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Author Topic: "True" Temperament  (Read 6002 times)

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melodeon

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"True" Temperament
« on: July 26, 2013, 04:20:56 PM »

Any comments ?
Is this really new?
Is this aqpplicable to free reed instruments?

I would imagine Paul Groff may have some insight into this also being an accomplished guitar player.

http://www.truetemperament.com/site/index.php?go=4&sgo=0
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pgroff

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Re: "True" Temperament
« Reply #1 on: July 26, 2013, 04:38:54 PM »

Hi Jeff,

These kinds of complex fretting systems have been around for a while.

Lutenists and gamba players, with frets tied on, have the option to position their frets for a non-equal tempered scale (proceeding up on one string).  Of course, this means that supposedly "equivalent" notes played on different strings may not be identical in pitch, and may make some intervals sourer while sweetening others.  Tied-on frets can be slanted (farther from the nut for some strings rather than others), and a gamba player tells me that this can help when using 1/6 th comma meantone, one historical non-equal temperament.

Similarly to the development of lute from fretless oud, the banjo in America started out as a fretless instrument, and I think non-equal tempered tunings were likely used for the open strings and for the fingered notes.  When frets began to be added to some examples, there were sometimes "split frets"  where the position of the fret was different for some strings than others.*

I've also seen split frets like that on some (prims? tambouritzas?) such as this one:
http://www.harmonycentral.com/t5/Acoustic-Guitars/quot-Old-East-European-Guitar/td-p/23150288
Here, as in some lap dulcimers, the fretting may relate more to diatonic scales with mixed half-steps and whole-steps, rather than temperament per se, but it's a related concept.

Important to remember, a complex fretting system like the one that melodeon referenced may only provide its benefits for *one particular tuning* of the instrument.  If you set up your guitar like that for the typical tuning of EADGBE, and then retune to open D for example (DADF#AD) you might have made many chords much worse than with a simple fretting design.

There's a lot more to say but maybe that's more than enough?

PG

* I've seen images of these banjos with a split 2nd fret (Ashborn?) but can't find one online to link here.  But check out this discussion: 
http://www.zither-banjo.org/pages/secondfret.htm
« Last Edit: July 26, 2013, 06:07:11 PM by pgroff »
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pgroff

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Re: "True" Temperament
« Reply #2 on: July 26, 2013, 05:57:03 PM »

Hi again,

Actually I will make one more point -- to bring out the relevance of "melodeon's" thread to actual melodeons, and keep this in the Instrument design section rather than "Other instruments."

Many of you know that cajun accordions have their own traditional family of tunings (they aren't all exactly the same).  Of course, cajun fiddlers are free to play notes of the exact pitches they want, and steel guitars likewise.  But most fretted guitars are going to be more or less in equal temperament.  I still think those ET guitars can sound great along with cajun-tuned accordions.  What do you think?

You can get similar issues when Irish pipers try to tune with fretted instruments.  I like to match up the tuning of concertinas with the sound of the regulators (harmony section ) of Irish pipes, but this can cause some tension with the tuning of fretted guitars, bouzoukis, etc.  I have seen, and heard of, some examples of 2 row button accordions used for Irish music that were tuned other than equal temperament, and some early Irish-American 1-row boxes that were specifically designed for Irish music are not in ET.

So maybe a complex fretting system as described in the original post could have some value when playing with cajun accordions or with some boxes used in Irish music -- as long as the string player could stick to one tuning of his open strings, and had a capo that would work with those weird frets going up the neck.

PG
« Last Edit: July 26, 2013, 05:58:58 PM by pgroff »
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LDbosca

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Re: "True" Temperament
« Reply #3 on: July 26, 2013, 06:09:53 PM »

I have some of the basses/chords on my B/C box tuned to unequal temperament. To my ear, ET 3rds are very harsh, particularly on the accordion, so for my D chord (technically has no D in it) I have an A and an F# with the F# tuned flat on the pull and less so on the push (so as not to clash with the right hand F#). The push D bass is sharpened so that it'll make a flatter 3rd with the right hand F#.

I think my G chord (G and B) is flattened slightly too. My C isn't and the difference is pretty striking.

If you want to hear this type of setup in action then check out Peter Carberry's solo album, he's a similar setup.

