standard
> tuning and standard 12EDO).
>
> So it was opportune that I just now read the following two
> old messages, from Bradley Lehman answering George
> Secor, and from George Secor answering Carl Lumma.
>
> I decided to make my own little (non-Bach) experiment.
> Having retuned the keyboard (to the nearest cent), I then
> proceeded to improvise in all major and minor keys for about
> 30 minutes. I then switched back to standard for 5 minutes,
> then again to Brad's tuning for another 5 minutes.
>
> Verdict: Brad's tuning is decidedly smoother in A major,
> and keys near to it in the cycle of fiths, than 12 EDO.
> There's a more singing tone, less roughness, slower beating.
> For contrast, I went to the other extreme, playing in Ab
> major and minor and also in Db. I was pleased to find how
> smooth these keys were.
>
> Of course, this has absolutely no bearing on what tunings
> Bach used! But I do like the sound of this tuning, both with
> the sampled piano and harpsichord sounds on this keyboard.
> Because it's late at night, I didn't let fly with the pipe organ
> :-) tho I must try that tomorrow.
>
> Regards,
> Yahya
>
>
> _______________________________________________
> Date: Thu, 25 Aug 2005
> From: Bradley P Lehman
> Subject: re: Further doubts about Lehman's 'Bach' scale
>
> > (...) While you might get some interesting results playing
> > some of Bach's music in it, I would not expect anything in the key of
> > A major (its worst triad) to fare particularly "well" (pun intended.
> >
>
> Rather than "expecting" some, or speculating, how about tuning a
> harpsichord and an organ this way and playing some? From more than
a year
> of doing so, A major has become one of my favorite keys to play in and
> listen to, with its melodic smoothness and the brightness of those
sharps.
> The note C#, as it turns out, is exactly midway between A and F. One
> could turn your observations right around and say them the other
way: in
> other temperaments, the interval Db-F is so much worse than A-C#
that the
> music played using it (such as quite a bit of Bach's in F minor)
"doesn't
> fare particularly well".
>
> ... [snipt]
>
> Bradley Lehman
> http://www.larips.com
>
> and:
> ________________________________________________________________________
>
> Date: Thu, 25 Aug 2005
> From: "George D. Secor"
> Subject: Re: scala file for Lehman's Bach tuning
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> > Could somebody post it?
> >
> > -C.
>
> ! lehman-bach.scl
> !
> Brad Lehman's Bach keyboard temperament
> 12
> !
> 98.04500
> 196.09000
> 298.04500
> 392.18000
> 501.95500
> 596.09000
> 698.04500
> 798.04500
> 894.13500
> 998.04500
> 1094.13500
> 2/1
>
> ________________________________________________________________________
>
> --
> No virus found in this outgoing message.
> Checked by AVG Anti-Virus.
> Version: 7.0.344 / Virus Database: 267.11.10/120 - Release Date: 5/10/05
>

> From: "Tom Dent" <stringph@gmail.com>
>The objective facts are these.
>
>In A major almost every interval of the basic I-IV-V cycle is less
>pure than ET, except E-B, so almost every interval beats faster than ET.
>
>Anyway, I have tried the tuning on a real instrument (harpsichord).
>While I expected that E major would be the worst, in the event it
>wasn't objectionable; but I didn't like the sound of a full A major
>chord at all. In total 3 noticeable faults: E too low, C# too high, F
>too high.
>
>~~~T~~~

And against your anecdote of disliking A major, Tom, I have an anecdote of at least equal weight, saying it works beautifully on a "real instrument". For what such anecdotes are worth.....

In a recent visit to the organ in Indiana, I videotaped myself playing the two "Orgelbuchlein" settings of "Liebster Jesu", BWV 633 and 634. Both are in A major and both have complicated canonic textures, with the various weirdnesses that arise from close canon. And they work perfectly fine, with no "noticeable faults" anywhere.

That's this organ in particular:
http://www-personal.umich.edu/~bpl/larips/tb41.html
There's also one in Finland now, as described on this page:
http://www-personal.umich.edu/~bpl/larips/usage.html

Likewise I play the A major English Suite for myself all the time at home, on harpsichord, and it works beautifully with a colorful and exciting "glow" to it; I especially like what it does with the Sarabande and the Allemande.

Use the tuning in real music, not just playing a couple of isolated chords and scales.... :) The linear motion of contrapuntal writing is really nothing like hitting a couple of chords in isolation; and this temperament fosters a melodically-oriented approach to performance anyway (i.e. not merely basking in chord progressions or static harmonic moments). I noticed that especially in BWV 633 and 634, as the temperament keeps the canonic voices moving forward with their tensions. The temperament sounds almost Pythagorean there, with high and tense leading-tones needing to resolve forward.

And listen to your harpsichord at 1, 2, 5, 10, and 20 meters away: you'll be surprised at the amount of "projection" this temperament has at the various distances. Play in various sizes and types of rooms, and on other people's harpsichords!

On my harpsichord recording I picked one of the most audacious A-major pieces where it allegedly shouldn't work, but it does: the Sarabande of Suite BWV 832, with big thick chords hitting the hottest spots in A major and E major. To be released later this month, in this album:
http://www-personal.umich.edu/~bpl/larips/cd1003.html

Further...on the assertion that my A major has "E too low, C# too high, F too high...."--how much time have you spent playing harpsichord repertoire using regular 1/6 comma all the way, as in leaving it on the instrument for at least a week and playing through piles of everything? The E and the F are exactly where they are in regular 1/6, vis-a-vis A! "Too low" and "too high" for what, according to what expectation? (They'd be even farther off your mark, if you're accustomed to play 16th-17th repertoire in 1/4 comma for long sessions, as is a pretty standard thing for harpsichordists to do nowadays! Coming into this from that side of history, i.e. chronologically moving forward out of the 17th century, this Bach thing sounds ultra-modern and suave; the same distinction that I believe CPE Bach made in the 1750s, drawing similar contrast of old vs current.)

Granted, the C# is rather higher than its corresponding position within many other contemporary temperaments, but it's only (and exactly) halfway up from A to F. That is, the note C#/Db is mean, creating two identical major 3rds A-C# and Db-F. For your assertion that C# is "too high" (for what?), someone could offer the equally important observation that Db is "too low" in all the other temperaments, making Bach's F-minor music (and some C minor and G minor as well) sound rotten!

Bradley Lehman
http://www.larips.com

Hi Tom,

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:

> Anyway, I have tried the tuning on a real instrument
> (harpsichord).

What makes the harpsichord a "real instrument"?

If your purpose is to differentiate it from electronic
instruments which are capable of producing sounds which
imitate or emulate a harpsichord, it would be less
inflammatory to refer to the harpsichord as an
"acoustic instrument".

My computer produces "real music", so apparently
my computer must be a "real instrument".

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> Hi Tom,
>
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:
>
> > Anyway, I have tried the tuning on a real instrument
> > (harpsichord).
>
> What makes the harpsichord a "real instrument"?

It's not a "virtual instrument". :-)

> If your purpose is to differentiate it from electronic
> instruments which are capable of producing sounds which
> imitate or emulate a harpsichord, it would be less
> inflammatory to refer to the harpsichord as an
> "acoustic instrument".

Perhaps, but then again, few would dispute the statement that a
recording made with acoustic instruments (competently played) is
preferable to one with sounds produced electronically.

> My computer produces "real music", so apparently
> my computer must be a "real instrument".

I'd say nope, it's a virtual instrument.

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> I'd say nope, it's a virtual instrument.

If a computer writes a wav file to disk, that's a virtual instrument.
If someone uses a computer to produce music in real time with a midi
keyboard, that's a real instrument.

The harpsichord is a real instrument because it doesn't
produce anything until a human being really plays it.

Cris Forster
www.Chrysalis-Foundation.org

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> Hi Tom,
>
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:
>
> > Anyway, I have tried the tuning on a real instrument
> > (harpsichord).
>
>
> What makes the harpsichord a "real instrument"?
>
> If your purpose is to differentiate it from electronic
> instruments which are capable of producing sounds which
> imitate or emulate a harpsichord, it would be less
> inflammatory to refer to the harpsichord as an
> "acoustic instrument".
>
> My computer produces "real music", so apparently
> my computer must be a "real instrument".
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
>
> > I'd say nope, it's a virtual instrument.
>
> If a computer writes a wav file to disk, that's a virtual instrument.
> If someone uses a computer to produce music in real time
> with a midi keyboard, that's a real instrument.
>

By that reasoning, it seems to me, if a performer plays a
piano for a recording of a Beethoven sonata, where "real time"
has no significance, then that piano is also a virtual instrument,
because what matters in the end is not the piano or the live
aspects of the performance, but the recording.

Therefore, i still maintain that my computer is a real instrument.

If you wish to argue this further, you might first want
to read _Ring Resounding_, by John Culshaw, the story of
the recording of Wagner's complete _Ring_ cycle with Georg
Solti conducting, in which the engineers performed *many*
tricks to make the recording reflect Wagner's vision as
much as they thought possible ... and, IMO, with great success.

-monz
http://tonalsoft.com
Tonescape microtonal music software

By definition, the term "virtual" acknowledges degrees of separation
from reality. Pilots who don't abandon their flight simulators
don't fly. Musicians who don't abandon their sound simulators don't
play. I have never heard of a pilot or a musician training on the
real thing to become skilled on the virtual thing.

Cris

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> >
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> >
> > > I'd say nope, it's a virtual instrument.
> >
> > If a computer writes a wav file to disk, that's a virtual
instrument.
> > If someone uses a computer to produce music in real time
> > with a midi keyboard, that's a real instrument.
> >
>
>
> By that reasoning, it seems to me, if a performer plays a
> piano for a recording of a Beethoven sonata, where "real time"
> has no significance, then that piano is also a virtual instrument,
> because what matters in the end is not the piano or the live
> aspects of the performance, but the recording.
>
> Therefore, i still maintain that my computer is a real instrument.
>
> If you wish to argue this further, you might first want
> to read _Ring Resounding_, by John Culshaw, the story of
> the recording of Wagner's complete _Ring_ cycle with Georg
> Solti conducting, in which the engineers performed *many*
> tricks to make the recording reflect Wagner's vision as
> much as they thought possible ... and, IMO, with great success.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

Hi all,

On Mon, 10 Oct 2005, Tom Dent wrote:
> That sounds very doubtful to me. The objective facts are these.

Of course, my experiment was subjective! I wasn't _measuring_
anything!

> In Lehman's D major the intervals D-A, G-D, A-C#, A-E beat *faster*
> than in ET; D-F# is the same as ET; only G-B is purer (i.e. beats
> less) or E-B if you count the II chord as important.

... [snipt]

> So I don't know why anyone would hear *less* beats than ET in these
> keys, particularly if the main source of beating is the thirds.

Perhaps the beats were fast enough to contribute to a low member
of the harmonic series in the various chords, whether held or
passing? But statistically, it seems highly unlikely that this would
happen.

How relevant, I wonder, is an analysis of the beat rates of dyads
in a much richer texture? A typical keyboard improv for me has
left hand arpeggios over pedal notes, with fairly full chords held
in the right hand in positions close enough to allow some play of
melody and occasional ornament either above or within the chord.
(I hope this description is adequate.) Oh yes, I prefer to play
mostly in a legato style. This all means that at any moment the
left hand usually has at least two held notes and the right hand
at least three held notes, all from the current harmony. In such
a style, I wonder whether I can really hear many of the beats at
all. Perhaps I should have written "less noticeable beats" rather
than "slower beats". But I did make some efforts to play a few
chords of two and three notes in each key, and generally found
these less objectionable in Brad's temp than in 12EDO.

> Perhaps it is due to the phenomenon of 'intermittent beating' noted
> for example by Lindley. This means that the most objectionable beats
> are not the fastest, but those at a frequency of about 10 per second.
> So at a certain point, it makes the sound 'smoother' to have *more*
> frequent beats.

This may be so, but I personally found beat rates of 0.5 to 3 Hz
much more objectionable than those of 10 to 15 Hz, with those
in between being more moderately tolerable. The slowest beats
I heard tended to cause the entire sound to flutter in volume
in a rather nauseating way. I imagined this might have something
to do with lower frequencies carrying greater power. But that
would make no sense unless the sound envelope can evolve in such
a way that one partial can "steal" power from others - and that
seems improbable given that my sound source was the samples
on a chip, rather than vibrating strings.

> Perhaps Yahya just likes near-Pythagorean tuning?

I don't think so! I prefer a just major third of 5/4 to one
of 81/64, and a minor third of 6/5 to one of 32/27. I don't,
frankly, think that I could possibly _hear_ either ofthe Pyth.
thirds as a ratio - rather, I would only be accepting them
as a notional representation (just as I do in 12EDO) of the
just intervals.

> Anyway, I have tried the tuning ...

This is good news! Your subjective experience of this
interests me greatly - more so than any of your or my
attempts at objective explanation could possibly do ;-o .

> ... on a real instrument (harpsichord).

... which creates several simultaneous and interacting sound
sources, rather than on independent samples from real
instruments, including harpsichords and pianos, which can
only interact in space and the listener's ear, rather than
in those places and also within the instrument itself ... Yes,
I guess we should expect _some_ differences in results.

> While I expected that E major would be the worst, in the event it
> wasn't objectionable; but I didn't like the sound of a full A major
> chord at all. In total 3 noticeable faults: E too low, C# too high, F
> too high.
>
> ~~~T~~~

Tom, was that F perhaps an A? Or were these faults of
intonation all relative to your accepting the temperament's
A as the starting point (in which case your "full A major
chord" would have been an A major chord with added minor
sixth)?

I would be interested to hear how others have fared -
_subjectively_ with Brad's tuning. As a tuning, how does
it feel to you, playing the kinds of music you play most
often? (Quite apart from any consideration of its
historical aptness to Bach's praxis.)

