Tuning to Meantone

[SteveS]

Here is a post by Paul in a previous discussion of essentially the same subject.

I recommend reading the entire thread. In fact, the second post refers to couple of additional threads.

This thread is extremely useful - thanks for taking the time to find and post it Jim.

 

I'm reading around the subject in temperament in general - of course like anything new I end up having more questions than answers - I know that my understanding will increase and then I'll make a decision about which way to go.

 

Right now with my relative ignorance (which is still with more knowledge than I had yesterday on the subject) I like the look and sound (from the snippets Ive heard on the Web) of Bachs temperament. How does it measure up with major & minor chords is my concern.

 

I guess with temperament and tuning, one must decide what the 'home' key is since this appears to affect the relative intervals.

[Dan Worrall]

The proof is in the pudding, or the playing. I have an ET CG Dipper and a quarter comma MT CG Tedrow.

 

The thirds on the Dipper, especially on the higher-pitched G row, tend to bite at the ears. A lot. Those thirds sound much better in MT. The fifths are of course pure on the ET, but on my MT instrument they don't sound too beat-y. I would say that, without measuring beats and such to perfection, the thirds and fifths sound about the same in MT. So you give up the pureness of the fifths and get playable thirds as a result.

 

On my GD Wheatstone, in ET, I don't find the thirds quite so piercing. At a lower pitch, the problem seems to be lessened a bit.

 

To over generalize a bit (no doubt not all will agree):

Most of the really old time players who frequently played chords--for example, William Kimber, or Hans Bodenstein, or Faan Harris--used more third interval partial chords than fifths, which is different than modern revival players who tend to avoid thirds and use fifths. Nineteenth century Anglo instruments were typically not tuned in ET, which may help explain that; the thirds sounded fine. And of course the thirds were easier to use when chording---there was not so much hunting and pecking for complex oompah chords by the old timers. Also, modern revival players seem to play fifth interval partial chords more for their antique-ish sound and/or their ambiguity (was that a minor or a major?)--or perhaps because they are simply avoiding the trashed third intervals on their ET instruments.

 

If you are going to play in a traditional manner, using mainly the home keys of C and G along with F and D, then in my humble opinion some sort of unequal temperment is much easier on the ears, especially if playing a lot in G on a metal-ended CG. If you are, however, prefer the unique sound of fifth partial chords, or have a fondness for the mental calculus of playing far-off keys, then I'd stick with ET.

Steve,

 

On re-reading, I see you are an EC player, not an angloist. A different discussion than that to which I was speaking!

Here are two articles that you might explore, just in case you haven't seen them:

 

The first treats the whole rocky interface between the science of acoustics and public preferences with regard to the EC during Wheatstone's day:

http://jmt.dukejournals.org/cgi/content/abstract/53/2/163

 

In this next one, Allan Atlas discusses Charlie Wheatstone's own thinking on temperaments for the ECs that he built...starting on p. 46

http://www.concertina.com/atlas/victorian-concertina-performance/atlas-victorian-concertina-some-issues-relating-to-performance.pdf

 

Maybe they will be useful. My guess is that, following a period of deep thinking, you will follow Allan's opinion of the perfect EC on a desert island--ET. As usual, I could be wrong! Be keerful though; endless discussions of temperament, if unchecked, can lead to madness...

[Dave Weinstein]

Dan,

 

What were the changes for the MT Tedrow?

[SteveS]

I looked again at the chromatic scale of the EC and the enharmonics that exist in equal temperament (ET), and which of the scales could be played in meantone temperament (MT) without resorting to the buttons that in ET are enharmonic equivalents.

 

This is a map of all the notes that may be tuned in MT:

 

| Bb Db Eb Gb Ab

|A B C D E F G

| A# C# D# F# G#

 

The MT notes marked in blue are not present on the EC.

 

This means that the following major keys (and their relative minors) may be played in MT without resorting to any of the enharmonic notes (in ET)

 

C, G, D, A, E, F, Bb, Eb

 

Which for the music I play should be fine.

 

Should I be concerned about modulating from # to b keys during the course of a piece - it certainly exists in the dance music that I play, but not in any of my current song repertoire.

But then I don't envisage using this instrument for playing for dance; it is more suited to song accompaniment I feel.

Edited January 2, 2011 by SteveS

[michael sam wild]

i've found this a very useful discussion in what can get pretty abstruse. On a post elsewhere I think someone had put up a sound recording of the various tunings , am I correct.

