Topic: [tuning] enharmonic difference and maqam Bayati tuning demo

1 scales

Thread (8 messages)

From: Marcel de Velde (2013-09-02)
Subject: [tuning] enharmonic difference and maqam Bayati tuning demo

Hi List,

I made 2 demonstrations comparing Pythagorean just intonation vs 
temperaments.

Enharmonic difference: http://youtu.be/pr7PTxGnI1I

Maqam Bayati tuning and harmonization: http://youtu.be/INjtv4grxzc

To me only the Pythagorean versions sound uncolored and "in tune", but 
your mileage may vary ;-)
Perhaps worth mentioning is that for the enharmonic difference demo, 
5-limit rational intonation would give about the same result as the 
quarter comma meantone version (not quite acceptable to my ears).

For Margo, in case you cannot view the youtube videos, the audio is on 
soundcloud as well:
https://soundcloud.com/justintonation/enharmonic-difference-tuning
https://soundcloud.com/justintonation/maqam-makam-bayati-tuning

Kind regards,
Marcel de Velde

From: Marcel de Velde (2013-09-03)
Subject: Re: [tuning] enharmonic difference and maqam Bayati tuning demo

And here a more clear demonstration of a simple but successfully 
harmonized maqam Bayati:

Youtube: http://youtu.be/JmPlrT4K86c
Soundcloud: 
https://soundcloud.com/justintonation/maqam-makam-bayati-harmonized

The Bayati melodic expression is clearly preserved, making a fusion 
between western triadic polyphony and eastern maqam music with "neutral 
intervals" for the first time.

Kind regards,
Marcel de Velde


> Hi List,
>
> I made 2 demonstrations comparing Pythagorean just intonation vs
> temperaments.
>
> Enharmonic difference: http://youtu.be/pr7PTxGnI1I
>
> Maqam Bayati tuning and harmonization: http://youtu.be/INjtv4grxzc
>
> To me only the Pythagorean versions sound uncolored and "in tune", but
> your mileage may vary ;-)
> Perhaps worth mentioning is that for the enharmonic difference demo,
> 5-limit rational intonation would give about the same result as the
> quarter comma meantone version (not quite acceptable to my ears).
>
> For Margo, in case you cannot view the youtube videos, the audio is on
> soundcloud as well:
> https://soundcloud.com/justintonation/enharmonic-difference-tuning
> https://soundcloud.com/justintonation/maqam-makam-bayati-tuning
>
> Kind regards,
> Marcel de Velde
>

From:  (2013-09-03)
Subject: RE: [tuning] enharmonic difference and maqam Bayati tuning demo

Hmm, there are not really neutral intervals in the second example, are there? Not in the melody, at least. In the first example, the 17edo version appears to be the most correct one to me. The wide fifths version works a little bit, too, but in all the others the corresponding interval is clearly minor and thus not really Bayati.

And again, I do not understand your harmonization choices. On the first note of Rast you put a minor, and on the first note of Bayati you put a major triad - the opposite of what I would expect.

BTW, how about making it sound more "human"? This terribly mechanical performance virtually hurts in my ears...

As before I will try to create a harmonization of my own.
-- 

Hans Straub

From: Marcel de Velde (2013-09-03)
Subject: Re: [tuning] enharmonic difference and maqam Bayati tuning demo

Hello Hans,

Thanks for your comments!

> Hmm, there are not really neutral intervals in the second example, are 
> there? Not in the melody, at least. In the first example, the 17edo 
> version appears to be the most correct one to me. The wide fifths 
> version works a little bit, too, but in all the others the 
> corresponding interval is clearly minor and thus not really Bayati.
>

I regularly listen to Turkish and Arabic maqam music. Have amassed quite 
a collection over the past few years.
And I can tell you by ear that the 17tet version is not much 
corresponding to how Bayati is usually tuned.
17tet is exaggerating too much and to me it becomes out of tune in a not 
very pleasant way. The neutral thirds (between 2nd and 4th step and 7th 
and 9th step in Bayati, both are played in this melody) in 17tet is ~350 
cents. This does not correspond to practice.
Perhaps you have become used to it by playing in 17tet a lot?