Regards,
Yahya

> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
> >
> >
> > Hi all,
> >
> > I've just recently found out how to *manually* re-tune my
> > Roland keyboard to any different 12-note tuning; yes, I
> > found the manual! But it doesn't seem there's any way to
> > download a tuning to it, or have it remember a tuning I've
> > set (except for a toggle between the current non-standard
> > tuning and standard 12EDO).
> >
> > So it was opportune that I just now read the following two
> > old messages, from Bradley Lehman answering George
> > Secor, and from George Secor answering Carl Lumma.
> >
> > I decided to make my own little (non-Bach) experiment.
> > Having retuned the keyboard (to the nearest cent), I then
> > proceeded to improvise in all major and minor keys for about
> > 30 minutes. I then switched back to standard for 5 minutes,
> > then again to Brad's tuning for another 5 minutes.
> >
> > Verdict: Brad's tuning is decidedly smoother in A major,
> > and keys near to it in the cycle of fiths, than 12 EDO.
> > There's a more singing tone, less roughness, slower beating.
> > For contrast, I went to the other extreme, playing in Ab
> > major and minor and also in Db. I was pleased to find how
> > smooth these keys were.
> >
> > Of course, this has absolutely no bearing on what tunings
> > Bach used! But I do like the sound of this tuning, both with
> > the sampled piano and harpsichord sounds on this keyboard.
> > Because it's late at night, I didn't let fly with the pipe organ
> > :-) tho I must try that tomorrow.
> >
> > Regards,
> > Yahya
> >
> >
> > _______________________________________________
> > Date: Thu, 25 Aug 2005
> > From: Bradley P Lehman
> > Subject: re: Further doubts about Lehman's 'Bach' scale
> >
> > > (...) While you might get some interesting results playing
> > > some of Bach's music in it, I would not expect anything in the
> > > key of A major (its worst triad) to fare particularly "well"
> > > (pun intended.
> > >
> >
> > Rather than "expecting" some, or speculating, how about tuning
> > a harpsichord and an organ this way and playing some? From
> > more than a year of doing so, A major has become one of my
> > favorite keys to play in and listen to, with its melodic
> > smoothness and the brightness of those sharps.
> > The note C#, as it turns out, is exactly midway between A and
> > F. One could turn your observations right around and say them
> > the other way: in other temperaments, the interval Db-F is so
> > much worse than A-C# that the music played using it (such as
> > quite a bit of Bach's in F minor) "doesn't fare particularly well".
> >
> > ... [snipt]
> >
> > Bradley Lehman
> > http://www.larips.com
> >
> > and:
> > ___________________________________________________
> >
> > Date: Thu, 25 Aug 2005
> > From: "George D. Secor"
> > Subject: Re: scala file for Lehman's Bach tuning
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...>
> > wrote:
> > > Could somebody post it?
> > >
> > > -C.
> >
> > ! lehman-bach.scl
> > !
> > Brad Lehman's Bach keyboard temperament
> > 12
> > !
> > 98.04500
> > 196.09000
> > 298.04500
> > 392.18000
> > 501.95500
> > 596.09000
> > 698.04500
> > 798.04500
> > 894.13500
> > 998.04500
> > 1094.13500
> > 2/1
> >
> > _______________________________________________
> >

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.11.13/126 - Release Date: 9/10/05

> (...)
> Perhaps the beats were fast enough to contribute to a low member
> of the harmonic series in the various chords, whether held or
> passing? But statistically, it seems highly unlikely that this
would
> happen.

Yes, quite unlikely, and also unlikely to have some sort of
proportional beating.

>
> > Perhaps Yahya just likes near-Pythagorean tuning?
>
> I don't think so! I prefer a just major third of 5/4 to one
> of 81/64, and a minor third of 6/5 to one of 32/27. I don't,
> frankly, think that I could possibly _hear_ either ofthe Pyth.
> thirds as a ratio - rather, I would only be accepting them
> as a notional representation (just as I do in 12EDO) of the
> just intervals.

I suppose what I meant was, if your preferences are in the direction
of 5/4 and 6/5, then it is curious that you would prefer a tuning
whose intervals (at least in the relevant keys) are farther from
those values than ET is. In fact C#-E is, exactly, 32/27.

> > ... on a real instrument (harpsichord).
>
> ... which creates several simultaneous and interacting sound
> sources, rather than on independent samples from real
> instruments, including harpsichords and pianos, which can
> only interact in space and the listener's ear, rather than
> in those places and also within the instrument itself ... Yes,
> I guess we should expect _some_ differences in results.
>

A good explanation of the point of wood-and-metal-and-leather as
opposed to electronically generated sounds. Also, any 'acoustic'
instrument has a *unique* profile of upper partials, thus setting any
tuning in a new light. However, all that is filtered again through my
opinions...

> > (...) I didn't like the sound of a full A major
> > chord at all. In total 3 noticeable faults: E too low, C# too
high, F
> > too high.
> >
> >
> Tom, was that F perhaps an A?

No, I meant what I think the faults are, not just focusing on one key
but taking the *whole* of the circle into account. Though, two of the
features I dislike do happen to crop up conspicuously in the same
key. I suppose it was not very clear.

> Or were these faults of
> intonation all relative to your accepting the temperament's
> A as the starting point

