Hermode tuning (was: how to add scale tuning to a digital piano?)

On 22 August 2012 06:56, Carl Lumma <carl@...> wrote:
>
>
>
> Hi Bogdan!
>
>
>
> > They claim to having solved Pythagora's comma.
>
> Those claims were greatly exaggerated.
>
> In case you are interested, here are some demos and a "review"
> of the Pitch Palette, that I first put on the web in 1997
>
> http://lumma.org/music/score/justonic/
>
>
> > But the ideea is great. Is the solution to all challenges created
> > by changing root and key on fixed key instruments. As I see it,
> > playing a 50+ tones per octave just to have all the harmonic
> > options available is cumbersome. I'd rather play a simple 7, 12
> > or 19-24 tones per octave, just and not tempered, on a thing that
> > could change manually or automatically the root in real time.
>
> Yes, it is great idea that many have worked on. But as yet,
> there is no 'reference' software implementation of any of them.
>
> Are you familiar with Hermode tuning? It is one of the best
> attempts so far
> http://www.hermode.com
> The algorithm is built in to Apple Logic, and was also built
> in to the famous Access Virus series keyboards.
>
> There is also a very exciting REAPER plugin under development
> by Kite Giedraitis. His very long demo starts here:
> http://www.youtube.com/watch?v=flqYtOtSeF0
>
> -Carl
>

Thank you Carl! I’ve been working on something similar (on and off)
for a few years, and this thread is the first reference to Pitch
Palette and & Hermode tuning that I’ve seen. Put it down to poor
Googling skills or something.

My area of interest is simulating how a well-trained choir would tune
(mainly) renaissance music. It would be useful for giving a less
experienced choir their notes without giving them equally-tempered
chords. Naturally the biggest obstacle I’ve come across is the
syntonic comma. Strangely this doesn’t seem to bother good choirs,
possibly because there is enough uncertainty of intonation to cover
the comma without being too obvious (a synth can produce an obvious
slide if you’re not careful).

I find it strange that the Hermode website contains baroque, classical
and romantic examples in their tuning, but have no examples of the
only period when just intonation was actually expected (ie.
renaissance vocal music). Especially given their very lucid
explanation of the introduction of the just third in the fifteenth
century. But that must just reflect their musical interests.

Vaughan

Hi Vaughan,

If you like those, I predict you will love these, which
pertain to what we call 'Vicentino-style adaptive tuning'

overview with MIDI demo
http://www.tonalsoft.com/enc/a/adaptive-ji.aspx
paper
http://www.musicstudies.org/JIMS2008/articles/Wild_JIMS_0821208.pdf
multimedia from paper
http://www.musicstudies.org/Wild_JIMS_0821208.html
http://www.music.mcgill.ca/~wild/priv/pz54e01/madonna_ilPocoDolce.aiff
recent work
http://soonlabel.com/xenharmonic/archives/627
hour-long BBC radio documentary which is unbelievably good
http://lumma.org/temp/TheArchMusician.mp3

I welcome further discussion!

-Carl

--- In tuning@yahoogroups.com, Vaughan McAlley <ockegheim@...> wrote:

> Thank you Carl! I’ve been working on something similar (on and off)
> for a few years, and this thread is the first reference to Pitch
> Palette and & Hermode tuning that I’ve seen. Put it down to poor
> Googling skills or something.
>
> My area of interest is simulating how a well-trained choir would
> tune (mainly) renaissance music. It would be useful for giving a
> less experienced choir their notes without giving them equally-
> tempered chords. Naturally the biggest obstacle I’ve come across
> is the syntonic comma. Strangely this doesn’t seem to bother good
> choirs, possibly because there is enough uncertainty of intonation
> to cover the comma without being too obvious (a synth can produce
> an obvious slide if you’re not careful).
>
> I find it strange that the Hermode website contains baroque,
> classical and romantic examples in their tuning, but have no
> examples of the only period when just intonation was actually
> expected (ie. renaissance vocal music). Especially given their
> very lucid explanation of the introduction of the just third in
> the fifteenth century. But that must just reflect their musical
> interests.
>
> Vaughan

Great resource Carl!