The 703.91 cents fifths version is close to actual practice and sounds 
about the same.

In my opinion the Pythagorean version expresses the same thing, but with 
the monophonic melody it is easy to interpret it as a minor second as 
well, as you say you hear it (and this is quite possible, especially 
after hearing an exaggerated augmented prime first).

In the fully harmonized versions there is not much room in hearing it as 
a minor second though and I'm quite sure you must be hearing it as an 
augmented prime as well in Pythagorean.
To harmonize it as a minor second would make the melody express a very 
different thing.
You can try this for yourself. Play the melody in 12tet with the chords 
Bbmin, Cmin, Dbmaj, Ebmaj, Fmin for the minor second version vs Bbmaj, 
Cmaj, C#min, Ebmaj, Fmaj for the augmented second version.
You will notice that even in 12tet where the tuning is exactly the same, 
that the melody expresses something truly different with the augmented 
prime version (in other words, it's not just put in a different 
perspective due to the different chords, it's truly a different note the 
C# vs the Db. My other demo on enharmonic difference also demonstrates 
this, and this is also a normal concept in classical music theory and 
exploited by countless famous composers including Bach, Mozart and 
Beethoven etc.)

Now if you listen to the fully harmonized versions, you will notice that 
both the 703.91 fifths version and Pythagorean express the same thing. 
The only difference is that with 703.91 fifths the tuning is a bit 
different and the chords are out of tune a bit.
17tet does pretty badly as the chords are now pretty badly out of tune 
but it still expresses the same thing.
And 1/4 comma meantone does so poorly that I don't know what to make of 
it, the chords indicate an augmented prime but the tuning is clearly a 
minor second of Db instead of C# (and a low one at that). I even get the 
same feeling as a comma shift at times from it.

Btw, here is the song I took the melody from: 
http://www.youtube.com/watch?v=P7Srkkc0iGU
And here it is again as made popular by the Chemical Brothers: 
http://www.youtube.com/watch?v=Xu3FTEmN-eg
I hope you can hear that my version does not ruin its expression. It is 
still the same melody. The original is tuned roughly the same as the 
703.91 version it seems to me.


> And again, I do not understand your harmonization choices. On the 
> first note of Rast you put a minor, and on the first note of Bayati 
> you put a major triad - the opposite of what I would expect.
>

Rast does not have a major third above the first degree but a diminished 
fourth instead. The minor third is therefore the most closely related 
third for the first degree in the circle of fifths.

While Bayati does have a minor third above its first degree i chose to 
use the major third for harmonizing the first degree as it is then a 
common tone for harmonizing the second degree which is an augmented 
second above the first degree so the second degree makes a minor third 
with that same note. It helps make the augmented second clear and 
prevents it from having a minor second as an alternative interpretation.

Furthermore I kept the harmonization very simple and clear, parallel 
fifths with triads following the melody.
Of course the possibilities are near endless with my technique and one 
can apply western counterpoint rules, different voicings, sixths 
sevenths ninths chords, etc.

> BTW, how about making it sound more "human"? This terribly mechanical 
> performance virtually hurts in my ears...
>

It is only a simple demo, didn't try to make it sound pretty :)
I was planning on making many demos but I think I'm going to focus now 
on producing quality music based on harmonized maqams which is general 
public friendly.
I have finished my theory enough that I can work without errors.


> As before I will try to create a harmonization of my own.
>
> -- 
>
> Hans Straub
>
>

Oh please do!
It would be interesting if you could use the same melody so an easy 
comparison can be made.

