"Negri" phrase in Tartini

I downloaded Tartini myself and loaded it up.

Here's the picture:
http://www.mikebattagliamusic.com/music/negritartini.png

Here's a plaintext tabulation of the data:
http://www.mikebattagliamusic.com/music/negritext.txt

Here's the wav file:
http://www.mikebattagliamusic.com/music/negri2.wav

In the plaintext tabulation, you can see I've placed certain numbers
throughout the file. Since there's vibrato and such for each of these
notes, I've grouped them into sections that delineate the difference
between where one note ends and another begins. By exporting the data
to MATLAB, I was able to obtain the mean MIDI note value for each
note, which is what Tartini offers. By subtracting from the first
note, and multiplying by 100, we can get the intervals present in this
little sample in cents. Here's the initial output, confounded by some
things I'll mention in just a second - | marks indicate the beginning
and end of a phrase:

0 101.0662 6.9587 115.9874 | 140.2259 269.1987 161.2747
255.3307 | 284.9845 365.8365 293.2587 380.1946

There are some strange values here - 255 and 365 cents are obviously
just too low. And in this case, the reason is as you can see from the
graph, Tartini sometimes will place one or two intermediate pitch
values right between adjacent notes as if there were portamento on the
signal, which in this case there isn't. So if I run this algorithm
again, but I throw away the first and last pitch value for each note
and then get the mean, I then obtain the following values are
obtained:

0 107.4533 7.1250 118.7861 | 140.1010 271.5875 157.6017
261.2908 | 286.6590 380.0879 282.9817 383.3003

By throwing the two values away at the end of each region as
portamento artifacts, here's what we instead get:

0 105.9100 9.2350 119.4342 | 138.9017 270.9900 157.7350
262.1585 | 285.4983 380.3490 274.8950 382.7712

Almost the same thing, except the 282 cents second to last note has
now dropped to 274 cents. This is because this note was shorter in
duration and likely too much data was thrown away; 282 cents was
likely more accurate.

These are pretty much the exact values that I through out in my
spectrogram results. Note that the during the second phrase, the minor
third is a few cents off from 7/6, which is exactly as I heard it. The
major third is played close to 5/4, which isn't what I heard but also
answers another one of the proposed questions.

The first note of each phrase is the last note of the phrase before
it. The first note is also generally a bit higher than the last one
(the 119 cents moves up to 138 cents, the 262 cents moves up to 285
cents).

In contrast, the negri generator is around 130 cents. In this case,
I'm not sure that it really does make sense to call this "negri"
tempered, although that's the cognitive paradigm that my brain likes
to snap this into (perhaps you could look at it like it's a negri
well-temperament of some kind). Either way, here's 7/6 for you.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I'm not sure that it really does make sense to call this "negri"
> tempered, although that's the cognitive paradigm that my brain likes
> to snap this into (perhaps you could look at it like it's a negri
> well-temperament of some kind). Either way, here's 7/6 for you.

And 5/4. Very interesting; one might wish for vastly more data along these lines and some conclusions. Should take you a year or so. But I notice nothing which would cause me to conclude that approximate JI ratios, and hence potentially tempering, were irrelevant to the issue.

On Mon, Mar 14, 2011 at 3:11 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I'm not sure that it really does make sense to call this "negri"
> > tempered, although that's the cognitive paradigm that my brain likes
> > to snap this into (perhaps you could look at it like it's a negri
> > well-temperament of some kind). Either way, here's 7/6 for you.
>
> And 5/4. Very interesting; one might wish for vastly more data along these lines and some conclusions. Should take you a year or so. But I notice nothing which would cause me to conclude that approximate JI ratios, and hence potentially tempering, were irrelevant to the issue.