Anahata

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Re: "True" Temperament
« Reply #4 on: July 26, 2013, 08:47:38 PM »

Any comments ?
Is this really new?
Is this applicable to free reed instruments?

I don't see how it applies to free reed instruments. Their main point seems to be that even it you try to make a guitar tuned to equal temperament (or any other specific temperament) by calculating the fret spacings it will be wrong because strings don't exactly follow the simple mathematical model used. (i.e. frequency inversely proportional to length)

It's the equivalent in the accordion world of "discovering" that when you tune a reed in a tuning pan, the pitch isn't quite the same after you put it back in the box. Any decent tuner knows that, tests the reed in the box and either tunes it in situ or compensates by tweaking the pitch in the right direction in the tuning jig, and double-checking afterwards.

Whether we want boxes tunes in equal, just, quarter meantone or any of the other systems in use is a separate issue, and has been much discussed here already. But at least when we decide what tuning we want, we can get it done exactly - we don't have the problem that the guitar makers seem to have.
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KLR

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Re: "True" Temperament
« Reply #5 on: July 26, 2013, 11:50:03 PM »

I play Irish pipes, a fiddler once asked a group of us pipers what was the deal with the tuning on the pipes.  My initial response didn't satisfy very much:  "We just tune the notes on the chanter to the drones until it doesn't sound awful any more."  But that's really all there is to it.  "Just Intonation."  How are the Cajun boxes tuned?  Close to that?  Pure JI would make for an interesting box.  I've never gotten the kind of charge you get with a full set of pipes when everything's bang on and you strike a 3 note regulator chord; it's like standing next to a cranked up Marshall amp, or full rank of organ pipes - there's a physical feeling in it, even with a quiet set of pipes.  Don't quite get that from an accordion, never mind a guitar.

Friend of mine has a fan fretted guitar .  Good conversation piece if nothing else; the selling points are uniform string tension, improve response, bit better intonation here and there.  Dunno if they'd be a bigger headache to install than the staggered fret jobs. 
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melodeon

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Re: "True" Temperament
« Reply #6 on: July 27, 2013, 12:02:50 AM »

What is applicable .. if there is a different tuning system that favors specific keys, or chords or a "sound" that may be different...

It is my undersdtanding of some of these tunings, as Paul mentioned, they are key specific.

Note:

The famed Cajun accordeon builder Marc Savoy does not tune to the "typical" Cajun tuning.

I , too, like the sound of a an ET guitar, banjjo or mandolin played against a "Cajun" tuned instrument. Simple complexity.
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pgroff

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Re: "True" Temperament
« Reply #7 on: July 27, 2013, 02:27:27 AM »

Any comments ?
Is this really new?
Is this applicable to free reed instruments?

I don't see how it applies to free reed instruments. Their main point seems to be that even it you try to make a guitar tuned to equal temperament (or any other specific temperament) by calculating the fret spacings it will be wrong because strings don't exactly follow the simple mathematical model used. (i.e. frequency inversely proportional to length)

It's the equivalent in the accordion world of "discovering" that when you tune a reed in a tuning pan, the pitch isn't quite the same after you put it back in the box. Any decent tuner knows that, tests the reed in the box and either tunes it in situ or compensates by tweaking the pitch in the right direction in the tuning jig, and double-checking afterwards.

Whether we want boxes tunes in equal, just, quarter meantone or any of the other systems in use is a separate issue, and has been much discussed here already. But at least when we decide what tuning we want, we can get it done exactly - we don't have the problem that the guitar makers seem to have.

Hi Anahata,

Good points, but I think in general terms, as melodeon & I mentioned, there are actually some points of contact between the ideas advanced on that website and issues in tuning free reed instruments. It's interesting that there may be ways to bring fretted instruments into closer tune with instruments like accordions and concertinas where (as you mention) there are sometimes fewer constraints on the tuning of individual notes.  [because each note is produced by its own reed or reeds, rather than 6 strings or so for all the notes, each string doing multiple duty]

Another excellent point made on that website, often unappreciated or just understood incorrectly, and definitely relevant to free reed instruments:  there is no one tuning for "just intonation" -- no set of 8 pitches for a diatonic scale, or 12 pitches for the 12 notes of the chromatic scale, that will keep all intervals acoustically pure. 