More or less, yes. Almost all reasonable Bach tunings have C-G-D-A in
common as more or less 1/6 comma tempered fifths, so the question is
what to do with the rest of the notes, relative to this kernel and to
each other.

~~~T~~~

--- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@c...> wrote:

> By definition, the term "virtual" acknowledges degrees
> of separation from reality. Pilots who don't abandon
> their flight simulators don't fly. Musicians who don't
> abandon their sound simulators don't play. I have never
> heard of a pilot or a musician training on the
> real thing to become skilled on the virtual thing.

If i am performing an improvisation, with another
musician playing a keyboard, another playing an acoustic
instrument, and me playing the Lattice on a computer
using Tonescape, then the computer i'm playing is not
a simulator or virtual anything, it's a "real instrument"
just like the keyboard and the acoustic instrument.

Any further discussion of this should go on metatuning,
as it's becoming off-topic for this list.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Not if you put it on autopilot, it ain't.

Cris

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@c...>
wrote:
>
> > By definition, the term "virtual" acknowledges degrees
> > of separation from reality. Pilots who don't abandon
> > their flight simulators don't fly. Musicians who don't
> > abandon their sound simulators don't play. I have never
> > heard of a pilot or a musician training on the
> > real thing to become skilled on the virtual thing.
>
>
>
> If i am performing an improvisation, with another
> musician playing a keyboard, another playing an acoustic
> instrument, and me playing the Lattice on a computer
> using Tonescape, then the computer i'm playing is not
> a simulator or virtual anything, it's a "real instrument"
> just like the keyboard and the acoustic instrument.
>
> Any further discussion of this should go on metatuning,
> as it's becoming off-topic for this list.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> >
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> >
> > > I'd say nope, it's a virtual instrument.
> >
> > If a computer writes a wav file to disk, that's a virtual
instrument.
> > If someone uses a computer to produce music in real time
> > with a midi keyboard, that's a real instrument.

Good point! But I would say that the *instrument* consists
essentially of the keyboard (and any other controllers used in
conjunction with it), plus the sound card or soundfont (or whatever
else might be creating the electronic waveforms). (Amplifiers and
speakers are IMO merely a means of making those waveforms audible.)
Any file created by the performance (for later playback) is
essentially a "recording".

However, if you're using a keyboard plus electronics to imitate a non-
keyboard instrument, e.g., a violin or clarinet, then I would think
of that as a virtual instrument, because the performing techniques
differ significantly from what is required of a violinist or
clarinetist performing on a real instrument. An electronic piano or
organ might thereby be considered "real" (as opposed to "virtual"),
insofar as such electronic imitations are designed to give the the
performer the "look and feel" of the real thing.

> By that reasoning, it seems to me, if a performer plays a
> piano for a recording of a Beethoven sonata, where "real time"
> has no significance, then that piano is also a virtual instrument,
> because what matters in the end is not the piano or the live
> aspects of the performance, but the recording.

Ah, but in a recording "real time" does matter, because you're
hearing the performance in an amount of time equivalent to what it
took to perform it, and the performer produced the original sound
using real piano technique.

Let's not confuse recordings with instruments.

> Therefore, i still maintain that my computer is a real instrument.

Only if you produced the music in real time. If you input the notes
one by one at leisure, then you're creating a virtual performance of
the music.

> If you wish to argue this further,

(I don't really have the time &/or inclination.)

> you might first want
> to read _Ring Resounding_, by John Culshaw, the story of
> the recording of Wagner's complete _Ring_ cycle with Georg
> Solti conducting, in which the engineers performed *many*
> tricks to make the recording reflect Wagner's vision as
> much as they thought possible ... and, IMO, with great success.

Of course there are all sorts of recording tricks -- a single person
can sing or play one track at a time and create an entire "virtual"
ensemble, but that doesn't make the source instrument(s) or voice
virtual.

--George

--- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@c...> wrote:
>
> By definition, the term "virtual" acknowledges degrees of separation
> from reality. Pilots who don't abandon their flight simulators
> don't fly. Musicians who don't abandon their sound simulators don't
> play. I have never heard of a pilot or a musician training on the
> real thing to become skilled on the virtual thing.

It seems to me this leaves you on the horns of a dilemma: either a
performer on an Ondes Martinot is not a real musician, or some
electronic instruments are more equal than others.

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> Only if you produced the music in real time. If you input the notes
> one by one at leisure, then you're creating a virtual performance of
> the music.

So a Conlon Nancarrow piece for player piano is a virtual performance?
What about music which is performed by the pianist on one piano, and
recorded using another? This has been done, and one could wish Glenn
Gould used the technique.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
>
> > Only if you produced the music in real time. If you input the
notes
> > one by one at leisure, then you're creating a virtual performance
of
> > the music.
>
> So a Conlon Nancarrow piece for player piano is a virtual performance?

Yep! A virtual performance of a virtual composition -- but in this case
the instrument is quite real. :-)

> What about music which is performed by the pianist on one piano, and
> recorded using another?

Would that would be real-to-real-to-reel?

> This has been done, and one could wish Glenn
> Gould used the technique.

Or a very special type of hum filter. ;-)

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > This has been done, and one could wish Glenn
> > Gould used the technique.
>
> Or a very special type of hum filter. ;-)

And the tape recorder placed on a specially constructed, *very low*
table. :)

Cheers,
Jon

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

>
> This may be so, but I personally found beat rates of 0.5 to 3 Hz
> much more objectionable than those of 10 to 15 Hz, with those
> in between being more moderately tolerable.

A very rare and surprising assessment. So you're saying you like 3 to 10 Hz beating less
than 10 to 15 Hz beating, and 0.5 to 3 Hz beating less still?

> The slowest beats
> I heard tended to cause the entire sound to flutter in volume
> in a rather nauseating way. I imagined this might have something
> to do with lower frequencies carrying greater power. But that
> would make no sense unless the sound envelope can evolve in such
> a way that one partial can "steal" power from others - and that
> seems improbable given that my sound source was the samples
> on a chip, rather than vibrating strings.

I think you're confusing the frequency of a pressure variation (which can carry power) with
the frequency of an amplitude variation (which can't). The former are "notes" or "partials",
the latter aren't.

Also, I'm not sure if you're clear on the causes and mathematics of beating . . . I'd love to
review that for you if need be.

> > Perhaps Yahya just likes near-Pythagorean tuning?
>
> I don't think so! I prefer a just major third of 5/4 to one
> of 81/64, and a minor third of 6/5 to one of 32/27. I don't,
> frankly, think that I could possibly _hear_ either ofthe Pyth.
> thirds as a ratio - rather, I would only be accepting them
> as a notional representation (just as I do in 12EDO) of the
> just intervals.

I think you're right!

Hi George,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > Therefore, i still maintain that my computer is a
> > real instrument.
>
> Only if you produced the music in real time. If you input
> the notes one by one at leisure, then you're creating a
> virtual performance of the music.

Well, my further argument to this concerned playing the
Lattice in Tonescape in real time, as part of an improvisation.
In that case, by your reasoning and mine, my computer is a
"real instrument".

This is an interesting topic that i'd like to pursue further
on metatuning. I'm not totally convinced that a .wav file,
produced in step-time fashion by inputting the notes "one
by one at leisure", is a "virtual performance". Is a composer's
printed score therefore also a "virtual performance"?

-monz
http://tonalsoft.com
Tonescape microtonal music software

On Tue, 11 Oct 2005, Gene Ward Smith wrote:
>
> --- In tuning ..., "George D. Secor" <gdsecor@y...> wrote:
>
> > I'd say nope, it's a virtual instrument.
>
> If a computer writes a wav file to disk, that's a virtual instrument.
> If someone uses a computer to produce music in real time with a midi
> keyboard, that's a real instrument.

Yep. A real instrument produces sound. A virtual instrument produces
the possibility that a real instrument will later produce sound.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.11.13/126 - Release Date: 9/10/05

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> I'm not totally convinced that a .wav file,
> produced in step-time fashion by inputting the notes "one
> by one at leisure", is a "virtual performance". Is a composer's
> printed score therefore also a "virtual performance"?

No, the score is an analogue of a sequence. The .wav file is an
analogue of a performance of the printed score. At least that is how
it would appear to me.

Cheers,
Jon

George wrote...
> Perhaps, but then again, few would dispute the statement that a
> recording made with acoustic instruments (competently played) is
> preferable to one with sounds produced electronically.

I might be one of the few. Live, acoustic wins every time.
But with recordings, I'm not so sure.

-Carl

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > I'm not totally convinced that a .wav file,
> > produced in step-time fashion by inputting the notes "one
> > by one at leisure", is a "virtual performance". Is a composer's
> > printed score therefore also a "virtual performance"?
>
> No, the score is an analogue of a sequence. The .wav file is an
> analogue of a performance of the printed score. At least that is
how
> it would appear to me.
>
> Cheers,
> Jon
>

When does it become incumbent upon the inventors of a new medium (a
new art form?) to jettison traditionally accurate terms (composer,
score, music, instrument) and to invent a new vocabulary?

For example, in the past, we have only had "instruments of music";
but now we have "instruments/machines of music." Perhaps the
practitioners of the latter could display some creativity in
defining a new term for their instruments/machines, and leave the
rest of us to quietly antiquate into the night…

Cris

> By definition, the term "virtual" acknowledges degrees of
> separation from reality. Pilots who don't abandon their flight
> simulators don't fly. Musicians who don't abandon their sound
> simulators don't play. I have never heard of a pilot or a
> musician training on the real thing to become skilled on the
> virtual thing.
>
> Cris

I've always been very proud that the list functioned as well
as it did with no moderation (except to remove spam). But if
there was ever a reason for it, it would be to keep off-topic
trolls like this from obscuring the huge (unmanageable for
many readers) amount of legitimate content here.

-Carl

Hi Cris,

--- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@c...> wrote:

> When does it become incumbent upon the inventors of a
> new medium (a new art form?) to jettison traditionally
> accurate terms (composer, score, music, instrument) and
> to invent a new vocabulary?
>
> For example, in the past, we have only had "instruments
> of music"; but now we have "instruments/machines of music."
> Perhaps the practitioners of the latter could display some
> creativity in defining a new term for their instruments/machines,
> and leave the rest of us to quietly antiquate into the night…

If you don't think a piano is a "machine of music", then
perhaps you need to open the wooden covering and take a
look inside. A modern piano has more moving parts than
an automobile ... and i'm not making that up -- it's true.

For that matter, any of the modern woodwinds are far
more complicated than a simple tube with holes in it.

So exactly where does one draw the line in distinguishing
an "instrument" from a "machine" ... or is there in fact
any difference at all?

As i see it, the gist of the argument in this discussion
revolves around the distinction between music being played
in real-time as opposed to that being recorded for posterity.

So my argumentative question is simply this: if i'm
playing music in real-time using software on a computer,
then what makes that computer any different from a piano
or clarinet (or any other "instrument") used for the same
purpose, or indeed in the same performance?

Is there some significance to the fact that the computer
needs the intermediary software to accomplish the task?

If so, then is this any different from the intermediary
keys, springs, and screws on the "instruments"?

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> Hi George,
>
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > >
> > > Therefore, i still maintain that my computer is a
> > > real instrument.
> >
> > Only if you produced the music in real time. If you input
> > the notes one by one at leisure, then you're creating a
> > virtual performance of the music.
>
> Well, my further argument to this concerned playing the
> Lattice in Tonescape in real time, as part of an improvisation.
> In that case, by your reasoning and mine, my computer is a
> "real instrument".

I'd say yes, as long as you're not trying to simulate some other
instrument that's normally played using a significantly different
technique.

> This is an interesting topic that i'd like to pursue further
> on metatuning.

Sorry, not with me -- I don't have the time.

> I'm not totally convinced that a .wav file,
> produced in step-time fashion by inputting the notes "one
> by one at leisure", is a "virtual performance".

It isn't. It's a recording of a virtual performance -- one not
produced in real time. You can hear the music by playing the .wav
file, but what you're hearing is *not* a recording (or reproduction)
of a real performance, for the simple reason that there was in fact
no performance at all prior to the existence of the .wav file. And
simple note-by-note input into a computer is not *performance* --
it's *composition* (or, if not original, *copying* from one medium of
storage to another), unless you take the time and effort to attend to
a bunch of other things (see following).

> Is a composer's
> printed score therefore also a "virtual performance"?

No, at least not until someone comes up with a device that can take
that score as input and convert it into audible sound as output. You
could still have someone perform the function of such a device by
inputting the notes of the score into a computer to produce a midi
file, but it would be at best a mechanical "performance", since
specific matters of nuance and interpretation (dynamics, expression,
tempo, phrasing, articulation, etc.) would not be addressed (not to
mention things such as selection of soundcard & patches, or
soundfonts, etc.). It takes a bit of skill to be a good performer,
whether real or virtual.

--George

Hi all,

On Wed, 12 Oct 2005, "wallyesterpaulrus" wrote:
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
> > This may be so, but I personally found beat rates of 0.5 to 3 Hz
> > much more objectionable than those of 10 to 15 Hz, with those
> > in between being more moderately tolerable.
>
> A very rare and surprising assessment. So you're saying you like 3 to 10
Hz beating less
> than 10 to 15 Hz beating, and 0.5 to 3 Hz beating less still?

Yep.

> > The slowest beats
> > I heard tended to cause the entire sound to flutter in volume
> > in a rather nauseating way. I imagined this might have something
> > to do with lower frequencies carrying greater power. But that
> > would make no sense unless the sound envelope can evolve in such
> > a way that one partial can "steal" power from others - and that
> > seems improbable given that my sound source was the samples
> > on a chip, rather than vibrating strings.
>
> I think you're confusing the frequency of a pressure variation (which can
carry power) with
> the frequency of an amplitude variation (which can't). The former are
"notes" or "partials",
> the latter aren't.

A sound wave is a pressure wave, isn't it? Please unconfuse me!

> Also, I'm not sure if you're clear on the causes and mathematics of
beating . . . I'd love to
> review that for you if need be.

Because of my slipping sideways from one state educational system
(Tasmania's) to another's (Victoria's), I ended up studying the maths
of beating both in high school and uni. As always, I welcomed the second
exposure, as a chance to clear up any weaknesses in my understanding.
So ... I think I understand this part of maths more than adequately, but!
am of course willing to listen to your exposition. Maybe I really don't
know what I'm talking about (it has happened). Go for it!

I also did quite a lot of mathematical research into the acoustics of pipes
- such as flutes - at one stage. You know how complicated that can get!
I'm interested in just about any aspect of wave motion.

> > > Perhaps Yahya just likes near-Pythagorean tuning?
> >
> > I don't think so! I prefer a just major third of 5/4 to one
> > of 81/64, and a minor third of 6/5 to one of 32/27. I don't,
> > frankly, think that I could possibly _hear_ either ofthe Pyth.
> > thirds as a ratio - rather, I would only be accepting them
> > as a notional representation (just as I do in 12EDO) of the
> > just intervals.
>
> I think you're right!

Yes, I'm convinced we all do a LOT of this - perhaps more
than we realise.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.12.0/132 - Release Date: 13/10/05

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> Hi Cris,
>
>
> --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@c...>
wrote:
>
> > When does it become incumbent upon the inventors of a
> > new medium (a new art form?) to jettison traditionally
> > accurate terms (composer, score, music, instrument) and
> > to invent a new vocabulary?
> >
> > For example, in the past, we have only had "instruments
> > of music"; but now we have "instruments/machines of music."
> > Perhaps the practitioners of the latter could display some
> > creativity in defining a new term for their instruments/machines,
> > and leave the rest of us to quietly antiquate into the night…
>
>
>
> If you don't think a piano is a "machine of music", then
> perhaps you need to open the wooden covering and take a
> look inside. A modern piano has more moving parts than
> an automobile ... and i'm not making that up -- it's true.
>
> For that matter, any of the modern woodwinds are far
> more complicated than a simple tube with holes in it.
>
> So exactly where does one draw the line in distinguishing
> an "instrument" from a "machine" ... or is there in fact
> any difference at all?
>
> As i see it, the gist of the argument in this discussion
> revolves around the distinction between music being played
> in real-time as opposed to that being recorded for posterity.
>
> So my argumentative question is simply this: if i'm
> playing music in real-time using software on a computer,
> then what makes that computer any different from a piano
> or clarinet (or any other "instrument") used for the same
> purpose, or indeed in the same performance?
>
> Is there some significance to the fact that the computer
> needs the intermediary software to accomplish the task?
>
> If so, then is this any different from the intermediary
> keys, springs, and screws on the "instruments"?
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software

Hello Monz,

I spent 20 years working as a piano technician; I have rebuilt
countless grands and uprights, including extracting plates,
refinishing soundboards, repairing bridges, restringing, and
replacing custom action parts and hammers.

I think I know the difference between a machine and an instrument,
or between a machine and a hand tool.

John Cage gave a lecture at U.C. Santa Cruz in 1970. It mainly
consisted of him lecturing us about how many hundreds of hours it
took him to splice thousands of bits of tape together. I guess that
was his attempt to convince us that he too toils as a concert artist.

When I attend concerts by great musicians, no such explanations are
necessary.

Horowitz: When I don't practice for one day it's alright; when I
don't practice for two days, I begin to notice; when I don't
practice for three days, the audience begins to notice.

Cris

Hi Tom,

On Wed, 12 Oct 2005, you wrote:
...[snipt]
> > > Perhaps Yahya just likes near-Pythagorean tuning?
> >
> > I don't think so! I prefer a just major third of 5/4 to one
> > of 81/64, and a minor third of 6/5 to one of 32/27. I don't,
> > frankly, think that I could possibly _hear_ either ofthe Pyth.
> > thirds as a ratio - rather, I would only be accepting them
> > as a notional representation (just as I do in 12EDO) of the
> > just intervals.
>
> I suppose what I meant was, if your preferences are in the
> direction of 5/4 and 6/5, then it is curious that you would
> prefer a tuning whose intervals (at least in the relevant keys)
> are farther from those values than ET is. In fact C#-E is,
> exactly, 32/27.

I have no explanation! :-)

> > > ... on a real instrument (harpsichord).
> > ... which creates several simultaneous and interacting sound
> > sources, rather than on independent samples from real
> > instruments, including harpsichords and pianos, which can
> > only interact in space and the listener's ear, rather than
> > in those places and also within the instrument itself ... Yes,
> > I guess we should expect _some_ differences in results.
>
> A good explanation of the point of wood-and-metal-and-leather as
> opposed to electronically generated sounds. Also, any 'acoustic'
> instrument has a *unique* profile of upper partials, thus setting any
> tuning in a new light. However, all that is filtered again through my
> opinions...

But musical tuning, no matter how mathematical or
experimental it becomes, will never be an exact science,
will it? There remains, I believe, quite a bit of room for
difference of musical opinion ...

> > > (...) I didn't like the sound of a full A major
> > > chord at all. In total 3 noticeable faults: E too low, C# too
> > > high, F too high.
> > >
> > Tom, was that F perhaps an A?
>
> No, I meant what I think the faults are, not just focusing on
> one key but taking the *whole* of the circle into account. Though,
> two of the features I dislike do happen to crop up conspicuously
> in the same key. I suppose it was not very clear.

I see; you were picking what you regard as the worst notes in
the whole 12-seimtone tuning, not just in the "A major chord".

> > Or were these faults of
> > intonation all relative to your accepting the temperament's
> > A as the starting point
>
> More or less, yes. Almost all reasonable Bach tunings have C-G-D-A
> in common as more or less 1/6 comma tempered fifths, so the
> question is what to do with the rest of the notes, relative to this
> kernel and to each other.

In this "kernel", isn't the C generally the point of departure?
Probably comes to the same thing ...

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.11.13/126 - Release Date: 9/10/05

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
>
> > By definition, the term "virtual" acknowledges degrees of
> > separation from reality. Pilots who don't abandon their flight
> > simulators don't fly. Musicians who don't abandon their sound
> > simulators don't play. I have never heard of a pilot or a
> > musician training on the real thing to become skilled on the
> > virtual thing.
> >
> > Cris
>
> I've always been very proud that the list functioned as well
> as it did with no moderation (except to remove spam). But if
> there was ever a reason for it, it would be to keep off-topic
> trolls like this from obscuring the huge (unmanageable for
> many readers) amount of legitimate content here.
>
> -Carl
>

Since you seem to have such a keen sense for decency and fair play,
perhaps you should not simply copy and paste my thoughts out of
context, and should equally respond to all responders on this topic
as well.

Cris

I thought Yahya had the best resolution of the dilemma. It comes down
to the method of producing tone and the question of whether tones are
exactly reproducible and combinable without alterations.

To be more explicit, 'real' (->acoustic) instruments produce tones
with definite characteristics through the resonance of vibrating
pieces of stuff or air activated at the moment of playing. Electronic
instruments do so as a result of digital information relayed through
loudspeakers.

The latter are (usually) designed so that any given tone is exactly
reproducible - i.e. the same input from the player produces the same
sound in whatever circumstance. They only have a finite repertoire of
possible sonorities - whereas different notes on acoustic instruments
influence each other's characteristics through acoustic coupling.
(Most noticeably on some organs where the pitch of a pipe can alter
depending on what other pipes are playing.)

Electronic synthesizers whose pitch and timbre is due to the player's
control of an electronic resonance (e.g. the ondes martenot) are an
intriguing exception in that they are in principle infinitely
sensitive.

Of course, any sufficiently clever programmer should be able to
introduce some sort of simulated acoustic coupling to produce a
closer approximation, but I don't know of any case where that has
really happened. And then there is the loudspeaker problem where the
typical electronic instrument doesn't have good enough built-in
loudspeakers to deal with many higher partials.

~~~T~~~

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> Hi Cris,
>
>
> --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@c...>
wrote:
>
> > When does it become incumbent upon the inventors of a
> > new medium (a new art form?) to jettison traditionally
> > accurate terms (composer, score, music, instrument) and
> > to invent a new vocabulary?
> >
> > For example, in the past, we have only had "instruments
> > of music"; but now we have "instruments/machines of music."
> > Perhaps the practitioners of the latter could display some
> > creativity in defining a new term for their instruments/machines,
> > and leave the rest of us to quietly antiquate into the night…
>
>
> If you don't think a piano is a "machine of music", then
> perhaps you need to open the wooden covering and take a
> look inside. A modern piano has more moving parts than
> an automobile ... and i'm not making that up -- it's true.
>
> For that matter, any of the modern woodwinds are far
> more complicated than a simple tube with holes in it.
>
> So exactly where does one draw the line in distinguishing
> an "instrument" from a "machine" ... or is there in fact
> any difference at all?
>
> As i see it, the gist of the argument in this discussion
> revolves around the distinction between music being played
> in real-time as opposed to that being recorded for posterity.
>
> So my argumentative question is simply this: if i'm
> playing music in real-time using software on a computer,
> then what makes that computer any different from a piano
> or clarinet (or any other "instrument") used for the same
> purpose, or indeed in the same performance?
>
> Is there some significance to the fact that the computer
> needs the intermediary software to accomplish the task?
>
> If so, then is this any different from the intermediary
> keys, springs, and screws on the "instruments"?
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software

I would love to witness the day when techy equipment coupled to a pair of state-of-the-art loudspeakers will be able to digitally reproduce the sounds of a full live philarmonic orchestra with all the partials and distinct timbres.
----- Original Message -----
From: Tom Dent
To: tuning@yahoogroups.com
Sent: 14 Ekim 2005 Cuma 12:35
Subject: [tuning] Re: real instruments (was: No doubt about Lehman's Bach scale)

I thought Yahya had the best resolution of the dilemma. It comes down
to the method of producing tone and the question of whether tones are
exactly reproducible and combinable without alterations.