 

Jim, Paul Groff sent me some interetsing information on this a while back. I think he is busy making a living and raising a family like a lot of us must once have had to do .

[Dan Worrall]

Dan,

 

What were the changes for the MT Tedrow?

 

Dave, not sure what you mean. It is a square-ended wooden-ended one (one of two "Harley" lookalikes he has built), in CG, and I asked him to tune it to Meantone (I had built myself a CG a few years earlier and tuned it myself to Quarter Comma MT, and liked the sound).

 

It has a peculiar reedy tone, probably the result of both the wooden ends and the square shape--it doesn't at all sound like his standard ones. Kind of like a German concertina with a much better action. Someone else on c.net has the other Harley-type; I cannot remember who. It isn't you, is it?

 

Cheers,

Dan

[Bill N]

<BR>It has a peculiar reedy tone, probably the result of both the wooden ends and the square shape--it doesn't at all sound like his standard ones. Kind of like a German concertina with a much better action. Someone else on c.net has the other Harley-type; I cannot remember who. It isn't you, is it?<BR><BR>Cheers,<BR>Dan<BR>

<BR><BR><BR>That's me Dan. My Harley repro is a Bb/F in ET. It too has a particularly reedy sound.<BR><BR>I can't check from here at work to see if it's still posted, but Bob had sound files on his website of the same tune played on your concertina in both ET & MT tunings (having initially forgotten that you had requested MT!) I don't read music or have any music theory, but I can hear a real difference in the "sweetness" of the chords.<BR><BR>Bill <BR><BR>Edited to add:<BR><BR>They must have changed our security filters, as I was able to check on the above. The sound files are still there, along with other info on his Harley reproductions. Tune is "Da Slockit Light". Edited January 3, 2011 by Bill N

[Dan Worrall]

<BR>It has a peculiar reedy tone, probably the result of both the wooden ends and the square shape--it doesn't at all sound like his standard ones. Kind of like a German concertina with a much better action. Someone else on c.net has the other Harley-type; I cannot remember who. It isn't you, is it?<BR><BR>Cheers,<BR>Dan<BR>

<BR><BR><BR>That's me Dan. My Harley repro is a Bb/F in ET. It too has a particularly reedy sound.<BR><BR>I can't check from here at work to see if it's still posted, but Bob had sound files on his website of the same tune played on your concertina in both ET & MT tunings (having initially forgotten that you had requested MT!) I don't read music or have any music theory, but I can hear a real difference in the "sweetness" of the chords.<BR><BR>Bill <BR><BR>Edited to add:<BR><BR>They must have changed our security filters, as I was able to check on the above. The sound files are still there, along with other info on his Harley reproductions. Tune is "Da Slockit Light".

Of course! It was you with the Harley, Bill. I don't know where my memory is...I had it a minute ago...must have left it in the car.

[David Barnert]

The fifths are of course pure on the ET...

Not so.

 

A pure 5th has a frequency ratio of 3/2 or 1.5.

 

An equal tempered 5th has a frequency ratio of 2 to the 7/12 power [7 ET half steps] = 1.498307...

 

Close, but not pure.

[Dan Worrall]

The fifths are of course pure on the ET...

Not so.

 

A pure 5th has a frequency ratio of 3/2 or 1.5.

 

An equal tempered 5th has a frequency ratio of 2 to the 7/12 power [7 ET half steps] = 1.498307...

 

Close, but not pure.

Dave,

 

Yes, I'm sure you are correct. And buffalos are really bison. And the twenty-first century began on 1/1/2001, not 1/1/2000.

 

Not to belittle the purists...you truly are correct. Its just that, not being a musical theorist, my ear tells me an interval is "pure" when it doesn't noticeably beat...not my handheld calculator.

 

But, whatever.(He says, as he takes cover!)

[shaunw]

It was the Ancient Greeks who discovered the mathematical formula for the relationship

between the length of a string and the note produced when it is plucked. That relationship

is the same as mean tuning. So strictly speaking mean tuning is the correct tuning and the

most pleasing to the ear. So why are almost all our musical instruments, e.g. all pianos,

tuned to equal temperament?