Here's Vicentino's 31 EDO mapped on the Terpstra (with sound!)
http://improvise.free.fr/bosanquet/bosanquet.html

Bogdan

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Vaughan,
>
> If you like those, I predict you will love these, which
> pertain to what we call 'Vicentino-style adaptive tuning'
>
> overview with MIDI demo
> http://www.tonalsoft.com/enc/a/adaptive-ji.aspx
> paper
> http://www.musicstudies.org/JIMS2008/articles/Wild_JIMS_0821208.pdf
> multimedia from paper
> http://www.musicstudies.org/Wild_JIMS_0821208.html
> http://www.music.mcgill.ca/~wild/priv/pz54e01/madonna_ilPocoDolce.aiff
> recent work
> http://soonlabel.com/xenharmonic/archives/627
> hour-long BBC radio documentary which is unbelievably good
> http://lumma.org/temp/TheArchMusician.mp3
>
> I welcome further discussion!
>
> -Carl
>
> --- In tuning@yahoogroups.com, Vaughan McAlley <ockegheim@> wrote:
>
> > Thank you Carl! I’ve been working on something similar (on and off)
> > for a few years, and this thread is the first reference to Pitch
> > Palette and & Hermode tuning that I’ve seen. Put it down to poor
> > Googling skills or something.
> >
> > My area of interest is simulating how a well-trained choir would
> > tune (mainly) renaissance music. It would be useful for giving a
> > less experienced choir their notes without giving them equally-
> > tempered chords. Naturally the biggest obstacle I’ve come across
> > is the syntonic comma. Strangely this doesn’t seem to bother good
> > choirs, possibly because there is enough uncertainty of intonation
> > to cover the comma without being too obvious (a synth can produce
> > an obvious slide if you’re not careful).
> >
> > I find it strange that the Hermode website contains baroque,
> > classical and romantic examples in their tuning, but have no
> > examples of the only period when just intonation was actually
> > expected (ie. renaissance vocal music). Especially given their
> > very lucid explanation of the introduction of the just third in
> > the fifteenth century. But that must just reflect their musical
> > interests.
> >
> > Vaughan
>

Hi,

Am 23.08.2012 03:39, schrieb Vaughan McAlley:
>
>
> On 22 August 2012 06:56, Carl Lumma <carl@...
> <mailto:carl%40lumma.org>> wrote:
> > > They claim to having solved Pythagora's comma.
> >
> > Those claims were greatly exaggerated.
> >
> > In case you are interested, here are some demos and a "review"
> > of the Pitch Palette, that I first put on the web in 1997
> >
> > http://lumma.org/music/score/justonic/
> >
> >
> > > But the ideea is great. Is the solution to all challenges created
> > > by changing root and key on fixed key instruments. As I see it,
> > > playing a 50+ tones per octave just to have all the harmonic
> > > options available is cumbersome. I'd rather play a simple 7, 12
> > > or 19-24 tones per octave, just and not tempered, on a thing that
> > > could change manually or automatically the root in real time.
>
> > Yes, it is great idea that many have worked on. But as yet,
> > there is no 'reference' software implementation of any of them.
>
If understand you right, Martin Vogel has discussed similar problems.
His solution to build a Just Intonated instrument was to use 170 and
something tones per octave. In order allow easy playing in the Tonnetz
as his idea was, he developed a logic that moves the hexagon which
selects the tones for the actual tuning according to the played chords.

In the 1980th, some mathematicians took his ideas and built an
electronic instrument named MUTABOR. While they experimented with it a
lot they developed a mathematical language for tone systems. One of its
dialects has been implemented as computer software and is availlable at
http://www.math.tu-dresden.de/~mutabor/. Though Werner Mohrlock pretends
Hermode to be a successor, its not. It's just a different approach using
different mathematical means and a different development model.

(If you need help don't hesitate to ask: Its free software, even the
support.)