PG
« Last Edit: July 27, 2013, 09:17:54 AM by pgroff »
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Chris Ryall

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Re: "True" Temperament
« Reply #8 on: July 27, 2013, 06:57:20 AM »

I normally keep out of tuning discussion as its something I pay cleverer people to do. But this has turned interesting, particuarly as like many here I started on guitar, and "philosophically" I regard our instrument as "fretted". That is to say that notes are pre-set, unlike violin. I can even bend them a bit, on the right occasion!

So there are considerable contact points. Not sure I yet agree with "or 12 pitches for the 12 notes of the chromatic scale". If the box is tuned to play in a lot of keys, doesn't that mean A=whatever, and mathematically defined intervals from there on, or our main rows always tempered?
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pgroff

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Re: "True" Temperament
« Reply #9 on: July 27, 2013, 09:33:41 AM »

I normally keep out of tuning discussion as its something I pay cleverer people to do. But this has turned interesting, particuarly as like many here I started on guitar, and "philosophically" I regard our instrument as "fretted". That is to say that notes are pre-set, unlike violin. I can even bend them a bit, on the right occasion!

So there are considerable contact points. Not sure I yet agree with "or 12 pitches for the 12 notes of the chromatic scale". If the box is tuned to play in a lot of keys, doesn't that mean A=whatever, and mathematically defined intervals from there on, or our main rows always tempered?

Hi Chris,

Looks like you may  be quoting me there in your second paragraph. Here's what I mean.  A typical modern piano/organ type keyboard has 12 different black and white keys per octave, each assigned a different pitch.  In equal temperament, the idea is that those 12 pitches will divide the octave equally.  [But on a logarithmic scale, since with every increase of an octave the frequency of a note is doubled.  A = 440, the next higher A = 880 Hz or vibrations/second.  Bb above middle A is (440)(12th root of 2) = 466.]   Yes, those equal-tempered scales are often used for modern free reed instruments and are mathematically defined.

But some modern electronic tuners or keyboard instruments claim to offer a "scale in just intonation" that assigns different pitches to those 12 notes of the octave, compared to the pitches assigned by ET. Similarly, some diatonic instruments with only 7 different pitches to the octave (such as C,D,E,F,G,A,B) are tuned to scales that have been called "just intonation." *  These scales have sometimes been used for accordions / melodeons also.  No problem to use them, IMO, if you understand their pros and cons, but a problem to think of these scales themselves as being or creating "just intonation."

I have always made the point, and the website linked above makes it too, that there is no one scale for "just intonation."  Just intonation (the use of acoustically pure intervals for harmony) is not a property of any one scale.  It's a property of the harmony that occurs in the music at any one time, and as such there is no one scale in just intonation.

PG

* for example, the following tuning for a scale is sometimes called "the scale in just intonation;" numbers in parentheses represent approximate deviation in cents from equal temperament, something approximating this:
C (0), D (+4 ), E (-14), F (-2 ), G (+2), A (- 16), B ( -12)
Derived from the table here:
https://en.wikipedia.org/wiki/Just_intonation
This scale does provide some just intervals such as the fifths C-G, G-D, F-C, and E-B, and the major thirds C-E, F-A, and G-B.  But the fifth D-A is not just.
« Last Edit: July 27, 2013, 09:48:54 AM by pgroff »
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Chris Ryall

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Re: "True" Temperament
« Reply #10 on: July 27, 2013, 06:36:35 PM »

Knew that (sort of). Actually my question was, are "our main rows always tempered?"
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pgroff

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Re: "True" Temperament
« Reply #11 on: July 27, 2013, 06:55:06 PM »

Knew that (sort of). Actually my question was, are "our main rows always tempered?"

Hi Chris, 

Ok, great question.  Leaving aside the concept of tremelo / musette, the answer is: almost always, in practice.

"Tempered"  refers to any tuning in which intervals are compromised from being acoustically pure. 

Equal Temperament as I described above is one temperament, very commonly used in accordions / melodeons. The mean-tone family of temperaments, and the "well temperaments" mentioned in the originally-posted link, are other temperaments.

Just intonation is playing without tempered intervals -- using only intervals that are acoustically pure.  Some accordions do have their main rows tuned with scales of pitches that can provide a lot of pure intervals.  If you only use those pure intervals (including the the major thirds in 1/4 comma meantone), and never use any tempered intervals, you could be said to be playing in just intonation.  You can do that, or close to it, on some 1-row boxes with special tunings.