 

As Bach discovered it made smooth modulation from one key to another possible and the

sound of equal temperament seems to be acceptable to most peoples ears. If you don't

play things that require you to modulate from one key to another then you don't need

equal temperament. I have been told that early Wheatstone English concertinas were

tuned to mean temperament and that that is the real reason for the 14 keys to the

scale arrangement but I don't know if that is true.

[RatFace]

Rather super article on this here.

 

You might want to right-click->open in new window for the little links in the article if they cause your browser window to resize.

[John Wild]

That's me Dan. My Harley repro is a Bb/F in ET.

 

I thought Steven Spielberg used pedal cycles in "ET". Is there a remake using Harleys?

[Alex West]

 

As Bach discovered .....

 

Shaun

 

I can't claim huge knowledge of the subject but I've read a lot about the various temperaments in an effort to understand. As I'm sure you realise (and certainly if you've read any of Paul Groff's threads I'm sure you will) it's not as simple as meantone versus equal temperament - there are a huge number of different temperaments available from the 16th century to the present day aimed at resolving or enhancing the tonal and "colour" differences between the keys we play in in Western music. (There are a whole bundle of other temperaments and aesthetics to grapple with in Middle Eastern and Chinese music as well as some experimental Western music where the scale is not limited to 12 notes!)

 

The purpose of this reply is just to point out that Bach - at least according to most modern references - did not compose "The Well Tempered Clavier" in order to highlight the benefits of equal temperament. Current opinion is that he was promoting well temperament, (which uses one or more of the sets of temperament between meantone and equal temperament to reduce or remove the harsh fifths and wolf notes) to illustrate the differences in colour and emotion between the different keys.

 

I hope this helps

 

Alex

[Anglo-Irishman]

But Geoff Wooff's meantone description of one of his 'tinas in another thread set me thinking could this be something I should consider for this instrument.

 

What are the advantages & disadvantages of tuning to meantone?

How might this sound in chords used for song accompaniment? (I have one song in mind that I think suits the key of Cm)?

What about playing together with other instruments - fiddle, harp?

What effect on playing technique might I expect?

 

Steve,

In a parallel existence, I am also an autoharper, and the autoharp Internet community seems to be the one that is most preoccupied with the meantone/equal temperament discussion. The modern factory autoharp is chromatic, with 12 strings to the octave, and the chord bars are set up for the major keys of Bb, F, C, G, D and A - i.e from 2 flats to 3 sharps.The standard tuning procedure is to use an equal-tempered electronic tuner, or a properly-tuned piano or keyboard.

 

However, some autoharpers find equal temperament "edgy". The 'harp has a lot of sustain, and the notes of a chord can ring together for a long time, exposing any compromised intervals. So some make their autoharps diatonic, by tuning the accidentals to the nearest note of a 7-note diatonic scale (the felts on the chord-bars are re-cut accordingly) and tweak the thirds and fifths to make this one key sound absolutely "sweet" as they call it.

But a one-key autoharp is almost as limiting as an old 10-button German concertina, so most diatonic 'harpers have two-key instruments, with a diatonic scale plus one accidental. This allows key combinations like F/C, C/G or D/A. (Does that sound familiar, you Angloists?) In this case, true "just" tuning is not quite right either, so some form of meantone tuning is used. Threads like this one are frequent on autoharp forums!

 

To answer your questions from an autoharper's standpoint:

One point is always made: meantone is for diatonic 'harps; chromatic 'harps need ET. This may be less hard and fast for concertinas, because you can choose to omit the notes that sound "sour" - on the autoharp, you can't. By analogy, you might postulate that meantone would be suitable for Anglo concertinas (especially 20-button ones) and ET is required for ECs and Duets.

 

Also, some users of meantone tune their diatonic 'harps to ET when playing with other even-tempered instruments, to avoid sounding out of tune. The same should apply to concertinas - whereby re-tuning between sessions is not an option!

 

For song accompaniment, you set up your 2-key diatonic autoharp in the keys you're going to need for your voice or the voice of the singer you habitually accompany. As a baritone, I would choose a C/G setup - which is what I have on my Anglo, thank goodness! Autoharps are relatively cheap, so some people have a quiver of them in different key combinations (like tin whistles). The sweetness of the meantone tuning is fine for song accompaniment - remember, vocal cords are not hard-wired to a certain temperament.