Kind regards,
Marcel de Velde


>
> --- In [email protected], <marcel@...> wrote:
>
> And here a more clear demonstration of a simple but successfully 
> harmonized maqam Bayati:
>
> Youtube: http://youtu.be/JmPlrT4K86c
> Soundcloud: 
> https://soundcloud.com/justintonation/maqam-makam-bayati-harmonized
>
> The Bayati melodic expression is clearly preserved, making a fusion 
> between western triadic polyphony and eastern maqam music with 
> "neutral intervals" for the first time.
>
> Kind regards,
> Marcel de Velde
>
>
>     Hi List,
>
>     I made 2 demonstrations comparing Pythagorean just intonation vs
>     temperaments.
>
>     Enharmonic difference: http://youtu.be/pr7PTxGnI1I
>
>     Maqam Bayati tuning and harmonization: http://youtu.be/INjtv4grxzc
>
>     To me only the Pythagorean versions sound uncolored and "in tune",
>     but
>     your mileage may vary ;-)
>     Perhaps worth mentioning is that for the enharmonic difference demo,
>     5-limit rational intonation would give about the same result as the
>     quarter comma meantone version (not quite acceptable to my ears).
>
>     For Margo, in case you cannot view the youtube videos, the audio
>     is on
>     soundcloud as well:
>     https://soundcloud.com/justintonation/enharmonic-difference-tuning
>     https://soundcloud.com/justintonation/maqam-makam-bayati-tuning
>
>     Kind regards,
>     Marcel de Velde
>

From:  (2013-09-05)
Subject: RE: [tuning] enharmonic difference and maqam Bayati tuning demo

Hi Marcel,

> I regularly listen to Turkish and Arabic maqam music. Have amassed
    quite a collection over the past few 

>years. And I can tell you by ear that the 17tet version is not much
    corresponding to how Bayati is usually 

> tuned. 17tet is exaggerating too much and to me it becomes out of tune in a
    not very pleasant way. The 

> neutral thirds (between 2nd and 4th step
    and 7th and 9th step in Bayati, both are played in this melody) in 

> 17tet is ~350 cents. This does not correspond to practice. Perhaps you have become used to it by playing
> in 17tet a lot?

    >> The 703.91 cents fifths version is close to actual practice and
    sounds about the same.

Compared
 to actual practice in real arabic and turkish music, 17tet is indeed 
only a rough approximation, this is true. I am aware of that. I have listened to your examples and the original again and possibly agree that second note of your wide fifth version is better. About the other examples, I keep stating that the econd note is too low.

> In the fully harmonized versions there is not much room in hearing
    it as a minor second though and I'm 

> quite sure you must be hearing
    it as an augmented prime as well in Pythagorean. To harmonize it as a 

> minor second would make the melody express a
    very different thing. You can try this for yourself. Play the 

> melody in 12tet with the
    chords Bbmin, Cmin, Dbmaj, Ebmaj, Fmin for the minor second version
    vs Bbmaj, 

> Cmaj, C#min, Ebmaj, Fmaj for the augmented second version. You will notice that even in 12tet where the 

> tuning is exactly the
    same, that the melody expresses something truly different with the
    augmented prime 

> version (in other words, it's not just put in a
    different perspective due to the different chords, it's truly a 

> different note the C# vs the Db. My other demo on enharmonic
    difference also demonstrates this, and this 

> is also a normal concept
    in classical music theory and exploited by countless famous
    composers including 

> Bach, Mozart and Beethoven etc.)

I think I am starting to see what your concept is.  Sure, a minor second and an augmented prime are conceptionally quite different things. So you see the second note of Bayati as an augmented prime and harmonize accordingly, right? 

Point is, however, my knowledge is that these characteristical neutral seconds of maqam music, of arabic maqam music in any case, do not really suit into a strictly pythagorean framework - the note in question, I would say, is neither a minor second nor an augmented prime. (Margo or Ozan, can one of you or someone else confirm or disprove?) That may be what distirbed me around your harmonizations since they all appear to be based on pythagorean thinking. I would say that an approach based on the mohajira (instead of meantone) or the maqamic temperament might work better.

> It is only a simple demo, didn't try to make it sound pretty :)

    > I was planning on making many demos but I think I'm going to focus
    now on producing quality music based 

> on harmonized maqams which is
    general public friendly. I have finished my theory enough that I can work 
> without errors.