That's the easy version anyway.

PG
« Last Edit: July 28, 2013, 07:17:13 PM by pgroff »
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Chris Ryall

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Re: "True" Temperament
« Reply #12 on: July 28, 2013, 08:42:57 AM »

thanks, will continue to leave this to the experts!
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Steve_freereeder

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Re: "True" Temperament
« Reply #13 on: July 28, 2013, 09:55:34 AM »

I first embarked into dark art of tuning melodeons following the EATMT 1-row melodeon-making course of 2008 in Stowmarket. I have gleaned much wisdom from Theo and Rees then and in the intervening years since, so a big "thank you" to them both!  :|glug  :|glug

I was aware that Cajun 1-row tuning approached just intonation. Typically the thirds and sevenths of Cajun boxes were tuned around 15 cents flat which is why many of the RH chords sounded so sweet and suited that style of music and playing. But I also knew that Cajun boxes sounded 'out of tune' when used for playing English-style music, which was what I wanted it for.

In Equal Temperament, it is the thirds and sevenths which can sound harsh, so following advice from Theo and Rees, I tuned the thirds and sevenths 5 cents flat, and the remaining notes to ET. This is a good compromise on a 1-row box which is going to be used for general, non-Cajun, music.

Instruments with two or more rows and hence being capable of playing in a good selection of keys need to be tuned in ET, otherwise certain intervals in keys away from the home-row keys are going to sound bad.

Again, following advice from Theo, on the LH side it is possible to tune the chords to a sweeter-sounding compromise. Basically, on all major chords, I tune the thirds in the chords 5 cents flat and the fifths 2 cents sharp. Not only does the chord sound sweeter like this, it also means that if there is a stop to remove the thirds from the chords, the 'bare fifth chord' now sounds beatless and pure. In ET, fifths are generally about 2 cents flat from just tuning, so it's a matter of putting that 2 cents back for a sweet sound.

Minor chords are a little different. For a minor third interval to sound sweet is much more subjective, but I have obtained good results by tuning minor thirds to be about 7 cents sharp. I have based this on studying the various well-temeraments used for baroque keyboard instruments.

These adjustments to the LH chords are relatively small and do not clash unduly with the ET-tuned RH side.

A final point to note is that when a two-voice MM or three-voice MMM instrument is tuned to anything wetter than a very light tremolo, the tremolo itself masks any roughness caused by tuning to ET, so in my opinion there is little or nothing to be gained by the RH side to anything other than ET.

All tuning on melodeons involves compromises of one sort or another!
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Theo

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Re: "True" Temperament
« Reply #14 on: July 28, 2013, 10:35:24 AM »

All tuning on melodeons involves compromises of one sort or another!

Correction:  All tuning on musical instruments involves compromises.
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pgroff

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Re: "True" Temperament
« Reply #15 on: July 28, 2013, 11:08:03 AM »

Great posts, Steve and Theo.

I have often read the "15 cents flat" estimate for the thirds and sevenths in "cajun tuning,"  mentioned by Steve. Those would be the notes E and B, in a one-row box, key of C.  If you leave all other notes of the scale at their ET values, that gives:

C (0), D (0), E (-15), F (0), G (0), A (0), B (-15)


Given that tuning reeds is imprecise for many reasons, it might be worth pointing out that if you are aiming for pure major thirds (such as C-E, G-B), and the lower of the two notes (such as C or G) is right at the value it would have in equal temperament, you actually would not want the higher note in the interval (such as E or B) to be tuned any more than approximately 13.7 cents flat of its value in ET:

C (0), D(0), E (-13.7), F (0), G (0), A (0), B (-13.7)

Of course you might want to round that deviation to "-14" -- but you wouldn't want to aim for -15, with possible error bars either side of that larger figure.  That's because the (approx) -13.7 figure, while optimal for the major third, is compromising a fifth interval.  In this case, the compromised fifth would be A - E, which is very narrow and can sound harsh.*  No point in narrowing the major third  more than needed for acoustical purity while making the associated fifth even worse.  That's a concept I've heard described as "harmonic waste."

