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fernandoamartin
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How do you play Nahawand?
Hi. Excuse me for the inconvenience. I know that arabic music is learned by ear and has regional changes, but I'm sequencing some arabic music on
computer and need some exact values.
I've looked at Alain Danielou's Comparative Table of Musical Intervals, at this link:
http://www.kylegann.com/DanielouTableauComparatif.pdf
He indicates some important tunings, including some used in arabic music. For example, I decided to use, for Eb in Kurd, the ratio 32/27 that is
equal to 294.135 cents, that Denielou indicates as "Wasta du diatonique arabe" and that is the same as pythagorean minor third.
But in Danielou's book the next lower value that he names is 75/64 = 274,58 cents, Tierce mimeure faible. He gives no name or importance to all the
values between 274,58 cents and 294.135 cents.
But then I wonder: Isn't 274,58 very low to be used as Nahawand Eb? Isn't 274,58 cents very far from 294.135 cents to be the difference between Kurd's
and Nahawand's Eb?
Can you give me some hint? How do you play or how have you heard in canonical recordings Nahawand's Eb? Please answer using numbers (ratio fractions
or cents), because as I said above I need numbers to adjust the tuning since I'm sequencing on a computer.
Thanks.
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Jody Stecher
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Quote: Originally posted by fernandoamartin  | Hi.
Can you give me some hint? How do you play or how have you heard in canonical recordings Nahawand's Eb? Please answer using numbers (ratio fractions
or cents), because as I said above I need numbers to adjust the tuning since I'm sequencing on a computer.
Thanks. |
I think when someone replies with a ratio you can safely use it in your computer sequencing. But this question of people *hearing* ratios has
perplexed me for decades. Ever since I first read about cents expressed as a ratio as a university student deep in the previous century I have been
puzzled by it.
I understand your problem vis a vis the computer. But I cannot hear in fractions. I have never met a human being who can. Can you give *me* some hint
how this can be done? Our brains can detect minute differences in pitch and we can replicate these pitches with our voices and/or musical instruments
but who in this world directly perceives a musical pitch as a ratio? I think it's likely that someone on this forum will be able to tell you the
numbers you seek but I will be surprised —astonished actually — if they know these numbers from direct perception rather than from arithmetic
calculation or from consulting a printed table of ratio values of intervals. And any ratio or measurement in cents will necessarily be a compromise or
a generalization.
You mentioned that you are aware of regional variations, and in earlier discussions about Eb in Nahawand and Kurd, replies to your questions made it
clear that within one performance by a musician playing in the style of any region there may be some small variation in pitch. That being the case
one might say that a standard Nahawand E flat does not exist, unless that pitch is one that somehow is not different, for instance, in Cairo from how
it is in Aleppo or in Baghdad. Choose one of your favorite Arab musicians and listen to a recorded performance of a taqsim or composition in the maqam
Nahawand. You will hear that the Eb occasionally varies according to the phrase being played, just as the other pitches vary. It's a very small
difference and can be detected by paying close attention. But as to each of these E flats expressed as a ratio, I don't see how anyone can know
without doing some calculation or by having memorized the ratios from a previous calculation. Is there anyone reading this who can directly hear a
pitch as a ratio? Please tell me how you do it!
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fernandoamartin
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Excuse me. I gave so many details that I may have ruined my question.
What I really need is ratios or cents to re-tune my midi system.
There are frequency measurement hardware and software out there, but I have none. 
And there are people who have perfect pitch by ear. They can hear a note, recognize and play it in the right tuning. Maybe some of those options could
help find a frequency for Eb. But even though we don't find those options with the people reading this, please, let me explain my intention.
I know and agree that Nahawand's Eb varies. All I want is some advice with suggestions of ratios or cents that would fit nicely to it. In a computer
we really have to compromise with tuning values.
Any advice would be appreciated.
Thanks.
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Brian Prunka
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| Quote: Originally posted by Jody Stecher | | Quote: Originally posted by fernandoamartin | Hi.
Can you give me some hint? How do you play or how have you heard in canonical recordings Nahawand's Eb? Please answer using numbers (ratio fractions
or cents), because as I said above I need numbers to adjust the tuning since I'm sequencing on a computer.
Thanks. |
But this question of people *hearing* ratios has perplexed me for decades. Ever since I first read
about cents expressed as a ratio as a university student deep in the previous century I have been puzzled by it.