> >
> > Are you familiar with Hermode tuning? It is one of the best
> > attempts so far
> > http://www.hermode.com
> > The algorithm is built in to Apple Logic, and was also built
> > in to the famous Access Virus series keyboards.
> >
> > There is also a very exciting REAPER plugin under development
> > by Kite Giedraitis. His very long demo starts here:
> > http://www.youtube.com/watch?v=flqYtOtSeF0
> >
> > -Carl
> >
>
> Thank you Carl! I’ve been working on something similar (on and off)
> for a few years, and this thread is the first reference to Pitch
> Palette and & Hermode tuning that I’ve seen. Put it down to poor
> Googling skills or something.
>
> My area of interest is simulating how a well-trained choir would tune
> (mainly) renaissance music. It would be useful for giving a less
> experienced choir their notes without giving them equally-tempered
> chords. Naturally the biggest obstacle I’ve come across is the
> syntonic comma. Strangely this doesn’t seem to bother good choirs,
> possibly because there is enough uncertainty of intonation to cover
> the comma without being too obvious (a synth can produce an obvious
> slide if you’re not careful).
>
When I started considering music this was one of the topic I wanted to
research. But somehow I ended up discussing partial order in tone
systems. Nevertheless, I don't think it's too strange that a good choir
can deal with syntonic commas. One of the reason is: You don't have to
care about them unless the composer produced a collision. And that needs
a strong melodic preparation or an unusual harmonic progression.
Harmonic resolution of the auditory system (including
consonance/dissonance or timbre) is much stronger than melodic. A singer
who is not keen on being a voice leader, can concentrate mainly on
something like resonance and fit his/her voice before the standing wave
has been established.

Another problem: Every singer in a well-trained choir has started some
time ago being a poorly trained one. During their education some of them
have developed their absolute hearing to a certain extent (not
necessarily reliable), which helps them to detune melodic intervals in
the “right way”. But this is more concerned with compensating the
pythagorean comma or one of its equivalents for major (3T-1O), minor
thirds (4t-1O), which are the building blocks of the syntonic comma.

If you need a third model, the idea of sensory dissonance might be
helpful (Sethares: “Tuning, Timbre, Spectrum, Scale”).

If you just want to simulate a choir, maybe one of the numeric models
(Hermode, sensory dissonance) might be sufficient. If you are interested
in musical consequences, an algebraic model can give you additional
insights. So far I don't know any higher language but Mutabor that has
existing Software that can perform such a model. (If this knowledge is
too limited I'd be glad to hear about other projects)

Tobias

>
> I find it strange that the Hermode website contains baroque, classical
> and romantic examples in their tuning, but have no examples of the
> only period when just intonation was actually expected (ie.
> renaissance vocal music). Especially given their very lucid
> explanation of the introduction of the just third in the fifteenth
> century. But that must just reflect their musical interests.
>
> Vaughan
>
>

--- In tuning@yahoogroups.com, Keinstein Junior <keinstein_junior@...> wrote:

> In the 1980th, some mathematicians took his ideas and built an
> electronic instrument named MUTABOR. While they experimented with it a
> lot they developed a mathematical language for tone systems. One of its
> dialects has been implemented as computer software and is availlable at
> http://www.math.tu-dresden.de/~mutabor/.

They say they have some sort of system, but not what it is. Is it documented somewhere?

Hi Tobias!

> If understand you right, Martin Vogel has discussed similar
> problems. His solution to build a Just Intonated instrument
> was to use 170 and something tones per octave. In order allow
> easy playing in the Tonnetz as his idea was, he developed a
> logic that moves the hexagon which selects the tones for the
> actual tuning according to the played chords.

Is there a document in English describing this? It seems that
you are describing an "automatic root detection" or "automatic
key detection" system. These are nice but don't solve the
comma problem.

> In the 1980th, some mathematicians took his ideas and built
> an electronic instrument named MUTABOR. While they
> experimented with it a lot they developed a mathematical
> language for tone systems. One of its dialects has been
> implemented as computer software and is availlable at
> http://www.math.tu-dresden.de/~mutabor/.

Thanks for mentioning MUTABOR. I didn't know development
was still going on. Just now I tried the 4.0 beta on Windows.
I tried to use it to play a MIDI file but got stuck.
I created a new input device (the file), box (with route),
and output device. But once this was done, the play button
was not enabled and I didn't see how to proceed.