I should also add, before people tell me that the first C was just
erroneously played sharp, that if you go back to the text I posted and
look at the second "xx" region, which is where the Eb from the second
phrase is still hanging and the C C' C C' figure an octave or two down
starts to get unmasked, you see this:

2.5542 29.1391 -95.0129
2.57741 29.2073 -96.7543
2.60063 29.182 -97.8146
2.62385 29.1328 -96.9624
2.64707 29.1127 -96.9476
2.67029 29.0855 -98.8506
2.69351 29.1146 -102.703
2.71673 29.0702 -104.645
2.73995 29.1399 -103.473
2.76317 48.1271 -104.447
2.78639 48.1149 -108.279
2.80961 48.1201 -109.718
2.83283 48.1042 -110.831
2.85605 48.0911 -112.535
2.87927 48.1268 -114.338
2.90249 48.1825 -111.312

See all of those 29's? Those 29's are F's, which means that Tartini
has taken the C and the decaying Eb and for a brief moment, decided
that the VF present was a low F - as though they formed a 7/6. And
then check out the 48.12, 48.11, etc - that's an octave below C, and
you can see that they're playing it consistently about 11 cents sharp.

-Mike

Mike, if you use the "intellectual and dry" method (LOL) of analizing tunings I do, which is jamming along with a fretless guitar, you'll find the Ockham's Razor description of the intervallic structure.

Get 4:3 and 7;6 into your ear and muscle memory. Now, go open string, drop your finger halfway between open and 7:6, go 7:6, drop your finger halfway between 7:6 and 4:3. Do it a bunch of times. Now transpose higher, with your "open string" at a fretted position, and remember that in "driving higher" you're going to tend towards sharping.

Voila, there it is. As explained in Cris Forster's book, the alleged "fantasies" of "RI" can largely be traced to some bonehead simple mechanical procedures. This is described in manuscripts from one to two thousand plus years ago.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I downloaded Tartini myself and loaded it up.
>
> Here's the picture:
> http://www.mikebattagliamusic.com/music/negritartini.png
>
> Here's a plaintext tabulation of the data:
> http://www.mikebattagliamusic.com/music/negritext.txt
>
> Here's the wav file:
> http://www.mikebattagliamusic.com/music/negri2.wav
>
> In the plaintext tabulation, you can see I've placed certain numbers
> throughout the file. Since there's vibrato and such for each of these
> notes, I've grouped them into sections that delineate the difference
> between where one note ends and another begins. By exporting the data
> to MATLAB, I was able to obtain the mean MIDI note value for each
> note, which is what Tartini offers. By subtracting from the first
> note, and multiplying by 100, we can get the intervals present in this
> little sample in cents. Here's the initial output, confounded by some
> things I'll mention in just a second - | marks indicate the beginning
> and end of a phrase:
>
> 0 101.0662 6.9587 115.9874 | 140.2259 269.1987 161.2747
> 255.3307 | 284.9845 365.8365 293.2587 380.1946
>
> There are some strange values here - 255 and 365 cents are obviously
> just too low. And in this case, the reason is as you can see from the
> graph, Tartini sometimes will place one or two intermediate pitch
> values right between adjacent notes as if there were portamento on the
> signal, which in this case there isn't. So if I run this algorithm
> again, but I throw away the first and last pitch value for each note
> and then get the mean, I then obtain the following values are
> obtained:
>
> 0 107.4533 7.1250 118.7861 | 140.1010 271.5875 157.6017
> 261.2908 | 286.6590 380.0879 282.9817 383.3003
>
> By throwing the two values away at the end of each region as
> portamento artifacts, here's what we instead get:
>
> 0 105.9100 9.2350 119.4342 | 138.9017 270.9900 157.7350
> 262.1585 | 285.4983 380.3490 274.8950 382.7712
>
> Almost the same thing, except the 282 cents second to last note has
> now dropped to 274 cents. This is because this note was shorter in
> duration and likely too much data was thrown away; 282 cents was
> likely more accurate.
>
> These are pretty much the exact values that I through out in my
> spectrogram results. Note that the during the second phrase, the minor
> third is a few cents off from 7/6, which is exactly as I heard it. The
> major third is played close to 5/4, which isn't what I heard but also
> answers another one of the proposed questions.
>
> The first note of each phrase is the last note of the phrase before
> it. The first note is also generally a bit higher than the last one
> (the 119 cents moves up to 138 cents, the 262 cents moves up to 285
> cents).
>
> In contrast, the negri generator is around 130 cents. In this case,
> I'm not sure that it really does make sense to call this "negri"
> tempered, although that's the cognitive paradigm that my brain likes
> to snap this into (perhaps you could look at it like it's a negri
> well-temperament of some kind). Either way, here's 7/6 for you.
>
> -Mike
>

