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  • 9 years later...

Apologies for raising an old thread - but in the lack of responses on the thread concerning Mander's use of unequal temperament the Cranleigh organ is important - as are others that Manders have built using Kellner, Young or other mild unequal temperament.

In recent years I have given focus to piano tuning and developed an implementation of unequal temperament, Kellner, which is capable of universal application on all pianos. It's been a privilege to have been able to study a number of historic instruments from the Colt Collection and formerly Finchcocks, and these have given me an insight into the tonal structure of the ancient instrument from which we can benefit in our approach to the modern.

The one thing that the temperament does is to enable the piano to resonate. It gets louder, and sweeter.  Of course this can't be demonstrated electronically but if anyone would like to experiment then Pianoteq from https://www.modartt.com/ provides useful facilties, even though the sound from a real instrument is more complex. It gives a useful idea of contrasts of still and moving that the temperament gives.

In research on tuning matters I've found electronic sound-laboratory facilities to be very helpful. Yesterday a friend came round for some experiments and I mentioned that last week I'd demonstrated the opening to the Couperin Mass in St Maximin style, and then put the demonstration into equal temperament and the bite of the music was lost. The subject of Cranleigh came up and he said that he'd done one of the early recitals there. He said that as a result of the temperament the organ sounded bigger than it is. He then said that he'd played it since its conversion into equal temperament and that now it merely sounds ordinary.

What a temperament with many perfect fifths is doing is to allow sympathetic vibrations which build in the resonance of the building. This is an important part of how an  instrument fits into an acoustic space. The pure thirds and pure fifths produce beat frequencies which reinforce the bass note and the harmonics of bass notes fall onto notes of the scale up above. So the whole sound is mutually supportive.

If Cranleigh can be converted back to the unequal temperament it was built in, perhaps future curators of the instrument might valuably consider returning the instrument to its original tuning.

Best wishes

David P.

 

 

 

 

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I'm sure I've read other threads on here regarding unequal temperament before, but I think here is as good as any.

What I find hard to believe is that unequal temperament is not employed more widely in organs.  Perhaps not concert room organs which  are required to work with orchestras and many other instruments, but why not churches and cathedrals.  How often do we see cathedral instruments being used with orchestras?  Surely, it is far more usual - normal, in fact - for them to be used with choirs.

I'd go so far as to say that a cathedral organ retuned in an unequal temperament like Kellner would not even be noticed as any different by most people, whereas many are likely to find that they like the sound in preference to how it was.

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23 minutes ago, John Robinson said:

Perhaps not concert room organs which  are required to work with orchestras and many other instruments, but why not churches and cathedrals.  How often do we see cathedral instruments being used with orchestras? 

The experience of the orchestra playing at the Nice International Piano Competition accompanying concertos 

 was that ,members of the orchestra came up to me in pleasant surprise saying that it was the first time they'd played with piano and found the piano and the orchestra playing at the same pitch. And the pianists liked the sound.

So I believe there to be substance in your assertion. And never throughout the varied repertoire of that concert was the unequal tuning at all unpleasant no matter which key was in use. At the other end of the musical spectrum with saxophone - 

 