> When I started considering music this was one of the topic I wanted
> to research. But somehow I ended up discussing partial order in tone
> systems. Nevertheless, I don't think it's too strange that a good
> choir can deal with syntonic commas. One of the reason is: You don't
> have to care about them unless the composer produced a collision.
> And that needs a strong melodic preparation or an unusual harmonic
> progression. Harmonic resolution of the auditory system (including
> consonance/dissonance or timbre) is much stronger than melodic.
> A singer who is not keen on being a voice leader, can concentrate
> mainly on something like resonance and fit his/her voice before the
> standing wave has been established.
> Another problem: Every singer in a well-trained choir has started some
> time ago being a poorly trained one. During their education some of
> them have developed their absolute hearing to a certain extent (not
> necessarily reliable), which helps them to detune melodic intervals
> in the “right way”. But this is more concerned with compensating the
> pythagorean comma or one of its equivalents for major (3T-1O), minor
> thirds (4t-1O), which are the building blocks of the syntonic comma.

Harmonic hearing resolution is only superior to melodic when
beats can be heard, or at least, long steady tones in controlled
circumstances. In musical settings like singing in a choir,
melodic perception is at least as accurate. Even casual listeners
often have a good sense of when a melody sounds 'wrong'.

Unlike the Pythagorean comma, the syntonic comma exists in an
unaltered diatonic scale. Rendering diatonic music in just
intonation results in melodic distortions that many listeners
find objectionable.

> If you just want to simulate a choir, maybe one of the numeric models
> (Hermode, sensory dissonance) might be sufficient. If you are interested
> in musical consequences, an algebraic model can give you additional
> insights. So far I don't know any higher language but Mutabor that has
> existing Software that can perform such a model. (If this knowledge is
> too limited I'd be glad to hear about other projects)

As far as software systems go, you may be right. (There is
the Groven piano project http://www.wmich.edu/mus-theo/groven/
)

As far as algorithms go, did you see this post?
/tuning/topicId_104937.html#104938

In addition to the links there, several tunings of
the same material can be heard at
http://lumma.org/music/theory/demo/lassus/

To my ear, it's clear that among the JI versions, only the
adaptive tuning has the right melodic contours. And it manages
to sound smoother than the meantone version.

Best, -Carl

Hi,

Am 26.08.2012 00:38, schrieb genewardsmith:
>
>
>
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>,
> Keinstein Junior <keinstein_junior@...> wrote:
>
> > In the 1980th, some mathematicians took his ideas and built an
> > electronic instrument named MUTABOR. While they experimented with it a
> > lot they developed a mathematical language for tone systems. One of its
> > dialects has been implemented as computer software and is availlable at
> > http://www.math.tu-dresden.de/~mutabor/.
> <http://www.math.tu-dresden.de/%7Emutabor/.>
>
> They say they have some sort of system, but not what it is.
>
Its some sort of tuning processor. I reads some musical data (e.g. MIDI)
depending on the read pattern it somehow detunes the music. The meaning
of the word "somehow" is defined by some sort of programming language
that has been designed to be easy to learn for musicians. The result is
an algebraic description using tones, intervals and patters. Thus, we
use the wording "tuning logic" for it. As it is related: I'll answer
Carl's more specific questions soon.

> Is it documented somewhere?
>

You mean English documentation I assume?
A tutorial is availlable at http://schlemmersoft.de/en/Mutabor%20tutorial
and an unreviewed translation of the language reference at
https://developer.berlios.de/project/showfiles.php?group_id=3845

There have been rumors that an English manual existed in ancient times.
But so far I was not able to get a copy of it. Personally, I doubt that
it ever existed.

Several academic papers about Mutabor and similar musical/mathematical
topics have been published by Rudolf Wille and his team, but all of them
I know have been written in German.

Tobias
>
>
>

Hi Carl,

Am 26.08.2012 03:35, schrieb Carl Lumma:
>
>
> Hi Tobias!
>
> > If understand you right, Martin Vogel has discussed similar
> > problems. His solution to build a Just Intonated instrument
> > was to use 170 and something tones per octave. In order allow
> > easy playing in the Tonnetz as his idea was, he developed a
> > logic that moves the hexagon which selects the tones for the
> > actual tuning according to the played chords.
>
> Is there a document in English describing this? It seems that
> you are describing an "automatic root detection" or "automatic
> key detection" system. These are nice but don't solve the
> comma problem.
>

The question on documentation I have answered with the reply to Gene's
mail.