To be more explicit, 'real' (->acoustic) instruments produce tones
with definite characteristics through the resonance of vibrating
pieces of stuff or air activated at the moment of playing. Electronic
instruments do so as a result of digital information relayed through
loudspeakers.

The latter are (usually) designed so that any given tone is exactly
reproducible - i.e. the same input from the player produces the same
sound in whatever circumstance. They only have a finite repertoire of
possible sonorities - whereas different notes on acoustic instruments
influence each other's characteristics through acoustic coupling.
(Most noticeably on some organs where the pitch of a pipe can alter
depending on what other pipes are playing.)

Electronic synthesizers whose pitch and timbre is due to the player's
control of an electronic resonance (e.g. the ondes martenot) are an
intriguing exception in that they are in principle infinitely
sensitive.

Of course, any sufficiently clever programmer should be able to
introduce some sort of simulated acoustic coupling to produce a
closer approximation, but I don't know of any case where that has
really happened. And then there is the loudspeaker problem where the
typical electronic instrument doesn't have good enough built-in
loudspeakers to deal with many higher partials.

~~~T~~~

Hey,

I like Tom's and Monz arguments/points below. My thoughts: I think I can say
for sure that I've heard both some really amazing electronic music and also,
obviously, acoustic music.

Yes, there is often a different 'aesthetic' to them, largly due to the nature
of the creation of the sounds in both cases. I can say that one of the
attractive qualities of EM to me is that there are in principle a limitless
number of vastly different timbres waiting to be explored. The possibility of
doing such things as Larry Austin did in 'Rompido!', where he takes the sound
of shattering granite and uses it to haunting music effect with electronic
manipulation is *extremely* exciting to me...

(((Anyway, I don't think it's a nice gesture to denigrate or question the
taste of those who have a taste for EM...if it doesn't float your boat,
please say so in a nice respectful way, or don't say anything, and maybe
continue to make the moving music that you *do* believe in.)))

I think people who don't listen to electronic music often or at all object to
some of the static tones one hears in it, esp. in the earlier prototypical
EM. I, for one, have a fondness for both 'warm music' (A Beethoven SQ played
by 'real' players) and 'cold music' (a cleverly written piece of music which
uses the say, the timbres of a GameBoy).

Could a moving requiem be written with GameBoy timbres? That's an open
question, very much dependant on the subjectivity of the listener, and the
skill of the composer. I certainly wouldn't rule it out based on the medium
of the EM instrumentation. I think sine waves alone can be extremely
effective and expressive, almost because they are so nakedly simple.

And let's also not forget that after all, there are those who find the 'real
acoustic piano', played by an expressive master, a lacking instrument in
terms of expression.....

-Aaron.

On Friday 14 October 2005 4:35 am, Tom Dent wrote:
> I thought Yahya had the best resolution of the dilemma. It comes down
> to the method of producing tone and the question of whether tones are
> exactly reproducible and combinable without alterations.
>
> To be more explicit, 'real' (->acoustic) instruments produce tones
> with definite characteristics through the resonance of vibrating
> pieces of stuff or air activated at the moment of playing. Electronic
> instruments do so as a result of digital information relayed through
> loudspeakers.
>
> The latter are (usually) designed so that any given tone is exactly
> reproducible - i.e. the same input from the player produces the same
> sound in whatever circumstance. They only have a finite repertoire of
> possible sonorities - whereas different notes on acoustic instruments
> influence each other's characteristics through acoustic coupling.
> (Most noticeably on some organs where the pitch of a pipe can alter
> depending on what other pipes are playing.)
>
> Electronic synthesizers whose pitch and timbre is due to the player's
> control of an electronic resonance (e.g. the ondes martenot) are an
> intriguing exception in that they are in principle infinitely
> sensitive.
>
> Of course, any sufficiently clever programmer should be able to
> introduce some sort of simulated acoustic coupling to produce a
> closer approximation, but I don't know of any case where that has
> really happened. And then there is the loudspeaker problem where the
> typical electronic instrument doesn't have good enough built-in
> loudspeakers to deal with many higher partials.
>
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > Hi Cris,
> >
> >
> > --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@c...>
>
> wrote:
> > > When does it become incumbent upon the inventors of a
> > > new medium (a new art form?) to jettison traditionally
> > > accurate terms (composer, score, music, instrument) and
> > > to invent a new vocabulary?
> > >
> > > For example, in the past, we have only had "instruments
> > > of music"; but now we have "instruments/machines of music."
> > > Perhaps the practitioners of the latter could display some
> > > creativity in defining a new term for their instruments/machines,
> > > and leave the rest of us to quietly antiquate into the night…
> >
> > If you don't think a piano is a "machine of music", then
> > perhaps you need to open the wooden covering and take a
> > look inside. A modern piano has more moving parts than
> > an automobile ... and i'm not making that up -- it's true.
> >
> > For that matter, any of the modern woodwinds are far
> > more complicated than a simple tube with holes in it.
> >
> > So exactly where does one draw the line in distinguishing
> > an "instrument" from a "machine" ... or is there in fact
> > any difference at all?
> >
> > As i see it, the gist of the argument in this discussion
> > revolves around the distinction between music being played
> > in real-time as opposed to that being recorded for posterity.
> >
> > So my argumentative question is simply this: if i'm
> > playing music in real-time using software on a computer,
> > then what makes that computer any different from a piano
> > or clarinet (or any other "instrument") used for the same
> > purpose, or indeed in the same performance?
> >
> > Is there some significance to the fact that the computer
> > needs the intermediary software to accomplish the task?
> >
> > If so, then is this any different from the intermediary
> > keys, springs, and screws on the "instruments"?
> >
> >
> > -monz
> > http://tonalsoft.com
> > Tonescape microtonal music software
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>

> To be more explicit, 'real' (->acoustic) instruments produce tones
> with definite characteristics through the resonance of vibrating
> pieces of stuff or air activated at the moment of playing.
> Electronic instruments do so as a result of digital information
> relayed through loudspeakers.

The info relayed to the loudspeakers is usually (and that relayed
to the drivers in all cases) analog, not digital. Loudspeakers
do resonate, but not in a musical way -- these resonances are
damped as much as possible, and tuned so that they're as hard to
hear as possible. Unless we're talking about NXT flat panel
drivers, which do create their sound by resonating...

http://www.nxtsound.com

> The latter are (usually) designed so that any given tone is
> exactly reproducible - i.e. the same input from the player
> produces the same sound in whatever circumstance. They only
> have a finite repertoire of possible sonorities

Whether any analog system (such as a harpsichord) is really
capable of an infinite number of states is debateable.
But subjectively, synthesizers have plenty enough possibilites
to be very musical (millions and millions agree). And
the anolog synths, remember, *are* analog, not digital.
And digital synths like Synful (discussed here recently) do
have an infinite output reperatoire.

> - whereas different notes on acoustic instruments
> influence each other's characteristics through acoustic coupling.

Piano synths such as Synthogy Ivory model the resonance
in unplayed, undamped strings. Generalmusic has been claiming
to do the same in their PRO series keyboards for almost 10
years.

> (Most noticeably on some organs where the pitch of a pipe can
> alter depending on what other pipes are playing.)

I'm not sure, but Kurt Bigler's physically-modeled pipe organ
may be capable of this. Kurt?

> Electronic synthesizers whose pitch and timbre is due to the
> player's control of an electronic resonance (e.g. the ondes
> martenot) are an intriguing exception in that they are in
> principle infinitely sensitive.

I'll stop here. The argument basically comes down to if you
believe in Turing Universality. If you do, computers can be
as good as musical instruments as anything else. If you don't,
they might not be. But the fact that they're used successfully
by musicians seems to indicate something or other.

-Carl

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> > More or less, yes. Almost all reasonable Bach tunings have C-G-D-A
> > in common as more or less 1/6 comma tempered fifths, so the
> > question is what to do with the rest of the notes, relative to this
> > kernel and to each other.
>
> In this "kernel", isn't the C generally the point of departure?

I certainly wouldn't say that, but why does it matter?

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> Hi all,
>
> On Wed, 12 Oct 2005, "wallyesterpaulrus" wrote:
> > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
wrote:
> > > This may be so, but I personally found beat rates of 0.5 to 3 Hz
> > > much more objectionable than those of 10 to 15 Hz, with those
> > > in between being more moderately tolerable.
> >
> > A very rare and surprising assessment. So you're saying you like
3 to 10
> Hz beating less
> > than 10 to 15 Hz beating, and 0.5 to 3 Hz beating less still?
>
> Yep.

Wow. Are all these beat rates referring to the beating of upper
partials in a not-quite-JI chord?

> > > The slowest beats
> > > I heard tended to cause the entire sound to flutter in volume
> > > in a rather nauseating way. I imagined this might have
something
> > > to do with lower frequencies carrying greater power. But that
> > > would make no sense unless the sound envelope can evolve in such
> > > a way that one partial can "steal" power from others - and that
> > > seems improbable given that my sound source was the samples
> > > on a chip, rather than vibrating strings.
> >
> > I think you're confusing the frequency of a pressure variation
(which can
> carry power) with
> > the frequency of an amplitude variation (which can't). The former
are
> "notes" or "partials",
> > the latter aren't.
>
> A sound wave is a pressure wave, isn't it?

Yes, but a beating isn't.

> Please unconfuse me!

Does everything I wrote above make sense to you? I'm not sure if I
know where we're diverging in our understanding . . .

> > > > Perhaps Yahya just likes near-Pythagorean tuning?
> > >
> > > I don't think so! I prefer a just major third of 5/4 to one
> > > of 81/64, and a minor third of 6/5 to one of 32/27. I don't,
> > > frankly, think that I could possibly _hear_ either ofthe Pyth.
> > > thirds as a ratio - rather, I would only be accepting them
> > > as a notional representation (just as I do in 12EDO) of the
> > > just intervals.
> >
> > I think you're right!
>
> Yes, I'm convinced we all do a LOT of this - perhaps more
> than we realise.

Well, that's part of the reason I invented Harmonic Entropy (and
started the list, now Yahoogroup, by that name).

Paul,

On Fri, 14 Oct 2005, you wrote:
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> > > More or less, yes. Almost all reasonable Bach tunings have C-G-D-A
> > > in common as more or less 1/6 comma tempered fifths, so the
> > > question is what to do with the rest of the notes, relative to this
> > > kernel and to each other.
> >
> > In this "kernel", isn't the C generally the point of departure?
>
> I certainly wouldn't say that, but why does it matter?

Sorry, I forget the context. Maybe it doesn't.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.12.0/132 - Release Date: 13/10/05

Paul,

On Fri, 14 Oct 2005, you wrote:
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
> >
> > Hi all,
> >
> > On Wed, 12 Oct 2005, "wallyesterpaulrus" wrote:
> > > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
> > > wrote:
> > > > This may be so, but I personally found beat rates of 0.5 to 3 Hz
> > > > much more objectionable than those of 10 to 15 Hz, with those
> > > > in between being more moderately tolerable.
> > >
> > > A very rare and surprising assessment. So you're saying you like
> > > 3 to 10 Hz beating less than 10 to 15 Hz beating, and 0.5 to 3 Hz
> > > beating less still?
> >
> > Yep.
>
> Wow. Are all these beat rates referring to the beating of upper
> partials in a not-quite-JI chord?

For example, if I play an A major triad on my piano with the A tuned
to 220 Hz, the C# to 275 Hz and the E tuned to 331 Hz, then I'll get
beats between the 3rd partial of the A at 660 Hz and the 2nd partial
of the E at 662 Hz. These beats will be at 662 - 660 = 2 Hz.

> > > > The slowest beats
> > > > I heard tended to cause the entire sound to flutter in volume
> > > > in a rather nauseating way. I imagined this might have
> > > > something to do with lower frequencies carrying greater power.
> > > > But that would make no sense unless the sound envelope can
> > > > evolve in such a way that one partial can "steal" power from
> > > > others - and that seems improbable given that my sound source
> > > > was the samples on a chip, rather than vibrating strings.
> > >
> > > I think you're confusing the frequency of a pressure variation
> > > (which can carry power) with the frequency of an amplitude
> > > variation (which can't). The former are "notes" or "partials",
> > > the latter aren't.
> >
> > A sound wave is a pressure wave, isn't it?
>
> Yes, but a beating isn't.

???

Are you saying that the difference tone created by playing two
pure sine waves of different frequency is not also a sound wave?
If that were so, it would be inaudible.

> > Please unconfuse me!
>
> Does everything I wrote above make sense to you? I'm not sure
> if I know where we're diverging in our understanding . . .

Clearly I don't understand you. Enrol me in Beating 101!
But please be gentle.

> > > > > Perhaps Yahya just likes near-Pythagorean tuning?
> > > >
> > > > I don't think so! I prefer a just major third of 5/4 to one
> > > > of 81/64, and a minor third of 6/5 to one of 32/27. I don't,
> > > > frankly, think that I could possibly _hear_ either ofthe Pyth.
> > > > thirds as a ratio - rather, I would only be accepting them
> > > > as a notional representation (just as I do in 12EDO) of the
> > > > just intervals.
> > >
> > > I think you're right!
> >
> > Yes, I'm convinced we all do a LOT of this - perhaps more
> > than we realise.
>
> Well, that's part of the reason I invented Harmonic Entropy
> (and started the list, now Yahoogroup, by that name).

... and the HE curves there make sense, in an intuitive kind of
way. Except perhaps they don't reflect the way, when you're
tuning, you become aware of (hypersensitised to?) smaller and
smaller differences.

There's a BIG difference between -
A. accepting a note as a notional representation of an exact
interval (which I do);
and