Looking forward to it!

I am still working on my tentative harmonization - is a little hard, that one!
-- 

Hans Straub

From:  (2013-09-05)
Subject: RE: [tuning] enharmonic difference and maqam Bayati tuning demo

> Point is, however, my knowledge is that these characteristical neutral 
seconds of maqam music, of arabic 

> maqam music in any case, do not really
 suit into a strictly pythagorean framework - the note in question, I 

> would say, is neither a minor second nor an augmented prime. (Margo or 
Ozan, can one of you or someone 

> else confirm or disprove?) That may be 
what distirbed me around your harmonizations since they all appear to 

> be
 based on pythagorean thinking. I would say that an approach based on 
the mohajira (instead of meantone) 

> or the maqamic temperament might work
 better

Replying myself - just saw that neutral seconds of Mohajira are even larger than those of 17edo, and in superpyth maqamic you would need a fifth larger than the on of 17edo to get a smaller neutral second. So those two won^t work, either... And I am sarting to think that Mohajira and maqamic temperament may be suited for Rats but less for Bayati...

-- 

Hans Straub

From: Marcel de Velde (2013-09-08)
Subject: Re: [tuning] enharmonic difference and maqam Bayati tuning demo

Hi Hans,

> Hi Marcel,
>
>
> > I regularly listen to Turkish and Arabic maqam music. Have amassed 
> quite a collection over the past few
>
> >years. And I can tell you by ear that the 17tet version is not much 
> corresponding to how Bayati is usually
>
> > tuned. 17tet is exaggerating too much and to me it becomes out of 
> tune in a not very pleasant way. The
>
> > neutral thirds (between 2nd and 4th step and 7th and 9th step in 
> Bayati, both are played in this melody) in
>
> > 17tet is ~350 cents. This does not correspond to practice. Perhaps 
> you have become used to it by playing
>
> > in 17tet a lot?
> >
>
> > The 703.91 cents fifths version is close to actual practice and 
> sounds about the same.
>
>
> Compared to actual practice in real arabic and turkish music, 17tet is 
> indeed only a rough approximation, this is true. I am aware of that. I 
> have listened to your examples and the original again and possibly 
> agree that second note of your wide fifth version is better. About the 
> other examples, I keep stating that the econd note is too low.
>

Ok. I see your point. And you may very well be right!
I have been in eternal limbo about whether that neutral second 
represents an augmented prime or double augmented seventh.
The Pythagorean double augmented seventh is not in those videos but it's 
tuning is a Pythagorean comma higher than the augmented prime and I'm 
sure you'll find it spot on tuning wise.
I'm starting to come back (yet again) from seeing all neutral intervals 
in maqam music as augmented primes and diminished thirds. They are used 
as such, but perhaps the double augmented seventh and triple diminished 
fourth as well.
I was never sure about this but gave the benefit of the doubt to 
augmented prime approach, though not anymore after yet more testing and 
thinking the past few days..


>
> > In the fully harmonized versions there is not much room in hearing 
> it as a minor second though and I'm
>
> > quite sure you must be hearing it as an augmented prime as well in 
> Pythagorean. To harmonize it as a
>
> > minor second would make the melody express a very different thing. 
> You can try this for yourself. Play the
>
> > melody in 12tet with the chords Bbmin, Cmin, Dbmaj, Ebmaj, Fmin for 
> the minor second version vs Bbmaj,
>
> > Cmaj, C#min, Ebmaj, Fmaj for the augmented second version. You will 
> notice that even in 12tet where the
>
> > tuning is exactly the same, that the melody expresses something 
> truly different with the augmented prime
>
> > version (in other words, it's not just put in a different 
> perspective due to the different chords, it's truly a
>
> > different note the C# vs the Db. My other demo on enharmonic 
> difference also demonstrates this, and this
>
> > is also a normal concept in classical music theory and exploited by 
> countless famous composers including
>
> > Bach, Mozart and Beethoven etc.)
>
>
> I think I am starting to see what your concept is. Sure, a minor 
> second and an augmented prime are conceptionally quite different 
> things. So you see the second note of Bayati as an augmented prime and 
> harmonize accordingly, right?
>