Mutabor is more and less than an "automatic root detection" system. The
same applies to key detection. In fact it can do some kind of anchor
detection. But I'd like to avoid the notions of root or key as they are
linked with a semantic meaning, but the anchor in Mutabor is "just" a
formal tool. In fact the root or key need not necessarily coincide with
the anchor. If they do, it has been the choice of the user who wrote the
logic. I think there exist at least one useful tuning logic where that
is impossible. It's probably still covered somewhere in the universe,
but maybe eventually someone will uncover it.

Regarding the comma question: I didn't say that Mutabor solves the
problem. But I'm convinced that it is possible to write a tuning logic
that acts more or less as a choir acts. In that case the solution is
provided by human intelligence. And Mutabor can provide the playground
to experiment with the current state of the theory. You can do interval
arithmetics, collect catalogs of actions, assign a different action for
each pattern. Patterns can be at least harmonies (sets of pitch classes)
and harmonic forms (equivalence classes of pitch class sets according to
transposition).

You have more freedom to write a tuning logic as you are limited only to
predefined operations while the formulae can be changed freely as well
as numerical parameters. As it saves you probably some time to use
formulae over numeric parameters laziness drives toward a more algebraic
model. Such a model usually expresses a deeper understanding than a
column of numbers, which can express the result of the calculations.

As I already wrote: If you are just interested in a black box, probably
predefined numeric approaches are easier to handle.
>
>
> > In the 1980th, some mathematicians took his ideas and built
> > an electronic instrument named MUTABOR. While they
> > experimented with it a lot they developed a mathematical
> > language for tone systems. One of its dialects has been
> > implemented as computer software and is availlable at
> > http://www.math.tu-dresden.de/~mutabor/.
> <http://www.math.tu-dresden.de/%7Emutabor/.>
>
> Thanks for mentioning MUTABOR. I didn't know development
> was still going on. Just now I tried the 4.0 beta on Windows.
> I tried to use it to play a MIDI file but got stuck.
> I created a new input device (the file), box (with route),
> and output device. But once this was done, the play button
> was not enabled and I didn't see how to proceed.
>
You probably did not activate the logic. You must open a logic file and
activate it (e.g. pressing the green traffic light). Unfortunately, I
must confess, that from 3.1 the file playing is broken on windows. It
might work but it might be about 7.5 times as slow as intended.
>
>
> > When I started considering music this was one of the topic I wanted
> > to research. But somehow I ended up discussing partial order in tone
> > systems. Nevertheless, I don't think it's too strange that a good
> > choir can deal with syntonic commas. One of the reason is: You don't
> > have to care about them unless the composer produced a collision.
> > And that needs a strong melodic preparation or an unusual harmonic
> > progression. Harmonic resolution of the auditory system (including
> > consonance/dissonance or timbre) is much stronger than melodic.
> > A singer who is not keen on being a voice leader, can concentrate
> > mainly on something like resonance and fit his/her voice before the
> > standing wave has been established.
> > Another problem: Every singer in a well-trained choir has started some
> > time ago being a poorly trained one. During their education some of
> > them have developed their absolute hearing to a certain extent (not
> > necessarily reliable), which helps them to detune melodic intervals
> > in the �EURoeright way�EUR?. But this is more concerned with
> compensating the
> > pythagorean comma or one of its equivalents for major (3T-1O), minor
> > thirds (4t-1O), which are the building blocks of the syntonic comma.
>
> Harmonic hearing resolution is only superior to melodic when
> beats can be heard, or at least, long steady tones in controlled
> circumstances. In musical settings like singing in a choir,
> melodic perception is at least as accurate. Even casual listeners
> often have a good sense of when a melody sounds 'wrong'.
>
Well, I'm not totally convinced without further references. In some
situations you are right, but casual listeners have also a good feeling
whether something is in tune or somehow detuned. If you were right most
people would find our JI demo piece detuned which is usually not the case.
>
>
> Unlike the Pythagorean comma, the syntonic comma exists in an
> unaltered diatonic scale. Rendering diatonic music in just
> intonation results in melodic distortions that many listeners
> find objectionable.
>
How many from which cultural background? I know that certain people with
musical background find everything strange that is slightly different
from their usual standard. This is a question that is located somewhere
in the grey zone between right and wrong, and a matter of taste. Maybe
I spent too much time on Mutabor development and other mathematical
stuff to provide well-founded knowledge. But the most important problems
I realized with JI are figures that are not modelled in our logic.
>
>
> > If you just want to simulate a choir, maybe one of the numeric models
> > (Hermode, sensory dissonance) might be sufficient. If you are interested
> > in musical consequences, an algebraic model can give you additional
> > insights. So far I don't know any higher language but Mutabor that has
> > existing Software that can perform such a model. (If this knowledge is
> > too limited I'd be glad to hear about other projects)
>
> As far as software systems go, you may be right. (There is
> the Groven piano project http://www.wmich.edu/mus-theo/groven/
> )
>
That's nice. I know only an enharmonic organ with Mutabor inside (at
least Volker Abel told me at some time):
http://www.eufonia.de/index.php/mikrotonale-kompositon/104-die-enharmonische-pfeifenorgel