B. being unaware of the difference (which apparently many
other people do).

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.12.0/132 - Release Date: 13/10/05

Hi Yahya (and Paul),

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> > > > > [Yahya]
> > > > > I don't, frankly, think that I could possibly
> > > > > _hear_ either ofthe Pyth. thirds as a ratio -
> > > > > rather, I would only be accepting them as a
> > > > > notional representation (just as I do in 12EDO)
> > > > > of the just intervals.
> > > >
> > > > [?]
> > > > I think you're right!
> > >
> > > [?]
> > > Yes, I'm convinced we all do a LOT of this - perhaps more
> > > than we realise.
> >
> > [Paul Erlich]
> > Well, that's part of the reason I invented Harmonic Entropy
> > (and started the list, now Yahoogroup, by that name).
>
> [Yahya]
> ... and the HE curves there make sense, in an intuitive kind of
> way. Except perhaps they don't reflect the way, when you're
> tuning, you become aware of (hypersensitised to?) smaller and
> smaller differences.

Yes they do.

If you look at the top of Paul's graphs on the Encyclopedia
page on Harmonic Entropy

http://tonalsoft.com/enc/h/harmonic-entropy.aspx

you'll see a variable called "s". Paul uses this to model
the "uncertainty factor", which varies according to how
perceptive the listener is to small tuning differences
(and also according to other factors, such as the frequency
range of the notes, timbres, etc.).

For someone who is tuning a piano, say, and who thus
becomes sensitive to small tuning differences, the "s"
value would be smaller. Paul generally uses 1% as a kind
of generic value.

(And if i'm stating anything incorrect, he'll post here
to correct me ...)

-monz
http://tonalsoft.com
Tonescape microtonal music software

> > Wow. Are all these beat rates referring to the beating of upper
> > partials in a not-quite-JI chord?
>
> For example, if I play an A major triad on my piano with the
> A tuned to 220 Hz, the C# to 275 Hz and the E tuned to 331 Hz,
> then I'll get beats between the 3rd partial of the A at 660 Hz
> and the 2nd partial of the E at 662 Hz. These beats will be at
> 662 - 660 = 2 Hz.

Hi Yahya,

I'll make a few comments. If you want to wait for Paul's reply
to reply, that's fine by me. I'm just thinking aloud waiting
for Paul's reply myself.

I'm not sure why you're subtracting these beat rates here.

As I think Paul was trying to say, beats are amplitude
modulation, which is sort of a second order sound wave.
They represent changes in the amplitude of a sound, not
a sound in and of themselves. AM is used for synthesis
and can create new pitches, called sidebands, but they
aren't at the frequency of the beats. Perhaps sidebands
could be evoked from beating in an acoustic musical
instrument, but I don't think it happens very often (though
multiphonics on instruments like the bassoon sometimes
sound like AM to me).

-Carl

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> Paul,
>
> On Fri, 14 Oct 2005, you wrote:
> > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > <yahya@m...> wrote:
> > >
> > > Hi all,
> > >
> > > On Wed, 12 Oct 2005, "wallyesterpaulrus" wrote:
> > > > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
<yahya@m...>
> > > > wrote:
> > > > > This may be so, but I personally found beat rates of 0.5 to
3 Hz
> > > > > much more objectionable than those of 10 to 15 Hz, with
those
> > > > > in between being more moderately tolerable.
> > > >
> > > > A very rare and surprising assessment. So you're saying you
like
> > > > 3 to 10 Hz beating less than 10 to 15 Hz beating, and 0.5 to
3 Hz
> > > > beating less still?
> > >
> > > Yep.
> >
> > Wow. Are all these beat rates referring to the beating of upper
> > partials in a not-quite-JI chord?
>
> For example, if I play an A major triad on my piano with the A
tuned
> to 220 Hz, the C# to 275 Hz and the E tuned to 331 Hz, then I'll get
> beats between the 3rd partial of the A at 660 Hz and the 2nd partial
> of the E at 662 Hz. These beats will be at 662 - 660 = 2 Hz.

So, as you tune the chord further and further away from JI, and the
beating gets faster and faster, the chord sounds better and better to
you?

>
> > > > > The slowest beats
> > > > > I heard tended to cause the entire sound to flutter in
volume
> > > > > in a rather nauseating way. I imagined this might have
> > > > > something to do with lower frequencies carrying greater
power.
> > > > > But that would make no sense unless the sound envelope can
> > > > > evolve in such a way that one partial can "steal" power
from
> > > > > others - and that seems improbable given that my sound
source
> > > > > was the samples on a chip, rather than vibrating strings.
> > > >
> > > > I think you're confusing the frequency of a pressure
variation
> > > > (which can carry power) with the frequency of an amplitude
> > > > variation (which can't). The former are "notes" or "partials",
> > > > the latter aren't.
> > >
> > > A sound wave is a pressure wave, isn't it?
> >
> > Yes, but a beating isn't.
>
> ???
>
> Are you saying that the difference tone created by playing two
> pure sine waves of different frequency is not also a sound wave?

Ah, this is a common confusion.

The difference tone is a result of the nonlinear response of the ear,
and is completely separate/distinct from the beating phenomenon.

Once through the nonlinear elements of the ear, the signal does
indeed contain frequency components corresponding to the difference
frequency, as well as other frequencies not present in the original
sound.

For quiet sounds, the nonlinearity is insignificant. The loudness of
the difference tone and other nonlinear combinational tones increases
*nonlinearly* (surprise) and generally in an accelerating manner as
one increases the loudness of the original sound.

> If that were so, it would be inaudible.

It *is* inaudible (that is, there is no heard pitch corresponding to
the difference frequency) under conditions of exactly linear
response. Beating, meanwhile is a variation in loudness, which is
heard to modulate a pitch which corrsponds to the average, not the
difference, of the two sine-wave frequencies. Beating does not
disappear at quiet volumes; difference tones and other combinational
tones do.

> > > Please unconfuse me!
> >
> > Does everything I wrote above make sense to you? I'm not sure
> > if I know where we're diverging in our understanding . . .
>
> Clearly I don't understand you. Enrol me in Beating 101!
> But please be gentle.

Where to begin? Let's see . . . there's an excellent explanation of
both the beating and the nonlinear combinational tone phenomena in
_The Feynman Lectures on Physics_. His explantions tend to be among
the clearest around, and I'm sure you have the necessary math
background. Do you have access to that reference? Either way, I'd be
happy to go through it myself, though I don't seem to have a good
track record of being understood lately . . .

> ... and the HE curves there make sense, in an intuitive kind of
> way. Except perhaps they don't reflect the way, when you're
> tuning, you become aware of (hypersensitised to?) smaller and
> smaller differences.

Well, you could say that s decreases as you train your ears better
and better. Would that satisfy you?

> There's a BIG difference between -
> A. accepting a note as a notional representation of an exact
> interval (which I do);
> and
> B. being unaware of the difference (which apparently many
> other people do).

I'm not sure if I understand what you mean by either A or B here :(

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
>
> > > Wow. Are all these beat rates referring to the beating of upper
> > > partials in a not-quite-JI chord?
> >
> > For example, if I play an A major triad on my piano with the
> > A tuned to 220 Hz, the C# to 275 Hz and the E tuned to 331 Hz,
> > then I'll get beats between the 3rd partial of the A at 660 Hz
> > and the 2nd partial of the E at 662 Hz. These beats will be at
> > 662 - 660 = 2 Hz.
>
> Hi Yahya,
>
> I'll make a few comments. If you want to wait for Paul's reply
> to reply, that's fine by me. I'm just thinking aloud waiting
> for Paul's reply myself.
>
> I'm not sure why you're subtracting these beat rates here.

Sorry if I'm behind, but . . . subtracting beat rates? It seems Yahya
is merely calculating beat rates here (and correctly, I might add),
not subtracting any.

> As I think Paul was trying to say, beats are amplitude
> modulation, which is sort of a second order sound wave.
> They represent changes in the amplitude of a sound,

a pitch

> not
> a sound

a pitch.

> in and of themselves. AM is used for synthesis
> and can create new pitches, called sidebands, but they
> aren't at the frequency of the beats.

They're at the frequency of the original sine waves in Yahya's
example, if what you're modulating is a sine wave whose frequency is
the average of the two. You've just turned the equivalence of beating
with AM around, and applied it backwards, which is of course
perfectly valid to do.

> Perhaps sidebands
> could be evoked from beating in an acoustic musical
> instrument,

I think you've gotten a bit confused. The sidebands "created" by the
AM applied to the heard frequency would be identical to the original
frequencies in the musical instrument; the AM itself would be
identical to the beating heard.

On Mon, 17 Oct 2005, "wallyesterpaulrus" wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
> >
> > Paul,
> >
> > On Fri, 14 Oct 2005, you wrote:
> > > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > > <yahya@m...> wrote:
> > > >
> > > > Hi all,
> > > >
> > > > On Wed, 12 Oct 2005, "wallyesterpaulrus" wrote:
> > > > > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > > > > <yahya@m...>
> > > > > wrote:
> > > > > > This may be so, but I personally found beat rates of 0.5 to
> > > > > > 3 Hz
> > > > > > much more objectionable than those of 10 to 15 Hz, with
> > > > > > those
> > > > > > in between being more moderately tolerable.
> > > > >
> > > > > A very rare and surprising assessment. So you're saying you
> > > > > like
> > > > > 3 to 10 Hz beating less than 10 to 15 Hz beating, and 0.5 to
> > > > > 3 Hz
> > > > > beating less still?
> > > >
> > > > Yep.
> > >
> > > Wow. Are all these beat rates referring to the beating of upper
> > > partials in a not-quite-JI chord?
> >
> > For example, if I play an A major triad on my piano with the A
> > tuned
> > to 220 Hz, the C# to 275 Hz and the E tuned to 331 Hz, then I'll get
> > beats between the 3rd partial of the A at 660 Hz and the 2nd partial
> > of the E at 662 Hz. These beats will be at 662 - 660 = 2 Hz.
>
> So, as you tune the chord further and further away from JI, and the
> beating gets faster and faster, the chord sounds better and better to
> you?

Not really better; just less bad. The only chords that sound good are
those that are perfectly in tune. The most annoying chords are the
_nearly_ perfect ones, those that sound most like JI but are just out
of tune. Once they get far enough away from that, it no longer seems
to me that the tuner has made any effort to achieve that particular
harmony. But, as I said earlier, in a given musical context I can accept
that the sounds I'm hearing are _supposed_ to represent that harmony
- that they are a "notional" rather than an actual major triad, for
instance.

{begin OT}
In this context, I don't know what (prime) limit I recognise in
tuning; certainly, some very tiny variations in pitch evoke entirely
different sensations in various oriental musics I'm familiar with,
including Chinese opera, erhu playing, shakuhachi playing, classical
Indian playing and singing, the best Bollywood singing. Do I hear
the 19-limit, or perhaps the 23-limit? I really couldn't say; nor do
I know how to find out. I've been following the recent discussion
on blues, and Joe Monzo's analysis of Robert Johnson's Drunken-
Hearted Man requires some fairly high-limit hearing. Over the past
few months, I've seen some proposals for tunings involving SUB-
microscopic divisions of the octave, and I'm having a hard time
reconciling that with the claim that in real music (as opposed to
listening to dyads played slowly in isolation) we can't really hear
differences less than about 2 to 3 cents. Can we readily detect
an interval of 11/10? Sure we can. 33/32? Yep. 101/100?
Think so. 333/332? Well ... that's getting a bit iffy, isn't it?
{end OT}

> > > > > > The slowest beats
> > > > > > I heard tended to cause the entire sound to flutter in
> > > > > > volume
> > > > > > in a rather nauseating way. I imagined this might have
> > > > > > something to do with lower frequencies carrying greater
> > > > > > power.
> > > > > > But that would make no sense unless the sound envelope can
> > > > > > evolve in such a way that one partial can "steal" power
> > > > > > from
> > > > > > others - and that seems improbable given that my sound
> > > > > > source
> > > > > > was the samples on a chip, rather than vibrating strings.
> > > > >
> > > > > I think you're confusing the frequency of a pressure
> > > > > variation
> > > > > (which can carry power) with the frequency of an amplitude
> > > > > variation (which can't). The former are "notes" or "partials",
> > > > > the latter aren't.
> > > >
> > > > A sound wave is a pressure wave, isn't it?
> > >
> > > Yes, but a beating isn't.
> >
> > ???
> >
> > Are you saying that the difference tone created by playing two
> > pure sine waves of different frequency is not also a sound wave?
>
> Ah, this is a common confusion.
>
> The difference tone is a result of the nonlinear response of the ear,
> and is completely separate/distinct from the beating phenomenon.
>
> Once through the nonlinear elements of the ear, the signal does
> indeed contain frequency components corresponding to the difference
> frequency, as well as other frequencies not present in the original
> sound.

OK. Sounds good. Show me the maths?

> For quiet sounds, the nonlinearity is insignificant. The loudness of
> the difference tone and other nonlinear combinational tones increases
> *nonlinearly* (surprise) and generally in an accelerating manner as
> one increases the loudness of the original sound.
>
> > If that were so, it would be inaudible.
>
> It *is* inaudible (that is, there is no heard pitch corresponding to
> the difference frequency) under conditions of exactly linear
> response.
... which don't exist except as an approximation good at very low
power ...

> ... Beating, meanwhile is a variation in loudness, which is
> heard to modulate a pitch which corrsponds to the average, not the
> difference, of the two sine-wave frequencies. Beating does not
> disappear at quiet volumes; difference tones and other combinational
> tones do.

I remember some maths trickery involving the basic trig identities:
sin (A+B) = sin A cos B + cos A sin B, and
cos (A+B) = cos A cos B - sin A sin B,
together with the substitutions u = (A+B)/2, v = (A-B)/2,
the semi-sum (average) and semi-difference of the original terms ...
or vice versa! ... but can't recall what this was used to prove ... it's too
many years ago now to remember this detail.

> > > > Please unconfuse me!
> > >
> > > Does everything I wrote above make sense to you? I'm not sure
> > > if I know where we're diverging in our understanding . . .
> >
> > Clearly I don't understand you. Enrol me in Beating 101!
> > But please be gentle.
>
> Where to begin? Let's see . . . there's an excellent explanation of
> both the beating and the nonlinear combinational tone phenomena in
> _The Feynman Lectures on Physics_. His explantions tend to be among
> the clearest around, and I'm sure you have the necessary math
> background. Do you have access to that reference?

No.