Yes right! This is what I did.
And I'm sure that it is a musically valid possibility, so my examples 
are correct.
However, there may be another Bayati where the neutral interval is 
indeed higher, and if you're expecting to hear that one then this one is 
too low indeed.
The fully harmonized version does indicate an augmented prime though, 
there's no room to hear a minor second or double augmented seventh in 
that one, but the monophonic and partially harmonized version do leave 
that room.


> Point is, however, my knowledge is that these characteristical neutral 
> seconds of maqam music, of arabic maqam music in any case, do not 
> really suit into a strictly pythagorean framework - the note in 
> question, I would say, is neither a minor second nor an augmented 
> prime. (Margo or Ozan, can one of you or someone else confirm or 
> disprove?) That may be what distirbed me around your harmonizations 
> since they all appear to be based on pythagorean thinking. I would say 
> that an approach based on the mohajira (instead of meantone) or the 
> maqamic temperament might work better.
>

I'm 100% fully convinced and have proven so to myself beyond doubt that 
Pythagorean is just intonation.
It is the only approach to harmonization I'm interested in, and the one 
that will succeed best. The other tunings will only confuse in such a 
complex and precise matter.

>
> > It is only a simple demo, didn't try to make it sound pretty :)
> > I was planning on making many demos but I think I'm going to focus 
> now on producing quality music based
>
> > on harmonized maqams which is general public friendly. I have 
> finished my theory enough that I can work
>
> > without errors.
>
>
> Looking forward to it!
>
>
> I am still working on my tentative harmonization - is a little hard, 
> that one!
>
> -- 
>
> Hans Straub
>
>

Looking forward to your version as well! :)

I'm also going to make yet another harmonized example which does use the 
stronger neutral tuning in Pythagorean (the double augmented prime and 
triple diminished fourth for the small and large neutral seconds).
I've figured out a way to do it using nonchord tones for the neutral 
intervals (the way I once described before), but still keep the harmonic 
framework intact by changing these neutral intervals by a comma when 
they become the root / temporary tonic of the maqam (so the underlying 
harmonic framework is still the same as the augmented primes etc version 
in the videos).
I'll explain when I post the audio. It seems to be working well.
I still can't get the roots to change by neutral intervals though, 
something sounds wrong about that and I don't see the logic in how that 
could work and not indicate an augmented prime / diminished third instead.

Kind regards,
Marcel de Velde

From: Margo Schulter (2013-09-10)
Subject: enharmonic difference and maqam Bayati tuning demo

Dear Hans and Marcel,

While I addressed the general question of tuning Maqam Bayyati
and related Near Eastern modalities in a new thread, I just
want to add a bit here about the strategy of tuning -- or,
often, temperament -- to obtain or approximate some Bayyati
tunings of a kind documented or recommended in the literature.

Certainly an extended chain of Pythagorean fifths is one
good strategy -- if we are ready to support a large tuning
set. In Pythagorean, it takes 19 fifths to generate a
near-13/12 step at 137.1 cents -- an excellent approximation,
of course!

Temperament in the wide direction is a way of reducing that
chain from 19 fifths to 7 fifths -- or, alternatively, of
using two chains of fifths with an "artificial diesis" so
that wherever in the lower chain of fifths we have a limma
(often around 22/21 or 81 cents in these temperaments), adding
this "artificial diesis" or spacing between the chains will
produce a just or near-just 13/12. The same system can use
both strategies to get two different sizes of small neutral
seconds, permitting two different flavors of Bayyati -- or
more, if we also consider forms where the larger neutral
second step precedes the smaller (as in 11:12:13).