>
> As far as algorithms go, did you see this post?
> /tuning/topicId_104937.html#104938
>
Thank you, I'll follow it next time.

Tobias
>
>
> In addition to the links there, several tunings of
> the same material can be heard at
> http://lumma.org/music/theory/demo/lassus/
>
> To my ear, it's clear that among the JI versions, only the
> adaptive tuning has the right melodic contours. And it manages
> to sound smoother than the meantone version.
>
> Best, -Carl
>
>

Thanks Carl, I have been going through all the different stuff!

On 27 August 2012 18:49, Keinstein Junior <keinstein_junior@...> wrote:

> **
>
>
> Hi Carl,
>
> Am 26.08.2012 03:35, schrieb Carl Lumma:
>
>
>
> Hi Tobias!
>
> > If understand you right, Martin Vogel has discussed similar
> > problems. His solution to build a Just Intonated instrument
> > was to use 170 and something tones per octave. In order allow
> > easy playing in the Tonnetz as his idea was, he developed a
> > logic that moves the hexagon which selects the tones for the
> > actual tuning according to the played chords.
>
> Is there a document in English describing this? It seems that
> you are describing an "automatic root detection" or "automatic
> key detection" system. These are nice but don't solve the
> comma problem.
>
>
> The question on documentation I have answered with the reply to Gene's
> mail.
>
> Mutabor is more and less than an “automatic root detection” system. The
> same applies to key detection. In fact it can do some kind of anchor
> detection. But I'd like to avoid the notions of root or key as they are
> linked with a semantic meaning, but the anchor in Mutabor is “just” a
> formal tool. In fact the root or key need not necessarily coincide with the
> anchor. If they do, it has been the choice of the user who wrote the logic.
> I think there exist at least one useful tuning logic where that is
> impossible. It's probably still covered somewhere in the universe, but
> maybe eventually someone will uncover it.
>
> Regarding the comma question: I didn't say that Mutabor solves the
> problem. But I'm convinced that it is possible to write a tuning logic that
> acts more or less as a choir acts. In that case the solution is provided by
> human intelligence. And Mutabor can provide the playground to experiment
> with the current state of the theory. You can do interval arithmetics,
> collect catalogs of actions, assign a different action for each pattern.
> Patterns can be at least harmonies (sets of pitch classes) and harmonic
> forms (equivalence classes of pitch class sets according to transposition).
>
> You have more freedom to write a tuning logic as you are limited only to
> predefined operations while the formulae can be changed freely as well as
> numerical parameters. As it saves you probably some time to use formulae
> over numeric parameters laziness drives toward a more algebraic model. Such
> a model usually expresses a deeper understanding than a column of numbers,
> which can express the result of the calculations.
>
> As I already wrote: If you are just interested in a black box, probably
> predefined numeric approaches are easier to handle.
>
>
I’m interested in doing a black box, controllable entirely from the
[electronic piano] keyboard. Ideally a choir director could play some
sixteenth century music on it, and it would be tuned the way the Tallis
Scholars (on a good day!) would sing it. I’ve tried a few different
approaches (root detection, key detection, sensory dissonance). One problem
is getting notes to adjust without a horrible-sounding glissando.

I like Keinstein’s approach using something like a catalog of chord
changes. Separating passing and other non-harmonic notes from the basic
harmony is tricky but possible. Any good choir will have a way of moving
from C major to A minor (or even C major to D minor).