I understand your problem vis a vis the computer. But I cannot hear in fractions. I have never met a human being who can. Can you give *me* some hint
how this can be done? Our brains can detect minute differences in pitch and we can replicate these pitches with our voices and/or musical instruments
but who in this world directly perceives a musical pitch as a ratio? |
At the risk of diverting fernando's question (which I will try to address also), I believe I can answer this for you, Jody.
In fact, I am sure that you perceive music in ratios. You may not realize that's what you are doing, but I am sure you are doing it.
First of all, melodic intervals as we understand them are expressions of harmonic intervals: the way they are heard is in relation to another
simultaneous note, even if that note is not being currently sounded (i.e., it is retained in our mind's ear). Mostly this harmonic note will be the
tonic.
Think of tapping quarter notes with your left hand, and 8th notes with your right. You are not mathematically counting the fractions of a second, yet
you are able to perceive when the two line up and whether the in-between 8th is exactly halfway between the beats. You can perceive this, often even
more accurately, when listening to someone else do it. If one person plays quarter notes, you could play 8ths, and vice versa.
This is a 2:1 ratio, which happens to be exactly what is happening when you sing an octave. The ability to divide the vibrations by two is an
inherent capacity of our brains, happening at an instinctive level, much like the way a baseball player is doing extremely complex physics
calculations beneath their conscious awareness.
The interval 3:2 is a perfect fifth, and is exactly the same as playing a triplet against a duple pulse. Tap quarter notes in your left and tap
quarter note triplets in your right. They line up every two LH cycles and every 3 RH cycles. Again, you're not really doing the math, but you've
refined your native ability to 'feel' it, and you know when the cycles are even and when they line up.
The 4:1 interval is two octaves, and is very easy and simple to hear.
The 5:4 interval is the most complex of the basic ratios, most professional musicians can tap this relatively reliably, but it can be a little wobbly.
This is exactly a major third. Our ears happen to be somewhat forgiving of a little variation in our major thirds, just as they'll usually be a
little forgiving if we heard a 5:4 rhythm.
All the other common intervals come from stacking the intervals above (including hearing the lower pitch as the second note in the interval).
While it becomes very difficult to play higher ratios rhythmically, we retain the aural ability to perceive complex resonances, even though we don't
directly perceive the ratio as a ratio.
To some extent, the ratio is still perceived, in that originating ratios have 4 discernible qualities:
1) Overtonal: this is the quality when the ratio is the same direction as heard in the overtone series. A 5:4 or 3:2 ratio is overtonal.
2) Reciprocal: this is the quality when the ratio is in the opposite direction from the overtone series. A 8:5 or 4:3 ratio is reciprocal (i.e., the
upper note is the fundamental, up an octave)
3) What I call "fifth-iness" — the quality of being derived from 3:2 intervals
4) What I call "third-iness" — the quality of being derived from 5:4 intervals.
Any interval has at least two and possibly all four of these qualities, and this mix of flavors is felt/heard if you have learned to pay attention to
it.
For instance, a M9 is purely overtonal and fifthy (two ascending P5ths stacked on top of each other), while a m7 is purely reciprocal and fifthy.
A m6 is purely reciprocal and thirdy.
A M7 is purely overtonal, but mixed fifthy and thirdy.
Now to the relevant part:
A standard m3 in western music is mixed overtonal/reciprocal and mixed fifthy and thirdy (overtonal 5th, reciprocal 3rd). The resulting ratio is 6:5
(3:2 x 5:4 or C -> G -> Eb) ~316¢
A Pythagorean third, as often used in Arabic music, is purely fifthy and reciprocal. The resulting ratio is 32:27 (2:3 x 2:3 x 2:3 x 4:1, or C ->
F -> Bb -> Eb) ~294¢
These are not just a matter of the ~22¢ difference between the two, but of the feeling of origination by pure descending fifths vs.
the feeling of originating from a mix of ascending fifths and descending thirds.
I hear both of these used in Arabic music, particularly if we are talking about contemporary practice. It may be that if you go back far enough that
the 6:5 m3 was not used, and that this is a result of Western influence. However, there is no question that both are currently in use, and they are
used for effect depending on the circumstances.
