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Perfect Tuning is a Mathematical Impossibility

I attended a viola da gamba concert, and one of the gambas had double frets spaced closely together. I asked the gambist about it, and he said it was so he could play in two different temperaments at once.
I attended a gamba workshop in Milan a couple of springs ago, and the maestro there had some of those double frets, which she casually adjusted every now and then. Those classes were a real eye-opener for me!
(Obligatory plug for Luciana Elizondo, my esteemed gamba teacher):
 
In Western Music, we most commonly use the Equal Tempered System and the A 440 Hz standard. An octave is an interval where the frequency ratio is 2. An octave is divided into 12 semitones, with two sequential semitones differing by a fixed ratio equal to 2 raised to the 1/12 power.

Two raised to the 1/12 power is an irrational number since 1/12 is irrational . Therefore, any integer power of (2 ^1/12) other than a multiple of 12 is also irrational.

So A is the only note with a precisely defined value. All other notes are an approximation to whatever degree of accuracy is desired.
that's why you can get more felt accuracy finding a note without using frets ( like piano keys - they're averaged sound). anyone in a string quartet is going to a slightly different place on the fingerboard when going upscale or downscale to find the Real Feeling note
 
I attended a gamba workshop in Milan a couple of springs ago, and the maestro there had some of those double frets, which she casually adjusted every now and then. Those classes were a real eye-opener for me!
(Obligatory plug for Luciana Elizondo, my esteemed gamba teacher):

Beautiful.

Interesting to see her land her finger right on the fret, where she'd play it if she didn't have frets.
 
That may be the modern calculation, but it originates as a division of the length of a day. A 60th of a 60th of a 24th of a day. Invented by people working in base 6.
Base 6 is cool. You can count up to 35 using only your fingers.

Binary is cooler, you can count up to 1023 on your fingers. My favorite number in binary is 132 (some prefer 645, but they're wrong). Count it out on your fingers and you'll see why.
 
While we are on this subject, can someone explain to me the wedding scene in The Godfather, Michael's wedding in Sicily, and why the band was so god awfuly %#£€#%£ out of tune but obviously it was on purpose, as the whole Coppolla family are musicians and it seems to fit the song and the mood of the scene.
Is this a specific style?
 
hi mikewalker :)

I attended a gamba workshop in Milan

Please!!!!!!!!! Stop talking about gambas :D


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It makes me hungry! drool :smug:

(nice video thx for sharing! :thumbsup:)


greetings

Wise
 
That may be the modern calculation, but it originates as a division of the length of a day. A 60th of a 60th of a 24th of a day. Invented by people working in base 6.
Base 6 is cool. You can count up to 35 using only your fingers.

I finally got around to counting on my fingers in base 6. I'm pretty sure you can count to 55 in base 6. Just one shy of 100.
 
that's why you can get more felt accuracy finding a note without using frets ( like piano keys - they're averaged sound). anyone in a string quartet is going to a slightly different place on the fingerboard when going upscale or downscale to find the Real Feeling note
I asked a pro viola player (Rice Shepherd School) about playing in non equal temperment and she said her string quartet used it, but exactly which temperment was used was a negotiated item . She implied it was a lengthy subject.
 
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Are the frets set or tied on a gamba?
On a true viola da gamba, always tied ( gut or nylon monofilament ). Some modern 'gamba-like' instruments use set metal frets (In addition to my ratty old 67-year-old German gamba, I also have a recent custom-made 15-fret 5-string arpeggione with brass frets installed in the fingerboard)
 
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I never quite grasped this until I saw a plot of the tuning of a piano, all 88 notes.

As you said, only the a below middle C was a spot-on 440hz. Looking at the plot, the lower you went from there it was progressively / fractionally flatter the lower you went, and going up from there was the same incremental curve, reversed, going sharp. Yet to play it upon completion, it sounded perfectly in tune. Tuned in perfect mathematical increments, and it would sound beyond bizarre, according to the tech that was giving me the USA TODAY short course in 'Piano Tuning for Dummies'. Some keyboard synths allow for 'unlatching' the standard tempered tuning and going to alternates tuning methodologies, if you want to experience this yourself. You won't want to do it twice . . .

Decades ago I work with a pianist and we would stay up to all hours playing with different intonations. After several nights (and several cases of beer later) we mastered the "old school house" piano sound (think of Rungrens We Got to Get You A Woman, and A Beautiful Song), a good rock tuning, and one where we got it to sound like steel drums in certain registers. Loads of fun.
 
A friend of mine has a Conn Strobo tuner & he used it to tune his piano--and was confused when he went & tuned each string perfectly (& it took a while--as there is more than one string for each of 88 keys.)
He went back & double checked some strings but couldn't find anything out of tune.
He told me about it & I laughed, because I knew piano tuners don't tune all the strings perfectly, and in a way piano tuning is an art-many do it all by ear.
But then it sounds better.
So he learned the hard way.
 
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Isn't that were you'd put your finger on a guitar or bass anyway? Fretting away from the fret causes you to stretch the string and pull the note sharp.

I guess that depends on how hard you mash the string into the fretboard, but no, I've always used a lighter touch and let the frets do the work of intonation, that's what they're there for - plus it eliminates the string buzzing against my fingertip, which is what you can hear happening with her occasionally in this video (she's an awesome player, don't get me wrong, I'm not critiquing her technique!). I don't think that's a big deal playing Rennaissance music, it's probably more part of the style and expectation, but that kind of fret buzz sounds gross and amateurish on a bass guitar through an amp. When I moved from upright to electric back around 1985 or so, this was the first thing my bass instructor told me to do. It was an adjustment back the other way for me when I started playing fretless, my fingers couldn't rely on muscle memory like they could with a fretted bass, and my left hand intention had become lazy from using frets.

My impression of her playing was that she's used to not using frets, and that her fingers knew right where to go, but I really know very little about viols or this artist - maybe she hasn't touched a fretless board in years and this is how one plays a viol da gamba.
 
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plus it eliminates the string buzzing against my fingertip,
Can't say i've ever had this problem when resting my fingers on the back side of the fret, and the string can be fretted much more positively without problems this way. But if it works for you that is fine.
I just suggest that people should play through a tuner and understand how their technique can effect the pitch.
Just because it has frets doesn't mean it's in tune.

Unleashing The Mysteries Of A Scalloped Fingerboard
This on the other hand seems idiotic too me as it's only function seems to be to let you push the strings more out of tune.