Best wishes

David P

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As might be apparent from some earlier posts and writings elsewhere, I'm deeply interested in temperament myself, though would not like to be seen to be too strongly wedded to either equal temperament on the one hand or unequal temperaments on the other.  It isn't a monochrome situation, at least to me, as both camps have their pros and cons.  But having said that, I feel some quite basic practical issues get swept under the carpet in the white heat of the debate, not only on this forum but just about everywhere.  The first issue I'll mention is to do with history and how ET came to be so dominant (ha, ha ... ).  A major factor which caused ET to emerge as a force to be reckoned with out of the increasingly sophisticated mathematical and musical developments of the post-Renaissance era was simply because lutes, viols and similar instruments such as guitars were fretted.  These had to be tuned in ET - no ifs or buts.  Why?  Because with fretted instruments, the pitch of a note produced by a stopped string must obviously be the same as that of an adjacent open string which is supposed to be tuned to the same note.  Otherwise the instrument would be out of tune with itself and would be useless for musical purposes.  The only temperament which can satisfy this practical criterion over all possible intervals and melodic sequences involving more than a single string is ET (maybe think about it for a bit if you're unsure ... ).  A way round this for unequally-tuned string instruments is to make the frets curved rather than straight, but these are about as common as keyboard instruments with split sharps or many more than 12 semitones to the octave, so we can safely ignore them here.  Consequently, with today's interests in early music in which lutes and viols figure prominently, together with the importance of classical and (much more importantly from a mass audience viewpoint) electric guitar, it is unthinkable that the other instruments which are often required to form ensembles with them can be tuned other than to ET either.

Then there is that 'instrument' called the human voice.  Consider someone, or a choir, singing the following sequence of notes: C, up a 5th to G, then down a 4th to D, then up a 5th to A, then down a 4th to E, then down a 3rd back to C.  If all these intervals were to be perfect (i.e. if played simultaneously there would be no beat), the two Cs will be out of tune by over a fifth of a semitone (the Syntonic comma, to use the conventional arcane argot)!  This is sometimes called Huygens's Paradox, though it wasn't paradoxical to him because he understood the maths behind it.  This note sequence is not unique, incidentally, as the problem can arise with others.  But continuing with this example for now, suppose also that the voice(s) start off in tune with an organ, say, which then leaves them unaccompanied until the final C when it comes in again.  Bang - the tuning discrepancy will be embarrassingly awful, because the organ's two Cs will obviously be the same whereas those of the singers will not.  In practice the only reason this does not happen (well, hopefully not very often ... ) is because good singers have a strong enough musical memory of the exact pitches they should be singing when unaccompanied.  One reason for the development of this acoustic memory is that they have grown up in a largely ET culture and musical environment.  But if the organ accompanying them were to be tuned to some unequal temperament, the singers and their conductor would need to have the most exquisitely acute ears regarding pitch to avoid being publicly humiliated. 

There are lots of similar practical issues similar to these which need to be taken into account when choice of temperament is up for discussion, but I've already probably said more than enough so will leave it there for now.

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With respect it's actually a misconception that fretted instruments had to be tuned to ET. At the Musée de la Palais Lascaris in Nice there is a phenomenal collection of historic musical instruments which are very much well worth the visit. Up until the end of the 19th century quite a few instruments had gut string for frets . . . so as to be adjustable.

I've been working on the mathematics of the influences of the 9th harmonic in piano tone and resonance. Whilst not entirely thought out and so apologies for errors of exactitude, many temperaments and especially those with 7 or 8 perfect intervals in the octave have three sets of four notes which are linked, and the characteristics of the temperament are governed by the relationship between the three blocks of notes.

Bb C D E

F G A (B)

(B) C# D# F# G#

When the whole tones in each of these sets is a 9/8 tone, 9th harmonic beating is minimised. Certainly Kellner and Kirnberger differ mainly by where they put the C# and F# and of course from these two notes radiate some perfect fifths.

So there may well have been perfect fourth or fifth based temperaments which worked with adjustable frets on such instruments.

is a good example of the temperament, here Kirnberger III, giving landmark key colour through the narrative traversed by the composition.

Best wishes

David P

 

 

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That link is fascinating.

Quote

Since Lindley’s book was written, it has become very common for lute players to use unequal temperaments, largely for practical reasons: when tuned in this way the lute sounds sweeter, louder, and more in tune with ensembles including keyboards, harps, citterns and bowed strings. So are modern lutenists going against the grain of the historical evidence?

The above is my experience with tuning pianos, both the Bosendorfer on which we did a specific test, and at Nice with orchestra, and again as reported by the organist experiencing the Cranliegh instrument before and after retuning into ET.

Sweeter, louder . . . 