Regarding the very low 75:64, this is an augmented second interval, and would be more appropriate for the distance between Db and E or Ab and B.
(5:4 x 5:4 x 3:2 x 1:2 or C -> E -> G# -> D#)
So 75:64 does not give you a minor third, but an augmented second.
I do not hear this note used in Arabic music for a minor third. It is used for A2 intervals, but in the old tradition the A2 is actually compressed
even further than this.
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Jody Stecher
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Thank you for the time and effort Brian but about half way through my eyes crossed and I despaired.
By the time you got to the Pythagorean third (which I can hear and discern from other thirds) and characterized it as 32:27 I was lost. There is no
way I could perceive that as a ratio. I have pretty refined hearing. When I play and sing the intervals of Indian dhrupad music the hereditary
ustads say it is correct. But I don't even perceive a fifth as 3:2. I'd be as likely to perceive it as as 767.22 grams of asparagus. I don't doubt
what you say. But this is beyond my abilities. I could easily understand the last part of your post about the difference between an augmented second
and a minor third. But I could never directly perceive an interval as 75: 64. I mean if you put 75 walnuts on one side of a table and 64 on the other
side, I'd have to count each group to know how many are there. I can't just look and know. Can you really see 75 items and know there are that many
and not 74 or 69 or 78?
So what's the answer to fernandoamartin who asked a reasonable question and is an innocent bystander in all this?
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Brian Prunka
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It's not "directly" perceivable "as" a ratio, in that you couldn't hear it and actually count the cycle relationship—it is happening way too fast
for that.
But they are perceivable in a more intuitive way, which you clearly already do if you are able to correctly sing the intervals in Hindustani music.
Maybe the way to think about it is that you are not perceiving ratios, but your brain is.
You can tell the difference if someone is playing 16ths, sextuplets, 32nds, quintuplets, etc., but you are not "counting" the number on notes and
comparing it to the subdivision of the pulse. It's the same way with intervals, just on another level. If you can hear a Pythagorean third as
distinct from a "normal" third, then you are hearing the ratio, you just haven't named it.
Regarding 75:64, this interval normally occurs as the byproduct of two simpler intervals, and not in relation to the tonic, if that makes sense.
Basically, you have a 8:5 minor 6th and a 15:8 major 7th, and the interval between the two happens to be 75:64.
If it's in relation to the tonic, it's heard as the M3 above the M7 (Tonic -> P5 -> M3 -> M3). It happens that a M3 above the M7 is 75:64.
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Brian Prunka
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To understand how 8:5 m6 and 15:8 M7 end up being 75:64 will probably make most peoples brains shut down, but you have to think of the m6 as the
tonic.
C -> Ab = 8:5
C -> B = 15:8
If we think of Ab as the tonic, then Ab -> 5:8, which we reduce to 5:4 so that the C is above the Ab. Then from C -> B is 15:8. 5*15 : 8 *8 =
75:64
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Jody Stecher
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Do you actually carry those numbers around in your head? In your immediately accessible memory?
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Jody Stecher
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Accepting the ratio as fact is easy for me. Directly perceiving it is what threw me for a loop. Now that you say it is feel-able but not knowable by
direct perception I don't feel quite so inadequate.
| Quote: Originally posted by Brian Prunka | To understand how 8:5 m6 and 15:8 M7 end up being 75:64 will probably make most peoples brains shut down, but you have to think of the m6 as the
tonic.
C -> Ab = 8:5
C -> B = 15:8
If we think of Ab as the tonic, then Ab -> 5:8, which we reduce to 5:4 so that the C is above the Ab. Then from C -> B is 15:8. 5*15 : 8 *8 =
75:64
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Brian Prunka
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1 - the classic Kurd note for Nahawand is indeed 32:27, this is the Pythagorean m3.
2 - the 6:5 m3 is commonly used in modern practice, and the lower note is often an expressive flavor, particularly at points of modulation (to
emphasize the change).
3 - the m3 in equal temperament is in between the 32:27 m3 and the 8:5 m3. It is slightly less than 6 cents higher than 32:27 and ~16 cents lower
than 8:5. It is a more than adequate approximation for most purposes.
4 - do not use the 75:64 interval, unless it is the leading tone to E or Sikah.