On Mon, Mar 14, 2011 at 4:56 AM, lobawad <lobawad@...> wrote:
>
> Mike, if you use the "intellectual and dry" method (LOL) of analizing tunings I do, which is jamming along with a fretless guitar, you'll find the Ockham's Razor description of the intervallic structure.
>
> Get 4:3 and 7;6 into your ear and muscle memory. Now, go open string, drop your finger halfway between open and 7:6, go 7:6, drop your finger halfway between 7:6 and 4:3. Do it a bunch of times. Now transpose higher, with your "open string" at a fretted position, and remember that in "driving higher" you're going to tend towards sharping.

Actually, that's a pretty good explanation. It seems pretty likely
that he just split the 5/4 into three physically equal parts on the
string, which would produce something close to 1/(12:13:14:15). The
only problem, though, is that this would produce a 250 cent interval,
whereas the data shows something higher up and closer to 270-280
cents. But if you're a musician on the level of Munir Bashir, I assume
that you'd instinctively know to not play 250 cents around here.

I assumed that the fact that each note started a bit sharper than the
last one is because he was moving his hand over so that the lower
finger matched the previous position of the upper finger, and he
either overshot or purposely sharpened the note to act as a sort of
leading tone. I'm not sure.

-Mike

Not 5:4, but halfway, in terms of string length, between 7:6 and 4:3.
56:45, right there where Ozan has always insisted there are maqam "thirds" to be found. And you'll find for yourself if you cruise through older recordings on YouTube, picking out riffs on a fretless guitar.

And the physical halfway point between 7:6 and 0 is 14:13.

Numerological "whoooo-whoooo!" guys will try to discount these simple explanations as they don't fit into harmonic entropy or whatever. Whatever. This kind of thing has been described for millenia, literally, and it's Ockham's Razor friendly.

Notice that it doesn't make that much difference, as you noticed, if you go for three string divisions of 5:4. For all we know there's a kind of "tempering", or blur, going on. Whatever.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Mar 14, 2011 at 4:56 AM, lobawad <lobawad@...> wrote:
> >
> > Mike, if you use the "intellectual and dry" method (LOL) of analizing tunings I do, which is jamming along with a fretless guitar, you'll find the Ockham's Razor description of the intervallic structure.
> >
> > Get 4:3 and 7;6 into your ear and muscle memory. Now, go open string, drop your finger halfway between open and 7:6, go 7:6, drop your finger halfway between 7:6 and 4:3. Do it a bunch of times. Now transpose higher, with your "open string" at a fretted position, and remember that in "driving higher" you're going to tend towards sharping.
>
> Actually, that's a pretty good explanation. It seems pretty likely
> that he just split the 5/4 into three physically equal parts on the
> string, which would produce something close to 1/(12:13:14:15). The
> only problem, though, is that this would produce a 250 cent interval,
> whereas the data shows something higher up and closer to 270-280
> cents. But if you're a musician on the level of Munir Bashir, I assume
> that you'd instinctively know to not play 250 cents around here.
>
> I assumed that the fact that each note started a bit sharper than the
> last one is because he was moving his hand over so that the lower
> finger matched the previous position of the upper finger, and he
> either overshot or purposely sharpened the note to act as a sort of
> leading tone. I'm not sure.
>
> -Mike
>

On Mon, Mar 14, 2011 at 6:20 AM, lobawad <lobawad@...> wrote:
>
> Not 5:4, but halfway, in terms of string length, between 7:6 and 4:3.
> 56:45, right there where Ozan has always insisted there are maqam "thirds" to be found. And you'll find for yourself if you cruise through older recordings on YouTube, picking out riffs on a fretless guitar.
>
> And the physical halfway point between 7:6 and 0 is 14:13.
>
> Numerological "whoooo-whoooo!" guys will try to discount these simple explanations as they don't fit into harmonic entropy or whatever. Whatever. This kind of thing has been described for millenia, literally, and it's Ockham's Razor friendly.
>
> Notice that it doesn't make that much difference, as you noticed, if you go for three string divisions of 5:4. For all we know there's a kind of "tempering", or blur, going on. Whatever.