Pitch drift doesn’t bother me much. My feeling is that in most pieces it
would even out more or less. Was the Lassus example chosen because it has
two comma-pumps in quick succession? My (cheating?) way of dealing with
pitch drift is to move all parts up or down towards the centre, slowly-
maybe a comma every five or ten seconds.

A theoretical question: if pitch drift doesn’t matter (which it doesn’t too
much with choirs), is just intonation within the context of
sixteenth-century rules of counterpoint a mathematically coherent system?
My feeling is that the syntonic comma makes compromise of some kind
essential. On the other hand, tuning the Lassus excerpt harmonically
perfectly is possible if you don’t mind melodic issues:

http://mcalley.net.au/examples/Lassus_tuning_harmonic.pdf

> When I started considering music this was one of the topic I wanted
> > to research. But somehow I ended up discussing partial order in tone
> > systems. Nevertheless, I don't think it's too strange that a good
> > choir can deal with syntonic commas. One of the reason is: You don't
> > have to care about them unless the composer produced a collision.
> > And that needs a strong melodic preparation or an unusual harmonic
> > progression. Harmonic resolution of the auditory system (including
> > consonance/dissonance or timbre) is much stronger than melodic.
> > A singer who is not keen on being a voice leader, can concentrate
> > mainly on something like resonance and fit his/her voice before the
> > standing wave has been established.
> > Another problem: Every singer in a well-trained choir has started some
> > time ago being a poorly trained one. During their education some of
> > them have developed their absolute hearing to a certain extent (not
> > necessarily reliable), which helps them to detune melodic intervals
> > in the “right way†. But this is more concerned with compensating the
> > pythagorean comma or one of its equivalents for major (3T-1O), minor
> > thirds (4t-1O), which are the building blocks of the syntonic comma.
>
> Harmonic hearing resolution is only superior to melodic when
> beats can be heard, or at least, long steady tones in controlled
> circumstances. In musical settings like singing in a choir,
> melodic perception is at least as accurate. Even casual listeners
> often have a good sense of when a melody sounds 'wrong'.
>
> Well, I'm not totally convinced without further references. In some
> situations you are right, but casual listeners have also a good feeling
> whether something is in tune or somehow detuned. If you were right most
> people would find our JI demo piece detuned which is usually not the case.
>

The thing I like about singing with good choirs or vocal ensembles is when
a chord ‘rings’. That’s only really obvious when the chord is long. Without
look-ahead, it’s not obvious to a black box whether a chord will be short
or long (ie. how crucial its tuning will be). With practice, aural
experience and a basic knowledge of interval sizes, singers can tune well.
The black box would be a short cut, especially for younger choirs, but the
question is whether it would make too many ‘mistakes’ to be useful.

>
> > If you just want to simulate a choir, maybe one of the numeric models
> > (Hermode, sensory dissonance) might be sufficient. If you are interested
> > in musical consequences, an algebraic model can give you additional
> > insights. So far I don't know any higher language but Mutabor that has
> > existing Software that can perform such a model. (If this knowledge is
> > too limited I'd be glad to hear about other projects)
>
> As far as software systems go, you may be right. (There is
> the Groven piano project http://www.wmich.edu/mus-theo/groven/
> )
>
> That's nice. I know only an enharmonic organ with Mutabor inside (at least
> Volker Abel told me at some time):
> http://www.eufonia.de/index.php/mikrotonale-kompositon/104-die-enharmonische-pfeifenorgel
>
>
Unfortunately I didn’t know about Groven when I was in Oslo (though my wife
might not have thought a visit to the Groven house was a romantic enough
thing to do on our honeymoon!). Obviously Groven was thinking about all
this stuff decades before we were, but to me, any fixed tuning of however
many notes seems unnecessary in the days of accurate MIDI intonation.

The enharmonic organ looks very interesting. It would be interesting to see
what it did with the Lassus...

In addition to the links there, several tunings of
the same material can be heard at
http://lumma.org/music/theory/demo/lassus/

To my ear, it's clear that among the JI versions, only the
adaptive tuning has the right melodic contours. And it manages
to sound smoother than the meantone version.

Best, -Carl

Yes, the adaptive JI version sounds quite good!

Cheers,
Vaughan