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Brian Prunka
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Many of them, yes, though not necessarily the very complex ones. Mostly I remember the "path" if that makes sense, and can figure the exact numbers
if I need to. The "path" is felt/heard — i.e., a M9 is 2 5ths, a M6 is a fifth down, a third up and up an octave OR 3 fifths up (the former in most
Major key music, the latter in most Pentatonic music), etc.
You are certainly not inadequate! Of course you know that . . . I think there was a difference in what was assumed to be meant by "hearing" the
ratios.
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fernandoamartin
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Thank you Brian for the detailed technical explanations.
I believe it's necessary to go from aural to numeric abilities to generate music in a computer. It's a machine and it works with numbers.
But there's still a doubt in my mind. I liked the part where you said that pythagorean Eb (294 cents) is widely used in arabic music. It really fits
nicely to arabic music, as much as the whole pythagorean tuning system, you suggested me in another thread, fits well to arabic music. But if I use
pythagorean minor third (294 cents) for kurd and other ordinary Eb phrases, how many cents should I lower Eb to make it sound clearly as a nahawand?
If nahawand's Eb is lower, Brian, Jody or any other reader, please, suggest me some values.
Thanks again.
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Brian Prunka
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| Quote: Originally posted by fernandoamartin | But if I use pythagorean minor third (294 cents) for kurd and other ordinary Eb phrases, how many cents should I lower Eb to make it sound clearly as
a nahawand?
If nahawand's Eb is lower, Brian, Jody or any other reader, please, suggest me some values.
Thanks again.
|
As an interval, your 294.1 cents is fine. But if you're asking about how many cents off from Equal Tempered tuning it needs to be, then the question
becomes more complex.
ET can be considered nearly equivalent to Pythagorean, except that each fifth is compressed by ~1.955 cents. To figure Pythagorean intervals, you
need to consider where your key center or tuning reference is.
In Arabic music (as written), the tuning reference is G.
So all your C's should be lowered by 1.955 cents, your F's by 3.91 cents, your Bb's by 5.865 cents,
and your Eb's by 7.82 cents. Note that this is not the ~<6¢ discrepancy I mentioned earlier, because we are adjusting from
G not from C.
If you are comparing your Eb to an ET tuner and your G is tuned ±0 cents, then your Eb should be 7.8 cents below the "tuner note".
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Brian Prunka
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In case it's not clear, your D's should be raised by the same amount you lower your C's by, and your A's should be raised by the same amount you lower
your F's by.
A = +3.91
D = +1.96
G = 0
C = -1.96
F = -3.91
Bb = -5.87
Eb = -7.82
E is tricky as it depends on what it's being used for, which is why we don't want an open string tuned to E, and why violinists must retune the E
string to D.
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fernandoamartin
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Well, Pythagorean tuning is considered a just intonation. And the frequencies of notes in a just intonation depend upon which note is selected to be
1/1. Ok.
But now I got really surprised with what you said: "In Arabic music (as written), the tuning reference is G."
What I always read is that in Arabic music Rast is the first note, is the first maqam, one of the most important maqamat, the beginning of maqamat
etc. And Scott Marcus in his "Arab Music Theory in the Modern Period" mentions some evidences that in the past the Arabic octave started on Rast and
the notes below it were not used. And then, when they started to be used they had no independent names and only later they received separate names
etc.
So wouldn't C (Rast) be the beginning of the Arabic octave, the most important note and the reference tuning?
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fernandoamartin
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Excuse me Brian for having asked I second time for values. When I entered the page, somehow, I missed this part where you had already explained the
values.
And thanks for suggesting 75:64 as leading tone for sikah. I've seen socres with D# as leading tone to Sikah. The same happens in maqam Sazkar. But I
always felt that it's too hard and unpleasant to the year to hear D# = 300 cents followed by E1/2b +/- 365 cents.
Thank you.
(Now, just one point. You mention 8:5 m3. When I type 8:5 in Scala tuning software it gives Ab = 813.6863 cents. The ratio that gives a third is 6:5 =
315.6413.)
| Quote: Originally posted by Brian Prunka |
1 - the classic Kurd note for Nahawand is indeed 32:27, this is the Pythagorean m3.
2 - the 8:5 m3 is commonly used in modern practice, and the lower note is often an expressive flavor, particularly at points of modulation (to
emphasize the change).