Good call. I can dig it. That's probably what he did, just physically
subdivided the string into a few equal parts in the middle of his
improvisation. I guess that's not really "negri" after all, but it
makes sense. I will say that something like 56/45 is obviously related
to the perception of 5/4, since it's just a few cents away. But if
maqam thirds often end up coming out a few cents flat of 5/4, this is
a pretty simple explanation of how a behavior like that could emerge.

-Mike

Drop a finger halfway between 4:3 and the nut, you've got 8:7, drop a finger halfway between there and 4:3 and you've got 16:13. Pretty much exactly "2 koma" down from the Pythagorean ditone, exactly where some guys will describe the "third" of certain makamlar, for example.

I'm not suggesting "mysteries of thee ancients solvedde" a la Schlesinger, just pointing out some Ockham's Razor stuff which happens to be clearly spelled out, even with "bearing plans", by ancient and medieval writers. The famous tanbur of Baghdad was fretted according to 40 equal divisions of string length for crying out loud.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Mar 14, 2011 at 6:20 AM, lobawad <lobawad@...> wrote:
> >
> > Not 5:4, but halfway, in terms of string length, between 7:6 and 4:3.
> > 56:45, right there where Ozan has always insisted there are maqam "thirds" to be found. And you'll find for yourself if you cruise through older recordings on YouTube, picking out riffs on a fretless guitar.
> >
> > And the physical halfway point between 7:6 and 0 is 14:13.
> >
> > Numerological "whoooo-whoooo!" guys will try to discount these simple explanations as they don't fit into harmonic entropy or whatever. Whatever. This kind of thing has been described for millenia, literally, and it's Ockham's Razor friendly.
> >
> > Notice that it doesn't make that much difference, as you noticed, if you go for three string divisions of 5:4. For all we know there's a kind of "tempering", or blur, going on. Whatever.
>
> Good call. I can dig it. That's probably what he did, just physically
> subdivided the string into a few equal parts in the middle of his
> improvisation. I guess that's not really "negri" after all, but it
> makes sense. I will say that something like 56/45 is obviously related
> to the perception of 5/4, since it's just a few cents away. But if
> maqam thirds often end up coming out a few cents flat of 5/4, this is
> a pretty simple explanation of how a behavior like that could emerge.
>
> -Mike
>

On Mon, Mar 14, 2011 at 6:45 AM, lobawad <lobawad@...> wrote:
>
> Drop a finger halfway between 4:3 and the nut, you've got 8:7, drop a finger halfway between there and 4:3 and you've got 16:13. Pretty much exactly "2 koma" down from the Pythagorean ditone, exactly where some guys will describe the "third" of certain makamlar, for example.
>
> I'm not suggesting "mysteries of thee ancients solvedde" a la Schlesinger, just pointing out some Ockham's Razor stuff which happens to be clearly spelled out, even with "bearing plans", by ancient and medieval writers. The famous tanbur of Baghdad was fretted according to 40 equal divisions of string length for crying out loud.

Are you suggesting that something around 16/13 is used for the neutral
thirds? Do you know of any musical examples where a third of this size
is used?

-Mike

Ozan will know, you should ask him. I lost the link I had to the oud player describing this online. If I find it again I'll post it of course.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Mar 14, 2011 at 6:45 AM, lobawad <lobawad@...> wrote:
> >
> > Drop a finger halfway between 4:3 and the nut, you've got 8:7, drop a finger halfway between there and 4:3 and you've got 16:13. Pretty much exactly "2 koma" down from the Pythagorean ditone, exactly where some guys will describe the "third" of certain makamlar, for example.
> >
> > I'm not suggesting "mysteries of thee ancients solvedde" a la Schlesinger, just pointing out some Ockham's Razor stuff which happens to be clearly spelled out, even with "bearing plans", by ancient and medieval writers. The famous tanbur of Baghdad was fretted according to 40 equal divisions of string length for crying out loud.
>
> Are you suggesting that something around 16/13 is used for the neutral
> thirds? Do you know of any musical examples where a third of this size
> is used?
>
> -Mike
>