The first strategy, of tuning 7 fifths up as a small neutral
second, can be used anywhere in the range from 29-EDO to
17-EDO, with the latter as an upper limit. At 29-EDO, or
703.447 cents, 7 fifths up -- the apotome, chromatic semitone,
or augmented prime -- is around 124 cents, about the minimum
for a neutral second. Hormoz Farhat places the range for small
neutral seconds in Persian music at around 125-145 cents.
At around 704 cents, we get a just or near-just 14:13 (128
cents); and around 705 cents, a just or near-just 13:12 (139
cents).

The second strategy makes most sense from around 29-EDO up
to a bit beyond 704 cents, with the spacing between the
two chains of fifths (which could each be at an MOS of
12, 17, 29, etc.) often at around 91/88, or 58 cents.
Typically we have a diatonic semitone or limma at around
81 cents, say, and a spacing at around 58 cents -- which
means a 13:12 approximation around 139 cents, near-just.

Systems using the second strategy also use the first,
yielding four sizes of neutral intervals, and lots of
ways to tune Bayyati and related modalities.

Systems using the first strategy only, with a single
chain of fifths (around 705 cents, say), yield two
sizes of neutral intervals -- for example, at 705 cents,
a step of 135 cents from 7 fifths up (the augmented prime
or apotome), and 150 cents from 10 fifths down (the
diminished third or double limma, equal to twice the limma
at 75 cents). There's thus a choice between 135-150-210
cents, a great Bayyati of the variety with the smaller step
first often preferred in the Arab world; and 150-135-210
cents, the kind of pattern that results when Bayyati is
tuned as a rotation of Rast. Thus in this 705-cent tuning
(a subset or possibly full set of 80-EDO, as it happens),
a usual Rast would be 210-150-135 cents, with the neutral
third at 360 cents or a near-just 16/13 (359.5 cents);
and 150-135-210 cents results as a simple rotation of
this.

So tempering the fifth slightly wide is precisely a way
of getting neutral intervals with shorter chains of fifths
than in Pythagorean.

One thing I should add is that the first tempering strategy
of using the apotome or augmented prime as a small neutral
second can be useful even with a 12-note set, while the
second strategy calls for two MOS sets of 12 or larger.

Also, first strategy, while it's fine for smaller sets of
12 or 17, can also be very useful with larger sets like 24,
29, or beyond. For example, at 705 cents, C#-Eb is a large
neutral second, the diminished third or double limma
(C#-D plus D-Eb) at 150 cents. However, we also have a
step C#-Cx at 135 cents. Thus it's possible to play Bayyati
as either C#-Cx-E-F# (135-150-210 cents) in the manner often
regarded as most stylish; or as C#-Eb-E-F# (150-135-210
cents), as is also preferred in some varieties of practice.
Note that a usual Rast would be B-C#-Eb-E (210-150-135 cents).

In fact, as an alternative to 17-EDO, a 17-note set at
705 cents might be very attractive.

! 705-17.scl
!
17-note MOS, fifth 705 cents, near-just 13/8
  17
!
  75.00000
  135.00000
  210.00000
  285.00000
  345.00000
  420.00000
  495.00000
  570.00000
  630.00000
  705.00000
  780.00000
  840.00000
  915.00000
  990.00000
  1050.00000
  1125.00000
  2/1


Note that for the kind of Bayyati tuning that Scott
Marcus describes, with a small neutral second but large
neutral sixth when that step is used in place of the
more common minor sixth, starting on Scala step 13,
or 915 cents -- the note A, if the tuning is read
as C-C -- gives the right intervals.

0 135 285 495 705 (780) 855 990 1200

Of course, if circulation is important, then either
17-EDO or a 17-note well-temperament such as George
Secor's 17-WT makes sense. And 29-EDO and 46-EDO
provide larger circulating systems.

But if circulation isn't needed -- as it often
isn't in Near Eastern music -- then the 705-cent
tuning in 17 notes occurs a near-just 13/8, plus
a few very good septimal approximations.

Two sizes of neutral intervals provide the kind
of contrast and variety that can make Near Eastern
music more stylish, for Bayyati and other maqamat.

Best,

Margo Schulter
mschulter@...