> ... Either way, I'd be
> happy to go through it myself,

Please do.

> ... though I don't seem to have a good
> track record of being understood lately . . .

But we're all sensitive types here! :-)

> > ... and the HE curves there make sense, in an intuitive kind of
> > way. Except perhaps they don't reflect the way, when you're
> > tuning, you become aware of (hypersensitised to?) smaller and
> > smaller differences.
>
> Well, you could say that s decreases as you train your ears better
> and better. Would that satisfy you?

See, I'd forgotten about the s factor since I last looked at
your HE pages ... must be old age creeping up! Yes, that allows
specifically for variation between listeners.

> > There's a BIG difference between -
> > A. accepting a note as a notional representation of an exact
> > interval (which I do);
> > and
> > B. being unaware of the difference (which apparently many
> > other people do).
>
> I'm not sure if I understand what you mean by either A or B here :(

A. Knowing the note's WRONG but saying in effect, "What
the heck, I know what you meant anyway".

B. Not knowing whether the note is wrong or right.

Because of arthritis and other limiting mechanical factors,
I have reason to extend the tolerant attitude of A. to my
own playing almost every day ... :-)

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.12.2/139 - Release Date: 17/10/05

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> Can we readily detect
> an interval of 11/10? Sure we can. 33/32? Yep. 101/100?
> Think so. 333/332? Well ... that's getting a bit iffy, isn't it?

What does it mean to "detect" an interval? Are you saying we can tell
101/100 is a ratio of integers, that we can distinguish it from
100/99, or what, exactly?

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> On Mon, 17 Oct 2005, "wallyesterpaulrus" wrote:
> >
> > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > <yahya@m...> wrote:
> > >
> > > Paul,
> > >
> > > On Fri, 14 Oct 2005, you wrote:
> > > > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > > > <yahya@m...> wrote:
> > > > >
> > > > > Hi all,
> > > > >
> > > > > On Wed, 12 Oct 2005, "wallyesterpaulrus" wrote:
> > > > > > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > > > > > <yahya@m...>
> > > > > > wrote:
> > > > > > > This may be so, but I personally found beat rates of
0.5 to
> > > > > > > 3 Hz
> > > > > > > much more objectionable than those of 10 to 15 Hz, with
> > > > > > > those
> > > > > > > in between being more moderately tolerable.
> > > > > >
> > > > > > A very rare and surprising assessment. So you're saying
you
> > > > > > like
> > > > > > 3 to 10 Hz beating less than 10 to 15 Hz beating, and 0.5
to
> > > > > > 3 Hz
> > > > > > beating less still?
> > > > >
> > > > > Yep.
> > > >
> > > > Wow. Are all these beat rates referring to the beating of
upper
> > > > partials in a not-quite-JI chord?
> > >
> > > For example, if I play an A major triad on my piano with the A
> > > tuned
> > > to 220 Hz, the C# to 275 Hz and the E tuned to 331 Hz, then
I'll get
> > > beats between the 3rd partial of the A at 660 Hz and the 2nd
partial
> > > of the E at 662 Hz. These beats will be at 662 - 660 = 2 Hz.
> >
> > So, as you tune the chord further and further away from JI, and
the
> > beating gets faster and faster, the chord sounds better and
better to
> > you?
>
> Not really better; just less bad. The only chords that sound good
are
> those that are perfectly in tune. The most annoying chords are the
> _nearly_ perfect ones, those that sound most like JI but are just
out
> of tune.

Wow. This is the first time I've seen this reaction, including in the
results of a number of experiments that have been performed on the
mistuning of chords.

> Once they get far enough away from that, it no longer seems
> to me that the tuner has made any effort to achieve that particular
> harmony. But, as I said earlier, in a given musical context I can
accept
> that the sounds I'm hearing are _supposed_ to represent that harmony
> - that they are a "notional" rather than an actual major triad, for
> instance.

If the beating is at a rate of 1 or 2 beats per second, but the
harmony moves along at a decent pace, you can no longer hear the
beating. Are the chords still annoying to you nonetheless?

> {begin OT}
> In this context, I don't know what (prime) limit I recognise in
> tuning;

How about odd limit?

> certainly, some very tiny variations in pitch evoke entirely
> different sensations in various oriental musics I'm familiar with,
> including Chinese opera, erhu playing, shakuhachi playing, classical
> Indian playing and singing, the best Bollywood singing. Do I hear
> the 19-limit, or perhaps the 23-limit? I really couldn't say; nor
do
> I know how to find out.

Are you sure the question is even meaningful, Yahya?

> > > > > > > The slowest beats
> > > > > > > I heard tended to cause the entire sound to flutter in
> > > > > > > volume
> > > > > > > in a rather nauseating way. I imagined this might have
> > > > > > > something to do with lower frequencies carrying greater
> > > > > > > power.
> > > > > > > But that would make no sense unless the sound envelope
can
> > > > > > > evolve in such a way that one partial can "steal" power
> > > > > > > from
> > > > > > > others - and that seems improbable given that my sound
> > > > > > > source
> > > > > > > was the samples on a chip, rather than vibrating
strings.
> > > > > >
> > > > > > I think you're confusing the frequency of a pressure
> > > > > > variation
> > > > > > (which can carry power) with the frequency of an amplitude
> > > > > > variation (which can't). The former are "notes"
or "partials",
> > > > > > the latter aren't.
> > > > >
> > > > > A sound wave is a pressure wave, isn't it?
> > > >
> > > > Yes, but a beating isn't.
> > >
> > > ???
> > >
> > > Are you saying that the difference tone created by playing two
> > > pure sine waves of different frequency is not also a sound wave?
> >
> > Ah, this is a common confusion.
> >
> > The difference tone is a result of the nonlinear response of the
ear,
> > and is completely separate/distinct from the beating phenomenon.
> >
> > Once through the nonlinear elements of the ear, the signal does
> > indeed contain frequency components corresponding to the
difference
> > frequency, as well as other frequencies not present in the
original
> > sound.
>
> OK. Sounds good. Show me the maths?

I just did that for the case of quadratic nonlinearity. Anything else
you need me to show at this point?

> > For quiet sounds, the nonlinearity is insignificant. The loudness
of
> > the difference tone and other nonlinear combinational tones
increases
> > *nonlinearly* (surprise) and generally in an accelerating manner
as
> > one increases the loudness of the original sound.
> >
> > > If that were so, it would be inaudible.
> >
> > It *is* inaudible (that is, there is no heard pitch corresponding
to
> > the difference frequency) under conditions of exactly linear
> > response.

> ... which don't exist except as an approximation good at very low
> power ...

Low loudness. Bill Sethares, in his book, claims that combinational
tones are irrelevant to music and tuning because they are too quiet
to matter at normal music listening levels. I think he needs
to "temper" this assessment somewhat.

> > ... Beating, meanwhile is a variation in loudness, which is
> > heard to modulate a pitch which corrsponds to the average, not the
> > difference, of the two sine-wave frequencies. Beating does not
> > disappear at quiet volumes; difference tones and other
combinational
> > tones do.
>
> I remember some maths trickery involving the basic trig identities:
> sin (A+B) = sin A cos B + cos A sin B, and
> cos (A+B) = cos A cos B - sin A sin B,
> together with the substitutions u = (A+B)/2, v = (A-B)/2,
> the semi-sum (average) and semi-difference of the original terms ...
> or vice versa! ... but can't recall what this was used to prove ...
it's too
> many years ago now to remember this detail.

As you can see, I used some similar identities to derive the results
of a quadratic nonlinearity on a pair of pure tones sounding together.

> > ... Either way, I'd be
> > happy to go through it myself,
>
> Please do.

Beating:

The hearing apparatus has a finite frequency resolution; this is a
mathematical necessity when you consider that we need to hear
*changes* in the world happening in time (due to the classical
uncertainty principle).

Hence a signal containing two very close frequencies at constant and
equal amplitude will be heard as a single pitch whose amplitude
changes over time.

The trig identities we need are the ones like

sin(x) + sin(y) = 2*sin((x+y)/2)*cos((x-y)/2)

I don't think I need to bring cosines in for full generality but I
welcome you to do so if you wish.

Anyway, what this identity tells us is that adding two equal-
amplitude sine waves very close in frequency is the same thing as
amplitude-modulating a sine wave at the average frequency by a cosine
wave at half the difference frequency. Since the cosine is zero twice
per cycle, and reaches its maximum absolute value twice per cycle,
the average-frequency sine wave will be heard to oscillate in
loudness at twice the modulation frequency, or twice half the
difference frequency, which of course equals the difference frequency.

If the ear is unable to resolve the two frequencies, the right side
of the equation is more directly relevant to how we hear the signal.
On the other hand, if the ear can distinguish them, the right side
becomes completely irrelevant to how we hear. However, it still may
be a relevant representation of a particular method of sound
synthesis; namely amplitude modulation. In that case, you reverse the
direction in which you read the equation: the left side tells you
what "goes in" in terms of how the AM is specified; the right side
tells you what the frequency components are. These are
called 'sidebands' because they normally straddle the modulated
frequency at equal frequency intervals on either side of it. And if
they are different enough, you hear them separately -- this is the
regime where AM results in audible sideband frequencies. When the
sidebands cannot be resolved, though, the original AM specification
on the right side of the equation becomes a direct description of how
we hear the sound -- as a single pitch modulated in amplitude at a
fairly slow rate.

The exact frequency ratios, over the entire spectrum of audible
absolute frequencies, that are just large enough to permit two sine
waves to be resolved separately, have been measured in a large body
of experiments on human subjects. They vary greatly over the
spectrum, but never become narrower than a whole tone (nearing it
only an an optimal "middle" absolute frequency range). Thankfully, we
rarely use a single pair of pure sine waves to make music!

> > > There's a BIG difference between -
> > > A. accepting a note as a notional representation of an exact
> > > interval (which I do);
> > > and
> > > B. being unaware of the difference (which apparently many
> > > other people do).
> >
> > I'm not sure if I understand what you mean by either A or B here :
(
>
> A. Knowing the note's WRONG but saying in effect, "What
> the heck, I know what you meant anyway".
>
> B. Not knowing whether the note is wrong or right.
>
> Because of arthritis and other limiting mechanical factors,
> I have reason to extend the tolerant attitude of A. to my
> own playing almost every day ... :-)

OK . . . Wouldn't B normally just be a matter of a much smaller
deviation than A? Why is B something you only associate with "other
people"? Perhaps this should be moved to a new thread?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> > Can we readily detect
> > an interval of 11/10? Sure we can. 33/32? Yep. 101/100?
> > Think so. 333/332? Well ... that's getting a bit iffy, isn't it?
>
> What does it mean to "detect" an interval? Are you saying we can tell
> 101/100 is a ratio of integers, that we can distinguish it from
> 100/99, or what, exactly?

I thought he meant we can distinguish 101/100 from 1/1, not
(necessarily) from 100/99.

This is great, Paul. Thanks. -Carl

> Beating:
>
> The hearing apparatus has a finite frequency resolution; this is
> a mathematical necessity when you consider that we need to hear
> *changes* in the world happening in time (due to the classical
> uncertainty principle).
>
> Hence a signal containing two very close frequencies at constant
> and equal amplitude will be heard as a single pitch whose
> amplitude changes over time.
>
> The trig identities we need are the ones like
>
> sin(x) + sin(y) = 2*sin((x+y)/2)*cos((x-y)/2)
>
> I don't think I need to bring cosines in for full generality but
> I welcome you to do so if you wish.
>
> Anyway, what this identity tells us is that adding two equal-
> amplitude sine waves very close in frequency is the same thing as
> amplitude-modulating a sine wave at the average frequency by a
> cosine wave at half the difference frequency. Since the cosine
> is zero twice per cycle, and reaches its maximum absolute value
> twice per cycle, the average-frequency sine wave will be heard
> to oscillate in loudness at twice the modulation frequency, or
> twice half the difference frequency, which of course equals the
> difference frequency.
>
> If the ear is unable to resolve the two frequencies, the right
> side of the equation is more directly relevant to how we hear
> the signal. On the other hand, if the ear can distinguish them,
> the right side becomes completely irrelevant to how we hear.
> However, it still may be a relevant representation of a
> particular method of sound synthesis; namely amplitude
> modulation. In that case, you reverse the direction in which
> you read the equation: the left side tells you what "goes in"
> in terms of how the AM is specified; the right side tells you
> what the frequency components are. These are called 'sidebands'
> because they normally straddle the modulated frequency at equal
> frequency intervals on either side of it. And if they are
> different enough, you hear them separately -- this is the
> regime where AM results in audible sideband frequencies. When
> the sidebands cannot be resolved, though, the original AM
> specification on the right side of the equation becomes a
> direct description of how we hear the sound -- as a single pitch
> modulated in amplitude at a fairly slow rate.
>
> The exact frequency ratios, over the entire spectrum of audible
> absolute frequencies, that are just large enough to permit two
> sine waves to be resolved separately, have been measured in a
> large body of experiments on human subjects. They vary greatly
> over the spectrum, but never become narrower than a whole tone
> (nearing it only an an optimal "middle" absolute frequency
> range). Thankfully, we rarely use a single pair of pure sine
> waves to make music!

On Thu, 20 Oct 2005, "Gene Ward Smith" wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> > Can we readily detect
> > an interval of 11/10? Sure we can. 33/32? Yep. 101/100?
> > Think so. 333/332? Well ... that's getting a bit iffy, isn't it?
>
> What does it mean to "detect" an interval? Are you saying we can tell
> 101/100 is a ratio of integers, that we can distinguish it from
> 100/99, or what, exactly?

Gene,

That's a good question, as usual. I should have been clearer.
I meant the second - that we can distinguish it from any other
ratio.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.12.4/143 - Release Date: 19/10/05

Hi Paul,

I've edited this dialogue to eliminate long strings of multiple
"accidentals" like "> > > > > > >", etc and the consequent wrapping