3 - the m3 in equal temperament is in between the 32:27 m3 and the 8:5 m3. It is slightly less than 6 cents higher than 32:27 and ~16 cents lower
than 8:5. It is a more than adequate approximation for most purposes.
4 - do not use the 75:64 interval, unless it is the leading tone to E or Sikah.
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Brian Prunka
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| Quote: Originally posted by fernandoamartin |
(Now, just one point. You mention 8:5 m3. When I type 8:5 in Scala tuning software it gives Ab = 813.6863 cents. The ratio that gives a third is 6:5 =
315.6413.)
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Yes, sorry for the typo, I fixed it. Sometimes happens when I repeat myself. 
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Brian Prunka
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| Quote: Originally posted by fernandoamartin |
But now I got really surprised with what you said: "In Arabic music (as written), the tuning reference is G."
What I always read is that in Arabic music Rast is the first note, is the first maqam, one of the most important maqamat, the beginning of maqamat
etc. And Scott Marcus in his "Arab Music Theory in the Modern Period" mentions some evidences that in the past the Arabic octave started on Rast and
the notes below it were not used. And then, when they started to be used they had no independent names and only later they received separate names
etc.
So wouldn't C (Rast) be the beginning of the Arabic octave, the most important note and the reference tuning? |
The Rast note is fingered, not an open string, and so can't reliably be used as the tuning note. The tuning reference has nothing to do with any of
the things you mention, anyway: it is a practical concern regarding which note a group of musicians will tune to.
In Western classical music, there is nothing special about "A" but all musicians tune to A. In jazz, people generally tune to Bb.
In Arabic music, musicians tune to G (Nawa, really). This is just how it is. It's not theoretical except to the extent that G is the dominant of
nearly every maqam and so tuning to G reduces tuning errors across all maqamat.
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Brian Prunka
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| Quote: Originally posted by fernandoamartin |
And thanks for suggesting 75:64 as leading tone for sikah. I've seen socres with D# as leading tone to Sikah. The same happens in maqam Sazkar. But I
always felt that it's too hard and unpleasant to the year to hear D# = 300 cents followed by E1/2b +/- 365 cents.
Thank you.
|
Yes, the Pythagorean Eb or the ET Eb are too high for the D# leading tone. Some musicians suggest that it really be considered a D half-sharp (D+),
while others consider it a D#.
An equal-tempered D+ would be 250 cents, so at ~275 cents, the 75:64 interval is about an 1/8 of a tone higher.
I play this interval by ear, and never checked the tuning . . . now I am curious. I would definitely expect the 75:64 to be close to what is used as
a leading tone to E, but for Sikah I am not sure.
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fernandoamartin
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Now I'm starting to understand things clearer.
The ~275 cents explain why Scott Marcus quotes sources that say that sikah leading tone D# and others D1/2#.
And finally I was able to find a plugin to audacity that analyzes pitches and gives an output in hertz. Than I type the hertz value in Scala and it
shows it as cents too.
Analyzing some samples from maqamworld.com, in maqam kurd, Eb seem to played at 300 cents almost all the time and in nahawand, Eb sometimes seem to
played +/- 294 as pythagorean tuning and sometimes lower, such as 288 cents.
I don't know if the software measured all the frequencies correctly.
But what do you think of the intonations mentioned above for maqamat kurd and nahawand?
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Brian Prunka
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I'm not sure how you are doing it in Audacity, but using a frequency analyzer in Logic, I checked the oud playing Kurd on A. This is Najib Shaheen so
should be a reliable reference for "traditional" intonation by a contemporary player.
Perhaps you have a better frequency analyzer, but I can't get enough granularity to really make a good determination that way.
If A = 220 Hz, then:
Pythagorean Bb = ~231.8 Hz (~90¢)
ET Bb = ~233.1 (100¢)
5-Limit JI Bb = 234.67 Hz (~112¢)
Note that the ET m2 is almost exactly halfway between the two just intervals, though very slightly closer to the Pythagorean.
I get the following range of values for A on the recording: 219-220 Hz (variance of 7 cents).
And for Bb: 228-233Hz (variance of 37.5 cents)
Some of this is the inaccuracy of the analyzer in context, some is inharmonicity in the string/attack, some is actual variation. Regardless, this
would seem to suggest that the central reference is the Pythagorean Bb of 256:243 (vs. A), since you could write the Bb as 230.5 ±2.5 Hz, which gets
you closer to the Pythagorean than anything.