 

With the autoharp, there are slightly different playing techniques for diatonic and chromatic, if you want to optimise the diatonic set-up. You can use adjacent strings without damping , because there are no "wrong" notes in between. This obviously doesn't apply to the concertina; just press the buttons and work the bellows in the usual way, and the reeds will give you the same intervals, only "sweeter".

 

Hope this little glance over the fence helps!

 

Cheers,

John

[Bill N]

That's me Dan. My Harley repro is a Bb/F in ET.

 

I thought Steven Spielberg used pedal cycles in "ET". Is there a remake using Harleys?

 

 

Go home!

[cboody]

Not to muddy the discussion or anything :

 

It is probably best to consider meantone and just intonation as solutions for a single "major scale," or at least for closely related scales (like G and D or perhaps F C G and D). Those tuning solutions are optimized for nice thirds within the diatonic scales. Yeah you can extend the concept to a chromatic situation, but the solutions get less and less useful as you move away from the note upon which you base the tuning. The last part of the previous sentence brings up another issue: You need to select the starting pitch for your meantone instrument. Probably for trad players that would be G or D. If you use C you will already have a less than "as good as it can be" third in one basic chord in G and in two basic chords in D. The Vallotti article mentioned above will help in understanding that issue and will also shed some light on my contention here that meantone is essentially a diatonic solution.

 

As to tuning to meantone vs. ET or some other system: What listeners and players respond to is the accuracy of unisons and the acceptability of various other intervals, thirds and fifths being the most noticeable for most folks. Most folks don't discriminate pitch differences less that 10 cents (and surely not less than 5 cents) when two notes are presented separately and without any harmonic situation given. They do much better presented with a unison of two pitches or with fifths and thirds. You can retune your instrument to whatever tuning and perhaps it will satisfy you better. In a group situation with other instruments ET it will probably not bother. That is so because in many cases our perceptions will adjust what we hear to what we want to hear. Consider the 7th in the bagpipe scale. It is conveniently perceived as major or minor (relative to the fundamental note of the chanter) depending on what mode you happen to be playing in. Psychoacoustics is a fascinating field! A little example from my past: I had a fine chamber choir with two well trained musicians singing tenor. One "heard" the kind of a third just or meantone intonation might have. The other heard "Pythagorean" thirds, as large or larger than the ET thirds. Every time the tenors had the third on the end of a piece they refought the battle as to which was correct!

 

In sum: diatonic tunings are really nice to listen to, and many musicians playing instruments like violins learn to adjust their tuning "on the fly" to the key center they are playing in at the moment. For those of use "stuck" with chromatic instruments that can't be retuned while playing and on which we play in many keys ET is an acceptable solution as are the solutions discussed in the Vallotti article. But mean and just "just" won't work well.

 

OK...flame proof suit donned.

Edited January 14, 2011 by cboody

[Anglo-Irishman]

It is probably best to consider meantone and just intonation as solutions for a single "major scale," or at least for closely related scales (like G and D or perhaps F C G and D). Those tuning solutions are optimized for nice thirds within the diatonic scales. Yeah you can extend the concept to a chromatic situation, but the solutions get less and less useful as you move away from the note upon which you base the tuning. The last part of the previous sentence brings up another issue: You need to select the starting pitch for your meantone instrument. Probably for trad players that would be G or D. If you use C you will already have a less than "as good as it can be" third in one basic chord in G and in two basic chords in D.

 

This is all true, but it comes sort of automatically, due to the fact that meantone tunings make most sense on diatonic instruments. If you have a D/G instrument, you won't be playing anything in C, so taking F or C as your starting pitch wouldn't make any sense, quite apart from the musical genre you'll be playing. And with an Bb/F instrument, you won't be playing with D-G-centric traditionalists, so Bb as your starting pitch won't be an issue. The instrument should simply be "meaned" to its own keys.

 

Most folks don't discriminate pitch differences less that 10 cents (and surely not less than 5 cents) when two notes are presented separately and without any harmonic situation given. They do much better presented with a unison of two pitches or with fifths and thirds.

 

This is why the meantone topic is so important with autoharpers. The basic strum of a major triad always results in root-third-fifth-root-third-fifth... sounding in one or two octaves. So even less musical listeners perceive any disharmony. It takes pretty advanced technique to omit the third or the fifth from a chord, should one of them be "sour", so optimal tuning is a must with the autoharp. As concertinists, we can omit any sour intervals at will, just by omitting to press the relevant button combination.

 

Cheers,

John