Yahoo Tuning Groups Ultimate Backup tuning Maqamic temperament

I hope that Margo still lurks the list these days!

I set out to find a suitable linear "Maqamic" temperament - something
that serves no further purpose than to be a shameless mimicry of maqam
music within the regular temperament paradigm, much as "pelogic"
temperament is a shameless mimicry of the gamelan pelog scale within
the regular temperament paradigm. I did this in relation to Arabic
maqam music to get the ball rolling, in which the two neutral thirds
and neutral seconds are the same size, just for starters. I think this
approach could be used to analyze regional variants in which they
differ as well.

This temperament simply describes how intervals are grouped together
as sharing a scalar position or function, without necessitating that
anyone mistune the intervals to hit some ugly middle of the road
tempered tuning that sucks the intonational fun out of maqam music.
Hence while it is a "temperament" in the sense that it does describe a
homomorphism from JI to a set of period/generator coordinates, it's
designed specifically to be adaptive, as any performance on something
like an oud will be. Hence while a fifth is mapped to two neutral
thirds, you're free to make those neutral thirds whatever size you
want, or even change them dynamically depending on musical context. So
tempered intervals should be thought of as "sharing an equivalence
class," rather than sharing a single mistuned approximation.

The three issues with approaching maqam music in this way have generally been

1) Whether the Almighty Maqam Tuning should incorporate all of the
intonational nuances inherent in the performance of actual maqam
music, which may include very complex RI ratios, or whether it should
reflect the much coarser structure of how the music is notated
2) Whether or not ratios should be picked as intonational pitch
markers, or if they should reflect whether or not the interval gets
resolved properly by the auditory system as a virtual pitch
3) Whether or not ratios should be used at all for melodic music,
since no F0 analysis is occurring for asynchronous harmonics

For point #1, since there are so terribly many different intonational
nuances, and since they vary from region to region, and since we can
continue to argue all day about whether or not the two neutral thirds
making up a fifth should be equal, I want to leave the issue entirely
open and treat it as a separate layer under what I'm doing here. This
is the coarse structure we're describing, and the finer discussion
about regional maqam intonational practices should continue
undeterred.

Point #2 represents whether or not you prefer to use ratios to denote
modes of virtual pitch resolution, or to denote sizes for pitches in
pitch space. For example, 11/9 sometimes sounds like a completely
unresolved, inharmonic, neutral third. Is that just "what 11/9 sounds
like" when played as a bare dyad apart from any musical context, or
does that mean that in that context it's "not 11/9 at all"? The issue
is primarily one of semantics, but I note that the "ic" suffix has
been used for shameless regular temperament models of naturally
occurring tunings in this way ("pelogic", "ragismic," etc). Hence, the
name "maqamic" is appropriate here, and the larger semantic issue (and
any related psychoacoustic nuances about pitch perception) need not be
brought up now.

Point #3 is adequately addressed by calling this "maqamic" temperament
and admitting it exists primarily as mimicry. It also serves as a cue
for the adventurous xenharmonicist to do something fun and different,
like reimagine maqam music in a harmonic context (those neutral thirds
can be 11/9 if you want them to be!), or expand maqam music out into a
larger chromatic context that uses the 10-note MOS, or to generally
create music that attempts to bridge cultures, etc.

So what's the coarse scalar structure for Arabic maqam music? Well,
24-equal itself is, if anything, too fine, as it reflects a particular
intonational choice for a more general rank-2 pattern: all of the
maqamat are MODMOS's of the 3L4s MOS (neutral third generator). This
suggests an even simpler rank-2 coarse structure of which 24-equal is
one supporting EDO, and for which our generator should be a neutral
third.

So what about harmony? Harmony is simple if you keep in mind that
intervals that are "tempered together" should be taken to represent an
equivalence class that maps intervals onto the same scale position and
nothing else. It should NOT be taken as an impetus to find the POTE
generator and deliberately mistune things to hit some neutral, blah,
middle of the road intonation that removes all of the fun from maqam
music. So start thinking in terms of JI dyads "sharing an equivalence
class" or "sharing a scale position" rather than being "mistuned
together" or something like that.

The short version: 36/35, 81/80, and 121/120 all define the basis for
the temperament in the 11-limit, but you do everything adaptively
instead of finding the POTE generator and playing on fixed pitch
instruments. So 7/4 and 16/9 share an equivalence class in the scale,
but there's no law forcing you to tune the minor sevenths to some
middle of the road blase 990 cent tuning - if you're playing on a
fretless instrument you can and should hit whatever specific
intonation you want for any particular musical context. The fact that
they "vanish" really means that they share an equivalence class with
1/1, meaning that motion by that interval is heard as an intonational
adjustment from the unison, rather than a melodic motion by step to
another fundamentally different interval in the scale. The 13-limit
version adds 144/143 as well, signifying that the generator could be
taken as a 16/13 as well as an 11/9.

What this means:
1) The neutral third is 11/9, and two of them get you to 3/2. This
implies that 27/22 also shares the class. Again, you don't have to
actually play two equal-sized neutral thirds, and you're free to make
the generators unequal if you want, or change dynamically in size due
to musical context, or not tune them strictly to JI at all.
2) The minor third is split into two neutral seconds, which could be
either 11/10 or 12/11, if you want, or anything in between. Whether
you want to make them equal or follow the Byzantine law of attraction
is up to you.
3) The perfect fourths of maqam music are often somewhere around 4/3,
but it's also sometimes seen that the minor sevenths are flattened to
be closer to 7/4
(/tuning/topicId_97031.html#97031). This
means that both 16/9 and 7/4 might conceivably end up being played for
the "minor 7th" interval within the same piece and hence both get
mapped to -4 generators.
4) As per the above analysis, the major thirds are sometimes close to
5/4, but might be closer sometimes to the Pythagorean 81/64, and the
minor third is supposed to be 6/5, but might sometimes be closer to
32/27. 7/6 was observed in the above analysis of the Bashir phrase.
I'm not sure if 9/7 ever pops up, but technically, if you wanted to
use it, it's there.
5) For the 13-limit, the generator could be taken as/intoned as 16/13
as well (or 39/32), and the middle seconds could be 13/12 or 14/13 as
well.