Best wishes

David P

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I don't disagree with the above concerning adjustable frets, indeed I correspond privately with a lute maker and lutenist about them.  But there's nevertheless a limit to the the amount of flexibility which such frets provide, and this helped to propel the unfretted violin family to the fore, which could play in just about any temperament.  However there was a cap as to how much I could put into an already over-long post, though some of what's been written following it has either missed my point, or maybe I didn't make it clearly enough.  What I was saying was simply that ET emerged quite early as a well known and fully understood tuning system with definite practical advantages, which either predated the unequal systems or continued to stand alongside them (depending on which temperament you are considering), rather than standing vaguely in the shadows until the 19th century which seems to be the position of many who write on this matter.  The issue of what we might prefer today is a separate question, and I'm always interested to hear of different views as to which temperaments people incline to.  As I said in my previous post, please don't think I'm pro-ET or anti-anything else.  I like and use a lot of temperaments, but wouldn't want to impose them on anyone, and I'm sorry if that didn't come over as well as it ought.  It's horses for courses - yer pays yer money and yer teks yer choice!

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1 hour ago, Colin Pykett said:

 What I was saying was simply that ET emerged quite early as a well known and fully understood tuning system with definite practical advantages, which either predated the unequal systems or continued to stand alongside them (depending on which temperament you are considering), rather than standing vaguely in the shadows until the 19th century which seems to be the position of many who write on this matter.

That is certainly a point worth making; thank you, Colin. But do we know if any non-fretted instruments used ET before the mid-C19? Did ET have a name in the C16, C17 and C18? If Bach was aware of it (he wrote for the lute and the viol) do we gather from his title “Das wohltemperierte Klavier” that he had rejected ET for Klavier music?

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Lovely questions, innate!  So much so that my ego can't resist having a go at answering them, but I'll thereafter run for cover ...

" do we know if any non-fretted instruments used ET before the mid-C19?  "

Yes, they must have done, if only because guitars did (but see ** below) - let's not bring lutes in this time because they have already muddied the water a little.  So ET was well known if only for this reason and therefore a candidate for tuning all sorts of other instruments including non-fretted ones.  But I'm not sure this is the right question.  Non-fretted instruments such as the violin are like the human voice, being played  monophonically most of the time and being continuously variable in pitch.  So there isn't really a temperament problem in the way that there is for keyboard and fretted instruments in that they can play in any temperament they like if the player is skilled enough and has a good enough ear to cotton on to what other instruments and voices around them are doing.  Thus the issue of how the open strings are tuned is pretty much secondary, within reason.  But I'd be the first to admit that I'm not really the person to answer this, and the impressively scholarly Catgut Society would probably be a better place to look, where it's no doubt been debated exhaustively (to death? Many times over?).  I do have some little experience as an amateur oboist, which although having fixed tone holes, does give the player the ability to 'pull' the pitch of a note up and down by quite a reasonable amount - hence the beautiful vibrato (largely frequency modulation) effects which the best players can coax out of the thing.  You become aware of the need to listen carefully to what an ET instrument such as a piano is doing when it is accompanying you, though that would also apply if was tuned in any other temperament such as those which David Pinnegar is pioneering.

A valuable perspective here might be coaxed from our colleague S_L who is a professional cellist.  I'd like to get his views.

" Did ET have a name in the C16, C17 and C18? "

Yes, but the names themselves can sometimes contribute more heat than light IMHO.  You have to dig into the accompanying maths or detailed tuning instructions to be sure that what the authors are talking about is really ET.  Werckmeister is an example.  In the late 17th century he was using such terms which translate as 'good temperament' and 'right temperament'.  He also used the term 'equal-beating temperament' which has been seized on by those keen to demonstrate that he favoured ET.  This was indeed the case towards the end of his written output when he came to reject some of his earlier predilections for unequal temperaments including his own, though it is unclear to me exactly what this particular term means.  It could just as easily mean a compromise temperament in which the 5ths beat at a similar rate to the major 3rds, which is certainly not the case with ET.