Oh, and I think it's important to lose the concept of "third"- it's "middle finger", I think.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Ozan will know, you should ask him. I lost the link I had to the oud player describing this online. If I find it again I'll post it of course.
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > On Mon, Mar 14, 2011 at 6:45 AM, lobawad <lobawad@> wrote:
> > >
> > > Drop a finger halfway between 4:3 and the nut, you've got 8:7, drop a finger halfway between there and 4:3 and you've got 16:13. Pretty much exactly "2 koma" down from the Pythagorean ditone, exactly where some guys will describe the "third" of certain makamlar, for example.
> > >
> > > I'm not suggesting "mysteries of thee ancients solvedde" a la Schlesinger, just pointing out some Ockham's Razor stuff which happens to be clearly spelled out, even with "bearing plans", by ancient and medieval writers. The famous tanbur of Baghdad was fretted according to 40 equal divisions of string length for crying out loud.
> >
> > Are you suggesting that something around 16/13 is used for the neutral
> > thirds? Do you know of any musical examples where a third of this size
> > is used?
> >
> > -Mike
> >
>

On Mon, Mar 14, 2011 at 6:52 AM, lobawad <lobawad@...> wrote:
>
> Ozan will know, you should ask him. I lost the link I had to the oud player describing this online. If I find it again I'll post it of course.

A few things:

1) Oz is, I thought, an expert on the specific brand of Maqam music
that is unique to Turkey; e.g. he sought with this thesis to find a
model to describe the deviation from the 24-tet model commonly seen in
Turkey's Maqam musicians. Munir Bashir is from Iraq, so I don't know
how relevant that is.
2) As you know, Oz has me placed on his spam filter because he thinks
that I'm an idiot with nothing valid to contribute to music theory.
And to be honest, I don't really feel like talking to him anyway.
3) Let me know if you find any 16/13 neutral third examples, they'd be
useful data points here.

-MIke

One thing you need to watch for is national/ethnic differences and let's face it bias/conflict. I don't have a problem admitting that I'm biased toward Turkic flavors, especially those regions where there's a tangible relation to Slavic music (which is what I grew up with). Try jamming along with some fretless Azeri music, I bet you'll find some "high neutral thirds" there. I'd do it again this week but I don't have time, argh.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Mar 14, 2011 at 6:52 AM, lobawad <lobawad@...> wrote:
> >
> > Ozan will know, you should ask him. I lost the link I had to the oud player describing this online. If I find it again I'll post it of course.
>
> A few things:
>
> 1) Oz is, I thought, an expert on the specific brand of Maqam music
> that is unique to Turkey; e.g. he sought with this thesis to find a
> model to describe the deviation from the 24-tet model commonly seen in
> Turkey's Maqam musicians. Munir Bashir is from Iraq, so I don't know
> how relevant that is.
> 2) As you know, Oz has me placed on his spam filter because he thinks
> that I'm an idiot with nothing valid to contribute to music theory.
> And to be honest, I don't really feel like talking to him anyway.
> 3) Let me know if you find any 16/13 neutral third examples, they'd be
> useful data points here.
>
> -MIke
>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Not 5:4, but halfway, in terms of string length, between 7:6 and 4:3.
> 56:45, right there where Ozan has always insisted there are maqam "thirds" to be found.

The harmonic mean of 7/6 and 4/3. Is this sort of thing why it's called the "harmonic mean", I wonder?

> And the physical halfway point between 7:6 and 0 is 14:13.

14/13 being the harmonic mean of 7/6 and 1.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Drop a finger halfway between 4:3 and the nut, you've got 8:7, drop a finger halfway between there and 4:3 and you've got 16:13.

If hm(a, b) = 2/(1/a+1/b), the harmonic mean of a and b, then hm(1, 4/3) = 8/7 and hm(8/7, 4/3) = 16/13.

Yes the "average" (mean) of rates. That can't be the official way of putting it, but you know what I mean, you can state it correctly. Pretty neat that it can be "calculated" with such a simple mechanical process.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > Drop a finger halfway between 4:3 and the nut, you've got 8:7, drop a finger halfway between there and 4:3 and you've got 16:13.
>
> If hm(a, b) = 2/(1/a+1/b), the harmonic mean of a and b, then hm(1, 4/3) = 8/7 and hm(8/7, 4/3) = 16/13.
>