of lines to the point of near-unreadability. My latest replies
are indented and set off with an asterisk, thus:

* YA's latest retort.

On Thu, 20 Oct 2005, "wallyesterpaulrus" wrote:
[snip]

[YA]
This may be so, but I personally found beat rates of 0.5 to 3 Hz
much more objectionable than those of 10 to 15 Hz, with those
in between being more moderately tolerable.

[PE]
A very rare and surprising assessment. So you're saying you
like 3 to 10 Hz beating less than 10 to 15 Hz beating, and 0.5 to
3 Hz beating less still?

[YA]
Yep.

[PE]
Wow. Are all these beat rates referring to the beating of upper
partials in a not-quite-JI chord?

[YA]
For example, if I play an A major triad on my piano with the A tuned
to 220 Hz, the C# to 275 Hz and the E tuned to 331 Hz, then I'll get
beats between the 3rd partial of the A at 660 Hz and the 2nd partial
of the E at 662 Hz. These beats will be at 662 - 660 = 2 Hz.

[PE]
So, as you tune the chord further and further away from JI, and the
beating gets faster and faster, the chord sounds better and better to
you?

[YA]
Not really better; just less bad. The only chords that sound good are
those that are perfectly in tune. The most annoying chords are the
_nearly_ perfect ones, those that sound most like JI but are just out
of tune.

[PE]
Wow. This is the first time I've seen this reaction, including in the
results of a number of experiments that have been performed on the
mistuning of chords.

- Hope I don't mess up your HE curves! :-)

[YA]
Once they get far enough away from that, it no longer seems
to me that the tuner has made any effort to achieve that particular
harmony. But, as I said earlier, in a given musical context I can accept
that the sounds I'm hearing are _supposed_ to represent that harmony
- that they are a "notional" rather than an actual major triad, for
instance.

[PE]
If the beating is at a rate of 1 or 2 beats per second, but the
harmony moves along at a decent pace, you can no longer hear the
beating. Are the chords still annoying to you nonetheless?

* Not if I can't hear the beating. In very fast music, my ability to
discriminate between pitches also goes WAY down.

[YA]
{begin OT}
In this context, I don't know what (prime) limit I recognise in
tuning;

[PE]
How about odd limit?

* No.

[YA]
... certainly, some very tiny variations in pitch evoke entirely
different sensations in various oriental musics I'm familiar with,
including Chinese opera, erhu playing, shakuhachi playing, classical
Indian playing and singing, the best Bollywood singing. Do I hear
the 19-limit, or perhaps the 23-limit? I really couldn't say; nor do
I know how to find out.

[PE]
Are you sure the question is even meaningful, Yahya?

* Sure? No. But I think it may be. Would a musical tuning that
requires 137-limit intervals be meaningful, Paul, if we couldn't
hear the difference between that and, say, the 19-limit?

[YA]
... The slowest beats
I heard tended to cause the entire sound to flutter in volume
in a rather nauseating way. I imagined this might have
something to do with lower frequencies carrying greater power.
But that would make no sense unless the sound envelope can
evolve in such a way that one partial can "steal" power from
others - and that seems improbable given that my sound source
was the samples on a chip, rather than vibrating strings.

[PE]
I think you're confusing the frequency of a pressure variation
(which can carry power) with the frequency of an amplitude
variation (which can't). The former are "notes" or "partials",
the latter aren't.

[YA]
A sound wave is a pressure wave, isn't it?

[PE]
Yes, but a beating isn't.

[YA]
???

Are you saying that the difference tone created by playing two
pure sine waves of different frequency is not also a sound wave?

[PE]
Ah, this is a common confusion.

The difference tone is a result of the nonlinear response of the ear,
and is completely separate/distinct from the beating phenomenon.

Once through the nonlinear elements of the ear, the signal does
indeed contain frequency components corresponding to the difference
frequency, as well as other frequencies not present in the original
sound.

[YA]
OK. Sounds good. Show me the maths?

[PE]
I just did that for the case of quadratic nonlinearity. Anything else
you need me to show at this point?

* Nope.

[PE]
For quiet sounds, the nonlinearity is insignificant. The loudness of
the difference tone and other nonlinear combinational tones increases
*nonlinearly* (surprise) and generally in an accelerating manner as
one increases the loudness of the original sound.

[YA]
If that were so, it [the beat] would be inaudible.

[PE]
It *is* inaudible (that is, there is no heard pitch corresponding to
the difference frequency) under conditions of exactly linear
response.

[YA]
... which don't exist except as an approximation good at very low
power ...

[PE]
Low loudness.

* Why is the distinction important here?

[PE]
Bill Sethares, in his book, claims that combinational
tones are irrelevant to music and tuning because they are too quiet
to matter at normal music listening levels. I think he needs
to "temper" this assessment somewhat.

* They'd make ALL the difference if you're trying to achieve
a totally inharmonic spectrum!

[PE]
... Beating, meanwhile is a variation in loudness, which is
heard to modulate a pitch which corrsponds to the average, not the
difference, of the two sine-wave frequencies. Beating does not
disappear at quiet volumes; difference tones and other combinational
tones do.

[YA]
I remember some maths trickery involving the basic trig identities:
sin (A+B) = sin A cos B + cos A sin B, and
cos (A+B) = cos A cos B - sin A sin B,
together with the substitutions u = (A+B)/2, v = (A-B)/2,
the semi-sum (average) and semi-difference of the original terms ...
or vice versa! ... but can't recall what this was used to prove ... it's too
many years ago now to remember this detail.

[PE]
As you can see, I used some similar identities to derive the results
of a quadratic nonlinearity on a pair of pure tones sounding together.

* Thought you might.

[PE]
... Either way, I'd be happy to go through it myself,

[YA]
Please do.

[PE]
Beating:

The hearing apparatus has a finite frequency resolution; this is a
mathematical necessity when you consider that we need to hear
*changes* in the world happening in time (due to the classical
uncertainty principle).

* I think I'll just let that one go by for now! And accept the
"finite resolution" bit.

[PE]
Hence a signal containing two very close frequencies at constant and
equal amplitude will be heard as a single pitch whose amplitude
changes over time.

The trig identities we need are the ones like

sin(x) + sin(y) = 2*sin((x+y)/2)*cos((x-y)/2)

I don't think I need to bring cosines in for full generality but I
welcome you to do so if you wish.

* Not at all - your expressions in a*sin(2pi*x) + b*cos(2pi*x)
might have been more compactly written, I think, as
k*sin(2pi*x+h), where h is a phase angle.

[PE]
Anyway, what this identity tells us is that adding two equal-
amplitude sine waves very close in frequency is the same thing as
amplitude-modulating a sine wave at the average frequency by a cosine
wave at half the difference frequency. Since the cosine is zero twice
per cycle, and reaches its maximum absolute value twice per cycle,
the average-frequency sine wave will be heard to oscillate in
loudness at twice the modulation frequency, or twice half the
difference frequency, which of course equals the difference frequency.

If the ear is unable to resolve the two frequencies, the right side
of the equation is more directly relevant to how we hear the signal.
On the other hand, if the ear can distinguish them, the right side
becomes completely irrelevant to how we hear. However, it still may
be a relevant representation of a particular method of sound
synthesis; namely amplitude modulation. In that case, you reverse the
direction in which you read the equation: the left side tells you
what "goes in" in terms of how the AM is specified; the right side
tells you what the frequency components are. These are
called 'sidebands' because they normally straddle the modulated
frequency at equal frequency intervals on either side of it. And if
they are different enough, you hear them separately -- this is the
regime where AM results in audible sideband frequencies. When the
sidebands cannot be resolved, though, the original AM specification
on the right side of the equation becomes a direct description of how
we hear the sound -- as a single pitch modulated in amplitude at a
fairly slow rate.

* Clear so far.

[PE]
The exact frequency ratios, over the entire spectrum of audible
absolute frequencies, that are just large enough to permit two sine
waves to be resolved separately, have been measured in a large body
of experiments on human subjects. They vary greatly over the
spectrum, but never become narrower than a whole tone (nearing it
only an an optimal "middle" absolute frequency range). Thankfully, we
rarely use a single pair of pure sine waves to make music!

* So what you're saying implies that at all audible frequencies,
we cannot hear a pair of pure sine waves differing only by a
semitone as such - our ears require that we hear them as an AM
tone at their average frequency?

I must dust off the Moog and go make myself some *very* simple
compound tones!

How much does this difference vary from one individual to
another, according to the "large body of experiments"?

[YA]
There's a BIG difference between -
A. accepting a note as a notional representation of an exact
interval (which I do);
and
B. being unaware of the difference (which apparently many
other people do).

[PE]
I'm not sure if I understand what you mean by either A or B here :(

[YA]
A. Knowing the note's WRONG but saying in effect, "What
the heck, I know what you meant anyway".

B. Not knowing whether the note is wrong or right.

Because of arthritis and other limiting mechanical factors,
I have reason to extend the tolerant attitude of A. to my
own playing almost every day ... :-)

[PE]
OK . . . Wouldn't B normally just be a matter of a much smaller
deviation than A? Why is B something you only associate with "other
people"? Perhaps this should be moved to a new thread?

* If the matter interests you enough. I'm just describing how
I hear things. I don't claim I have perfect pitch discrimination
- far from it. But I may be more than usually _aware_ of pitch
differences that most people don't pick up on - not because
they couldn't, but because they just don't - a matter of how
we use our hearing, rather than of what we hear.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.12.4/143 - Release Date: 19/10/05

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> [YA]
> Not really better; just less bad. The only chords that sound good are
> those that are perfectly in tune. The most annoying chords are the
> _nearly_ perfect ones, those that sound most like JI but are just out
> of tune.

I think chords which are detuned about a cent in some ways sound
better than more exact tunings; they sound in tune, but not completely
static. However, ennealimmal tunings to me sound very much like JI. At
what point does it become not almost-JI and therefore annoying, but
truly sensibly-JI and therefore "good"?

Hi Gene,

On Fri, 21 Oct 2005, "Gene Ward Smith" wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
>
> > [YA]
> > Not really better; just less bad. The only chords that sound good are
> > those that are perfectly in tune. The most annoying chords are the
> > _nearly_ perfect ones, those that sound most like JI but are just out
> > of tune.
>
> I think chords which are detuned about a cent in some ways sound
> better than more exact tunings; they sound in tune, but not completely
> static.

I understand your point. Perfect consonances can be rather
lacking in character, particularly when the instruments in use
do not have very rich spectra of overtones in their timbres.
But used ocasionally, these purer or simpler spectra can give
us a respite from music that uses only very dirty or active
timbres.

> However, ennealimmal tunings to me sound very much like JI.

I must make time to try one out; which would you recommend?
And when you say "very much like", are you still able to
distinguish between the two tunings in music played lento?
moderato? allegro?

> At
> what point does it become not almost-JI and therefore annoying, but
> truly sensibly-JI and therefore "good"?

Presumably, it only becomes sensibly-JI at the point where
the individual listener can no longer sense a difference from
JI! That's not meant entirely facetiously - I'm saying I think
the answer to this question depends very much on the listener.

I'd be interested to know what range of variability has been
measured between listeners on this question. Some psycho-
metric data would be useful, if it exists. Does anyone know?

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.344 / Virus Database: 267.12.4/146 - Release Date: 21/10/05

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> > However, ennealimmal tunings to me sound very much like JI.
>
> I must make time to try one out; which would you recommend?

441 or 612 edo work fine. 1494 is perhaps more interesting; it is
7-limit poptimal, and the brat (beat ratio) is very near the synch
beat tuning, brat=-1.01. These should be used for 5-, 7- or 9-limit
harmonies for the most part, which is what ennealimmal is designed for.

> And when you say "very much like", are you still able to
> distinguish between the two tunings in music played lento?
> moderato? allegro?

It sounds the same as JI to me at reasonably brisk tempos; I've never
tried a hearing test to see what I could discern at very slow tempos.
One problem is that I am by no means sure my sound fonts are tuned
accurately enough; such a test would need to be made using Csound, or
some other system you trust, such as a soundcard you've tested to
ensure it is accurate to small fractions of a cent. It might be
interesting to try sustaining chords in the synch tuning, and see if
the very long period synchronized beating can be heard.

Gene,

On Sun, 23 Oct 2005, "Gene Ward Smith" wrote:
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
> > > However, ennealimmal tunings to me sound very much like JI.
> >
> > I must make time to try one out; which would you recommend?
>
> 441 or 612 edo work fine. 1494 is perhaps more interesting; it is
> 7-limit poptimal, and the brat (beat ratio) is very near the synch
> beat tuning, brat=-1.01. These should be used for 5-, 7- or 9-limit
> harmonies for the most part, which is what ennealimmal is designed
> for.

Thanks for this.

> > And when you say "very much like", are you still able to
> > distinguish between the two tunings in music played lento?
> > moderato? allegro?
>
> It sounds the same as JI to me at reasonably brisk tempos; I've never
> tried a hearing test to see what I could discern at very slow tempos.
> One problem is that I am by no means sure my sound fonts are tuned
> accurately enough; such a test would need to be made using Csound, or
> some other system you trust, such as a soundcard you've tested to
> ensure it is accurate to small fractions of a cent. It might be
> interesting to try sustaining chords in the synch tuning, and see if
> the very long period synchronized beating can be heard.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.361 / Virus Database: 267.12.4/146 - Release Date: 21/10/05

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> On Thu, 20 Oct 2005, "Gene Ward Smith" wrote:
> >
> > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
wrote:
> >
> > > Can we readily detect