AGAIN - This does not mean that no informational difference exists
between 16/13 or 11/9 in maqam music, or that you have to make the
neutral thirds equal, or that you have to stick to any sort of JI
paradigm at all! It just means, quite literally, that these intervals
are both types of "neutral third," no more, no less. You can
dynamically retune them to whatever you want. Also, the choice of
intervals listed above as sharing an equivalence class aren't random
and are consistent with the comma basis above.

Thus is the essence of maqam music to me - it treats lots of intervals
as being intonational variants within the same equivalence class, is
notated as such, but is strongly adaptive. The solution is to
deliberately construct a temperament that is designed to be adaptive
from the ground up, which we do by simply specifying how intervals map
via the homomorphism and nothing else, even if it means "tempering" a
comma like 36/35. It's a new way of thinking about temperaments, and I
hope it'll reopen an exploration into adaptive JI.

http://xenharmonic.wikispaces.com/Meantone+family#Maqamic

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗hstraub64 <straub@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> The three issues with approaching maqam music in this way have
> generally been
>
> 1) Whether the Almighty Maqam Tuning should incorporate all of the
> intonational nuances inherent in the performance of actual maqam
> music, which may include very complex RI ratios, or whether it
> should reflect the much coarser structure of how the music is
> notated
> 2) Whether or not ratios should be picked as intonational pitch
> markers, or if they should reflect whether or not the interval gets
> resolved properly by the auditory system as a virtual pitch
> 3) Whether or not ratios should be used at all for melodic music,
> since no F0 analysis is occurring for asynchronous harmonics
>
> For point #1, since there are so terribly many different
> intonational nuances, and since they vary from region to region,
> and since we can continue to argue all day about whether or not the
> two neutral thirds making up a fifth should be equal, I want to
> leave the issue entirely open and treat it as a separate layer
> under what I'm doing here. This is the coarse structure we're
> describing, and the finer discussion about regional maqam
> intonational practices should continue undeterred.
>

If point 1 is to be left aside, we can as well stay with 24edo, for this is, as far as a understand, already a sort of established standard exactly for this purpose. If, OTOH, there is an even coarser system serving this purpose comparably well, this might be worth a try.

For me, the big issue in a lot of the maqam temperament research I have seen so far is to find a system adequate for fretted and other fixed-pitch instruments, the tradeoff between intonational accuracy and the not too high number of notes.

But Margo, Ozan or Jacques can sure give more qualified input than I can...
--
Hans Straub

🔗Mike Battaglia <battaglia01@...>

On Sun, Sep 4, 2011 at 7:51 AM, hstraub64 <straub@...> wrote:
>
> If point 1 is to be left aside, we can as well stay with 24edo, for this is, as far as a understand, already a sort of established standard exactly for this purpose. If, OTOH, there is an even coarser system serving this purpose comparably well, this might be worth a try.

There is a coarser system, because it's not like we're just using
random notes in 24-EDO. All of the maqamat revolve around a certain
scalar structure. In 24-EDO this structure implies a generator of
7\24, and the maqamat are all MODMOS's of the 7 note MOS that results
from the use of this generator. Once you analyze it like this, it
becomes clear that 24-equal is only one of a number of EDOs that
supports this scalar structure; other options include 17-EDO, 27-EDO,
and 31-EDO.

If, on the other hand, you don't care about the neutral thirds being
equal, then that implies a you're working within rank 3, with your
generators being the 2/1, the 3/2, and some sort of neutral third, two
of which don't make a 3/2. I started with the rank 2 case to keep it
simple, and until we better understand rank 3 MOS it's going to be
difficult to define. Maqamic temperament is the simplest harmonic
mapping that yields that generator and which is consistent with some
of the intonational choices made by maqam performers.

> For me, the big issue in a lot of the maqam temperament research I have seen so far is to find a system adequate for fretted and other fixed-pitch instruments, the tradeoff between intonational accuracy and the not too high number of notes.

This temperament was designed with adaptive instruments in mind. For
fixed-pitch instruments, which right now use 24-EDO, this is a bit
more accurate than that. For a fixed pitch instrument that can
adequately represent all of the intonational nuances in live maqam
music, this temperament won't fit the bill and isn't supposed to.

The question of how to design a fixed pitch set to handle an adaptive
temperament, which any temperament could theoretically be, is an
interesting question. It could be very well modeled by a
dimensionality increase of 1, with the extra generator being half the
size of the "average" size comma in the kernel. The complexity of the
primes should be taken into account as well.

> But Margo, Ozan or Jacques can sure give more qualified input than I can...

I'd love to hear Margo or Jacques weigh in. Oz doesn't hang round
these parts anymore, but you can find him on Facebook.

It would be fun to analyze the data on regional maqam intonational
practices as well. The whole thing might make sense as a rank 3
temperament, with generators set to 2/1, 11/9, and some comma.

-Mike

--
-Mike

Maqamic temperament

🔗Mike Battaglia <battaglia01@...>

🔗Mike Battaglia <battaglia01@...>

🔗hstraub64 <straub@...>

🔗Mike Battaglia <battaglia01@...>

🔗Valentine, Bob <bob.valentine@...>