" do we gather from his title “Das wohltemperierte Klavier” that he [Bach] had rejected ET for Klavier music? "

You are really trying to put my neck into a noose here aren't you, and I'm not going to fall for it!!  'Well-tempered' (wohltemperierte) probably does not exclude ET but is probably not limited to it is all I feel able to say on the matter.  Again, one can find evidence to support this, but no more than this, in Werckmeister.  He didn't actually use the term all that often, and even then it was sometimes printed as two words rather than one and with variable spellings.  Again, the maths (when available) is the final arbiter.  But the meaning of the title of the WTC and the wider question of which temperament(s) Bach favoured, if any, still lie firmly in the realm of speculation and I'm surprised that so many otherwise sensible authors see it as otherwise.  We'll have to wait until some lucky musicologist discovers a hidden and previously unknown manuscript that resolves it unequivocally one way or the other ...  Oh for the equivalent of the Dead Sea Scrolls turning up somewhere to settle this one on a better basis than upside-down squiggles or whatever!

-------------------------------

** : when we talk about which temperaments were used hundreds of years ago, we need to remember that tuning was perforce only rather approximate then.  For a long time theoreticians, let alone tuners, did not really understand what beats were for example, but only that they existed and they were simply the way things were.  And beats couldn't be timed easily until about the mid-18th century at the earliest, nor did tuners appreciate the need to time them until then or even later.  This was partly because pitch standards were all over the place, and beat rates depend on pitch (A440 or whatever).  So tuning instructions were typically of the form 'let this fifth be nearer perfect than the last', or 'tune this fifth pretty flat', etc, until well after the death of Bach and Handel.  So when saying that this or that instrument was tuned to ET, it would only have been an approximation to ET until at least 1800 or so, and often later still.  Similarly for most other temperaments.  The only intervals which could be tuned really accurately were pure (just) ones which are tuned perfectly with no beat, and this must have been a factor in the preferences for those unequal temperaments which contained them - in fact, the more the merrier.  Werckmeister III for example has 8 pure 5ths out of the 11 which are tuned, making it one of the easiest to tune, hence its popularity.  All the meantone temperaments and ET have none, making them really tricky to tune in those days.  Unless we recall these practical realities of musical life at that time we can easily fall into an anachronistic trap, and many modern writers have done so.  Tuning then wasn't like tuning now!

 

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This debate was extending into the piano tuning realm with a friend today in response to comments on  

 that it sounds like equal temperament. And this is the Schubert Impromptu in Ab which should be the very worst of keys in one of the classical unequal "well temperaments".

So the point is that if tuned sympathetically to the instrument Kellner can be used in the place of pure Equal Temperament without damage to the music. At some stage I might put together the Priere a Notre Dame played on my organ sound-laboratory in Kellner and in ET as certainly when as a teenager I played this on my pipe organ tuned to Werkmeister III it was unbearable and caused me to hate WIII.

And the other point about that recording is that the sound recordist doing the video had to turn down his recording levels by 6dB as the instrument became louder - exactly in line with the report about the Cranleigh organ sounding bigger than its size when first built and tuned to Kellner.

Attached is the viol with gut frets at the Palais Lascaris. There are also a number of other instruments extending almost into the 20th century with sympathetic strings. These work only by means of resonance and this requires tunings with significant numbers of perfect harmonic intervals. Likewise we know from his correspondence that Chopin practised on a Pantalon, a simple form of piano without dampers. This is only possible without creating a mess of sound if scale notes accord with harmonics. Our experience of tuning pianos likewise is that the harmonic tunings, which require forms of unequal temperament, enable Chopin and Beethoven use of the sustaining pedal to be restored, being held down for many bars. 

Instruments which employ resonance can achieve power subtly but instruments without resonance have to use brute force.

Best wishes

David P

 

 

 

20191101_122844_NIGHT.jpg

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