As Steve said, this version of a "cajun-like" scale is not exactly the diatonic scale often listed as "just."  For the latter, see my post above; that scale gives many more pure thirds and fifths.

Other scales I have sometimes discussed with cajun accordion makers also sharpen the fourth note of the scale to get a better major third interval between fa and la (F and A in the key of C). That's a different approach to a sweet F-A third than is taken in the published "just diatonic scale" above but it has some real advantages!  For example, this would be nice for three just thirds, using a sharp F:

C (0), D (0), E ( -14), F (+14), G (0), A (0), B (-14).

If you want the tonic chord's fifth tuned "just" as well, that could morph into:

C (0), D (0), E (-14), F (+14), G (+2), A (0), B (-12).

A very nice scale for a 1-row box.   (:)   Modifying that last scale by tuning the D sharp by 2 to 4 cents would improve the G-D fifth but hurt the D -A fifth a little; might be worth it depending on your style and repertoire on the box.


Steve's own proposed scale for the melody side I think would come out this way for the key of C:

C (0), D (0), E (-5), F (0), G (0), A (0), B (-5)

Although "well temperaments" are not precisely defined except for a 12 note scale, those small deviations proposed by Steve, that do sweeten a couple of important intervals, are close to the degree and the concept of temperament that can be found in the well temperaments.  Steve might want to look into those well temperaments, because he might find that a few more such slight deviations might contribute some other improved intervals.

Good points about sweetening up the bass-side chords also.  Those general guidelines will improve the sound of many ET melodeons, IMO.

I personally can hear a difference, when a note on the melody side, wet-tuned and set to its ET value, is played together with a chord on the bass side in which that same note has been flattened or sharpened.  But it's not usually a striking dissonance.

PG

* True, the notes A and E will not be sounded together on a typical 1-row melodeon in the key of C, but  may interact with other instruments to pull overall tuning away from purity, and again that "15 cents flat for thirds and sevenths" is actually making the third intervals worse than would a "14 cents flat" target.
« Last Edit: July 28, 2013, 07:19:18 PM by pgroff »
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Re: "True" Temperament
« Reply #16 on: July 28, 2013, 11:33:12 AM »

I personally can hear a difference, when a note on the melody side, wet-tuned and set to its ET value, is played together with a chord on the bass side in which that same note has been flattened or sharpened.  But it's not usually a striking dissonance.
Yes, I can also hear the difference when deliberately sustaining the LH chord and and the equivalent third on the RH side, but as you say, it's not a striking dissonance and in most normal playing/performing situations it passes unnoticed.
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Re: "True" Temperament
« Reply #17 on: July 28, 2013, 11:56:24 AM »

Is this aqpplicable to free reed instruments?

Not directly, but in relation to subsequent posts we have a peculiar advantage on some push-pull instruments.  On a fourth apart box we several some notes repeated on push and pull, a some not repeated. As a result it is possible to use different pitches for the push and pull versions of the same note in order to sweeten useful chords, and avoid some of the ill effects on other chords.  I'm aware of this as a theoretical possibility, but I've not felt able to explore the practical application.
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Re: "True" Temperament
« Reply #18 on: July 28, 2013, 04:11:57 PM »

Is this aqpplicable to free reed instruments?

Not directly, but in relation to subsequent posts we have a peculiar advantage on some push-pull instruments.  On a fourth apart box we several some notes repeated on push and pull, a some not repeated. As a result it is possible to use different pitches for the push and pull versions of the same note in order to sweeten useful chords, and avoid some of the ill effects on other chords.  I'm aware of this as a theoretical possibility, but I've not felt able to explore the practical application.

Excellent point Theo, and many older diatonic accordions and anglo concertinas were tuned exactly the way you describe. This is a little different from the complex fretting systems that aim to bring a fretted instrument in tune all over, with one of several scales that have 12 tones to the octave.  The very complex tuning systems of some historical free reed instruments had more than 12 tones to the octave, providing more options to optimize the harmonic beauty of intervals when played properly.

PG
« Last Edit: July 28, 2013, 04:30:46 PM by pgroff »
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Re: "True" Temperament
« Reply #19 on: July 29, 2013, 09:45:10 AM »

dipping again … please excuse my ignorance but does this mean the eg pull G on my D row will not be the same as the push on G row, of for that matter all the other notes available both ways?
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