> > > an interval of 11/10? Sure we can. 33/32? Yep. 101/100?
> > > Think so. 333/332? Well ... that's getting a bit iffy, isn't
it?
> >
> > What does it mean to "detect" an interval? Are you saying we can
tell
> > 101/100 is a ratio of integers, that we can distinguish it from
> > 100/99, or what, exactly?
>
> Gene,
>
> That's a good question, as usual. I should have been clearer.
> I meant the second - that we can distinguish it from any other
> ratio.
>
> Regards,
> Yahya

Then I completely misunderstood you. You're claiming you can
distinguish 101/100 from 100/99? That's a pretty extreme claim. I'd
like to see some evidence of that. Are you also claiming you can
distinguish 101/100 from 1010001/1000001? Because you did say "any
other ratio" . . .

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

>> [YA]
>> {begin OT}
>> In this context, I don't know what (prime) limit I recognise in
>> tuning;
>
>> [PE]
>> How about odd limit?
>
>> * No.

OK, then there's no constraint on the size of the numbers in the
ratios, only on the sizes of their largest prime factors. Are you
sure this is the kind of 'limit' you want?

>
>> [YA]
>> ... certainly, some very tiny variations in pitch evoke entirely
>> different sensations in various oriental musics I'm familiar with,
>> including Chinese opera, erhu playing, shakuhachi playing,
>classical
>> Indian playing and singing, the best Bollywood singing. Do I hear
>> the 19-limit, or perhaps the 23-limit? I really couldn't say; nor
>do
>> I know how to find out.
>
>> [PE]
>> Are you sure the question is even meaningful, Yahya?
>>
>> * Sure? No. But I think it may be. Would a musical tuning that
>> requires 137-limit intervals be meaningful, Paul, if we
>couldn't
>> hear the difference between that and, say, the 19-limit?

Musical tunings "meaningful"? That's not the question. But the
question of whether a particular prime limit is or isn't in
force . . . since there's no limit on the sizes of the numbers in the
ratios, you can always find more and more ratios within the prime
limit that are closer and closer to a given ratio. At what point do
these high-numbered ratios leave the realm of musical relevance? Of
course it depends on the tuning system, but my point is that a prime
limit alone doesn't seem to be capable of unambiguously corresponding
or not corresponding, in general, to an arbitrary tuning system, via
any aural or even mathematical test, as long as one recognizes a
finite uncertainty in hearing intervals (or even merely the minimal
uncertainty allowed by the classical uncertainty
principle . . .) . . . The exceptions would seem to be cases where an
odd, integer, or other "finitary" limit is ascertained first, and
then the prime limit is simply taken as the largest prime not
exceeding that limit.

>> [PE]
>> For quiet sounds, the nonlinearity is insignificant. The loudness
of
>> the difference tone and other nonlinear combinational tones
increases
>> *nonlinearly* (surprise) and generally in an accelerating manner as
>> one increases the loudness of the original sound.
>
> [YA]
>> If that were so, it [the beat] would be inaudible.
>
> [PE]
>> It *is* inaudible (that is, there is no heard pitch corresponding
to
>> the difference frequency) under conditions of exactly linear
>> response.
>
> [YA]
>> ... which don't exist except as an approximation good at very low
>> power ...
>
> [PE]
>> Low loudness.
>
>> * Why is the distinction important here?

Because the nonlinearity of the response happens in the ear, so what
matters is how loud the sound is when it reaches the ear, not its
power at the source.

> [PE]
>> Bill Sethares, in his book, claims that combinational
>> tones are irrelevant to music and tuning because they are too quiet
>> to matter at normal music listening levels. I think he needs
>> to "temper" this assessment somewhat.
>
>> * They'd make ALL the difference if you're trying to achieve
>> a totally inharmonic spectrum!

Bill Sethares seems to disagree. His book is all about
consonance/dissonance and making music with *inharmonic spectra* and
he completely dismisses the relevance of combinational tones to this
enterprise.

>> [PE]
>> The exact frequency ratios, over the entire spectrum of audible
>> absolute frequencies, that are just large enough to permit two sine
>> waves to be resolved separately, have been measured in a large body
>> of experiments on human subjects. They vary greatly over the
>> spectrum, but never become narrower than a whole tone (nearing it
>> only an an optimal "middle" absolute frequency range). Thankfully,
we
>> rarely use a single pair of pure sine waves to make music!
>
>> * So what you're saying implies that at all audible frequencies,
>> we cannot hear a pair of pure sine waves differing only by a
>> semitone as such - our ears require that we hear them as an
AM
>> tone at their average frequency?

We may hear aspects of both -- there's a "roughness" region between
the "beating" region and the "two tones" region where the sound is a
confused compromise between the two latter sensations. But the
beating tone at the average frequency doesn't completely disappear
from our hearing until the sine waves differ by at least a whole tone.

> How much does this difference vary from one individual to
> another, according to the "large body of experiments"?

Not a lot, and the interval in question is called the "critical
band" -- one of the most familiar, and hence well-documented,
entities in psychoacoustics. It seems to relate to the physical
properties (such as elasticity) of the membrane in the cochlea which
physically "analyzes" sound into its component frequencies.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> > [YA]
> > Not really better; just less bad. The only chords that sound good
are
> > those that are perfectly in tune. The most annoying chords are the
> > _nearly_ perfect ones, those that sound most like JI but are just
out
> > of tune.
>
> I think chords which are detuned about a cent in some ways sound
> better than more exact tunings; they sound in tune, but not completely
> static.

I agree with this latter sentiment! Pure JI implies phase-locked
partials, with permanent destructive and constructive interference of
certain partials an unfortunate consequence, which you can partially
mitigate only if you're very careful with staggering your onset times
in an appropriate way . . .

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> Hi Gene,
>
> On Fri, 21 Oct 2005, "Gene Ward Smith" wrote:
> >
> > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > <yahya@m...> wrote:
> >
> > > [YA]
> > > Not really better; just less bad. The only chords that sound
good are
> > > those that are perfectly in tune. The most annoying chords are
the
> > > _nearly_ perfect ones, those that sound most like JI but are
just out
> > > of tune.
> >
> > I think chords which are detuned about a cent in some ways sound
> > better than more exact tunings; they sound in tune, but not
completely
> > static.
>
> I understand your point. Perfect consonances can be rather
> lacking in character, particularly when the instruments in use
> do not have very rich spectra of overtones in their timbres.

I would say that it's precisely the instruments with *rich* harmonic
spectra that can sound oddly static, with permanent destructive or
constructive interference of certain partials, when truly exact JI is
used.

> But used ocasionally, these purer or simpler spectra can give
> us a respite from music that uses only very dirty or active
> timbres.

With sine waves, the simplest spectrum of all, the aural distinction
between exact JI and a mere very close approximation disappears.

Dear, exasperating Paul,

On Tue, 25 Oct 2005 "wallyesterpaulrus" wrote:
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
> >
> > On Thu, 20 Oct 2005, "Gene Ward Smith" wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
> > > wrote:
> > >
> > > > Can we readily detect
> > > > an interval of 11/10? Sure we can. 33/32? Yep. 101/100?
> > > > Think so. 333/332? Well ... that's getting a bit iffy, isn't
> > > > it?
> > >
> > > What does it mean to "detect" an interval? Are you saying we can
> > > tell
> > > 101/100 is a ratio of integers, that we can distinguish it from
> > > 100/99, or what, exactly?
> >
> > Gene,
> >
> > That's a good question, as usual. I should have been clearer.
> > I meant the second - that we can distinguish it from any other
> > ratio.
> >
> > Regards,
> > Yahya
>
> Then I completely misunderstood you.

It has happened.

> You're claiming you can
> distinguish 101/100 from 100/99? That's a pretty extreme claim. I'd
> like to see some evidence of that. Are you also claiming you can
> distinguish 101/100 from 1010001/1000001? Because you did say "any
> other ratio" . . .

Picky, picky! :-) The last is a wilfully ridiculous interpretation
of my words - and you know it. Why stop at a difference of
1010001/1010000? You could clearly add a googolplex of
zeroes to both terms if you felt so inclined. I know I sometimes
say silly or provocative things, but ... ! I doubt that I could ever
choose my words well enough to defeat every possible
misinterpretation.

Still, maybe I could have been clearer. I was confirming Gene's
second interpretation: that we can distinguish 101/100 from
100/99. I should have written: that we can distinguish it from
any other nearby ratio.

I hereby resolve not to reply to tuning list messages after 2am
or before breakfast.

Let's get back to context here ... I wrote, as you quoted:
> > > > Can we readily detect
> > > > an interval of 11/10? Sure we can. 33/32? Yep. 101/100?
> > > > Think so. 333/332? Well ... that's getting a bit iffy, isn't
> > > > it?

Surely it's obvious that I'm selecting a set of increasingly
finer ratios that tend downward to 1?
11/10 ... 33/32 ... 101/100 ... 333/332 ...

And that I'm saying that each is harder to "detect" than
the previous? When I get to 33/32, I say, yes, I can
detect it; when I get to 101/100, I only say I think I can
detect it.

But since you ask ... Let me see now.

To detect 33/32, I need to distinguish it from its nearest
neighbours in this series of epimores, namely from 32/31
and, even closer, 35/34. Here is some data from an Excel
spreadsheet I just rustled up, called "discriminating
epimores". I've saved the data in CSV form, so Monz and
others can format it as they like, expanding the commas to
tabs, spaces or whatever.

n,n-1,n/(n-1),cents,difference
32,31,1.032258065,54.96,
33,32,1.03125,53.27,1.69
34,33,1.03030303,51.68,1.59

99,98,1.010204082,17.58,
100,99,1.01010101,17.40,0.18
101,100,1.01,17.23,0.17

In plain English, the ratio 32/31 is 1.69 cents bigger than
33/32, which is 1.59 cents bigger than 34/33; since these
are less than 2 cents, I'd have to say it is quite possible I
couldn't distinguish one from the other in actual music.
That is, if I hear what I think is a 33/32, but you tell me
you actually tuned it as a 32/31, then I probably have to
accept that - I can't argue, unless I can show that I can
reliably discriminate intervals smaller than 2 cents. Which
I have not yet done. How might I do so?

But I'd need Superman's hearing to distinguish 100/99
from 101/100, a difference of a mere 0.17 cent. One point
to Paul! :-)

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.361 / Virus Database: 267.12.4/146 - Release Date: 21/10/05

Paul,

On Tue, 25 Oct 2005, "wallyesterpaulrus" wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
> >
> > Hi Gene,
> >
> > On Fri, 21 Oct 2005, "Gene Ward Smith" wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > > <yahya@m...> wrote:
> > >
> > > > [YA]
> > > > Not really better; just less bad. The only chords that sound
> > > > good are those that are perfectly in tune. The most annoying
> > > > chords are the _nearly_ perfect ones, those that sound most
> > > > like JI but are just out of tune.
> > >
> > > I think chords which are detuned about a cent in some ways
> > > sound better than more exact tunings; they sound in tune, but
> > > not completely static.
> >
> > I understand your point. Perfect consonances can be rather
> > lacking in character, particularly when the instruments in use
> > do not have very rich spectra of overtones in their timbres.
>
> I would say that it's precisely the instruments with *rich* harmonic
> spectra that can sound oddly static, with permanent destructive or
> constructive interference of certain partials, when truly exact JI is
> used.

You would! :-) But I don't think I've actually ever heard such
a thing, so I can't judge. I was thinking of -
1. a choir of boy sopranos.
2. simple spectra produced on my Moog.

> > But used ocasionally, these purer or simpler spectra can give
> > us a respite from music that uses only very dirty or active
> > timbres.
>
> With sine waves, the simplest spectrum of all, the aural distinction
> between exact JI and a mere very close approximation disappears.

Is there a simple, useful measure of the "richness" or complexity
of pitch spectra?

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.361 / Virus Database: 267.12.4/146 - Release Date: 21/10/05

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> Paul,
>
> On Tue, 25 Oct 2005, "wallyesterpaulrus" wrote:
> >
> > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > <yahya@m...> wrote:
> > >
> > > Hi Gene,
> > >
> > > On Fri, 21 Oct 2005, "Gene Ward Smith" wrote:
> > > >
> > > > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> > > > <yahya@m...> wrote:
> > > >
> > > > > [YA]
> > > > > Not really better; just less bad. The only chords that
sound
> > > > > good are those that are perfectly in tune. The most
annoying
> > > > > chords are the _nearly_ perfect ones, those that sound most
> > > > > like JI but are just out of tune.
> > > >
> > > > I think chords which are detuned about a cent in some ways
> > > > sound better than more exact tunings; they sound in tune, but
> > > > not completely static.
> > >
> > > I understand your point. Perfect consonances can be rather
> > > lacking in character, particularly when the instruments in use
> > > do not have very rich spectra of overtones in their timbres.
> >
> > I would say that it's precisely the instruments with *rich*
harmonic
> > spectra that can sound oddly static, with permanent destructive
or
> > constructive interference of certain partials, when truly exact
JI is
> > used.
>
> You would! :-) But I don't think I've actually ever heard such
> a thing, so I can't judge. I was thinking of -
> 1. a choir of boy sopranos.
> 2. simple spectra produced on my Moog.

It would be difficult to acheive the exactness of JI needed to hear
this without 'artificial' means -- which includes certain
synthesizers and of course creating the waveforms directly on a
computer. A really cool demostration (assuming the latter) is to use
a different speaker for each note -- then you can change the various
interferences from constructive to destructive, or vice versa, just
by moving your head!

> > > But used ocasionally, these purer or simpler spectra can give
> > > us a respite from music that uses only very dirty or active
> > > timbres.
> >
> > With sine waves, the simplest spectrum of all, the aural
distinction
> > between exact JI and a mere very close approximation disappears.
>
> Is there a simple, useful measure of the "richness" or complexity
> of pitch spectra?

I don't know -- I'd just say that you can get any of the upper
partials to beat against a "probe sine wave", these partials have to
be considered significant, and lend some richness or complexity to
the sound.

There are demonstrations of JI and ET.
http://www.geocities.jp/imyfujita/wtcpage004.html

Music of Sacred Temperament;
http://www.geocities.jp/imyfujita/index.html