He does play some B's in passing around 238 Hz, but this is high enough to be regarded as B half-flat I think (quarter tone would be ~240 Hz).
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Brian Prunka
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For Nahawand, it is trickier as it's difficult to get a good reference for the C. I don't think the frequency analysis is accurate enough to draw
meaningful conclusions, other than it is generally on the low side. Using similar methods above, I get an average somewhere between 275 and 308
cents. Which again suggests that Pythagorean is the reference but there is variability.
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fernandoamartin
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I did this in Audacity the plugin in pitch-detect.ny file that I found online.
Surely, nahawand samples in maqamworld were very trickier. I analyzed only the scales, not taqasim, and the output of this plugin gives me only round
hertz values. Sometimes 310 hz, 309 hz. But the problem is that 310 hz = 293.71 cents and 309 hz = 288.12 cents, a large difference. So a better pitch
analyzer would be more helpful.
I found some results in nahawand similar to yours. Sometimes Eb were as low as 275 or 282 cents or as high as 294 or 300 cents.
The samples generated some confusion because some throw us to the standard nahawand's Eb lower than kurd's. But comparing other samples they do the
reverse. Some seem to have kurd's Eb lower than nahawand's.
That's puzzling because we always learn that Eb in nahawand is lower than in kurd. But if we use pythagorean Eb (294 cents) in both, there will be no
longer such difference.
I've watched some performances of your band Brian and I liked it very much. You're very creative.
Do you know the ratio and/or cents at which you play Eb in kurd and in nahawand? How do you handle this difference when performing?
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fernandoamartin
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Note: Definitely, using ratios to tune maqamat sounds better. Just for a test I took a piece in rast that I had tuned earlier using 72-ET.
Now I re-tuned it using D#=75/64, E1/2=100/81 and B1/2b=50/27 and all the other notes from pythagorean tuning.
Everything sounds smoother and sweeter, even D# followed by E1/2b to modulate to Sikah doesn't hurt the ear. And when the drone accompaniment plays
4ths or 5ths there are not that beat sensation. They simply seem to fit harmonically.
It's laborious but it's worth the effort. 
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Brian Prunka
Oud Junkie
Posts: 2916
Registered: 1-30-2004
Location: Brooklyn, NY
Member Is Offline
Mood: Stringish
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| Quote: Originally posted by fernandoamartin | I did this in Audacity the plugin in pitch-detect.ny file that I found online.
Surely, nahawand samples in maqamworld were very trickier. I analyzed only the scales, not taqasim, and the output of this plugin gives me only round
hertz values. Sometimes 310 hz, 309 hz. But the problem is that 310 hz = 293.71 cents and 309 hz = 288.12 cents, a large difference. So a better pitch
analyzer would be more helpful.
I found some results in nahawand similar to yours. Sometimes Eb were as low as 275 or 282 cents or as high as 294 or 300 cents.
The samples generated some confusion because some throw us to the standard nahawand's Eb lower than kurd's. But comparing other samples they do the
reverse. Some seem to have kurd's Eb lower than nahawand's.
That's puzzling because we always learn that Eb in nahawand is lower than in kurd. But if we use pythagorean Eb (294 cents) in both, there will be no
longer such difference.
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According to the theory, it would seem that the Eb in Kurd and Nahawand should be the same. The name of this note is "Kurd" after all. There may be
a clue in that the Ottoman musicians consider Nihavent (Nahawand) to be a subset of Buselik (which would start from D, not C in this case). The third
of Buselik must be Pythagorean based on the open strings: A D G C F, the D-F third must be Pythagorean. So if Nahawand aims to emulate this third, it
must also be Pythagorean.
But this music uses expressive intonation and it is not tied to ratios in the way more harmonic/chordal music is.
| Quote: Originally posted by fernandoamartin |
I've watched some performances of your band Brian and I liked it very much. You're very creative.
Do you know the ratio and/or cents at which you play Eb in kurd and in nahawand? How do you handle this difference when performing?
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Thank you, it's kind of you to say so.
In the end, I listen to recordings and the musicians I play with and adjust by ear. Sometimes this means a note is low, sometimes high. Depending
on the phrase, it may be higher or lower even in the same piece. And I'm hardly perfect in my results! Nor am I an authority, just an explorer.
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