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The Best And Most Appropriate Temperaments?


Guest spottedmetal

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Guest spottedmetal

Dear All

 

Having pondered temperaments since teenhood, I've been advocating steering away from equal wherever possible.

 

This afternoon I had the task of persuading an eminent pianist to perform Chopin on an unequal temperament, which was fun! Whilst possibly having been one of the first to recommend unequal tuning for Chopin a dozen or more years ago, some other commentators on the net appear to be endorsing the hunch.

 

On the piano I favour Kellner for its musicality, mildness, sheer common sense in making the home keys pure and defined progression towards the remote keys.

 

I've flirted with Bradley Lehman but found it too mild and without the direction achieved by Kellner, whilst on a former house organ I lived with Werkmeister III, and loving the Boellman Priere, came to hate Werkmeister despite the purity of all its pure intervals.

 

By the way, tuning Werkmeister without a meter is really easy, although I could not remember how after all these years.

 

Using a meter, whilst attacking a two manual harpsichord, I set one manual to Kirnberger and one to Kellner by accident :) and rather liked the slightly stronger Kirnberger but haven't dared to take the piano that far!

 

Three questions:

1. To what temperament would you dare to tune a piano

2. who would be the latest composer's music for which an unequal temperament would be appropriate

3. to which unequal temperament would you dare to tune a house organ without compromising the repertoire playable.

 

With regard to pianos, Broadwoods were still tuning "Broadwood's Best" unequal temperament in the 1880s and legendarily it appears that St George's Windsor was the last organ to adopt equal temperament in the 1890s.

 

It would be interesting to hear the story from the Continent also, those of you who are in mainland Europe!

 

Best wishes

 

Spot

 

PS (By the way, contrary to a posting on a former thread which was not so potently relevant as it was about a tuning problem rather than tuning per se I recommend DIY piano tuning - I've become distinctly unimpressed by the local professional piano tuners nowadays and one can achieve much greater stability of the instrument doing it yourself - and someone correctly mentioned octave stretching - 440, 881, etc adding one or two Hz per octave - and down the bass tune by 10ths ).

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Using a meter, whilst attacking a two manual harpsichord, I set one manual to Kirnberger and one to Kellner by accident :) and rather liked the slightly stronger Kirnberger but haven't dared to take the piano that far!

Kirnberger II or Kirnberger III ? When the version is not specified, the usual assumption is that the IIIrd is used. In the clavichord world Miklos Spanyi has been making a lot of use of Kirnberger II, very effectively.

 

Recently I heard David Breitman perform Mozart, CPE Bach, Haydn and early Beethoven on a Paul McNulty fortepiano, using this temperament, and it sounded wonderful, far better to my ears than KIII. Of course one of the issues is how far you are prepared to be restricted in the range of keys that you can use.

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Guest spottedmetal
Kirnberger II or Kirnberger III ? When the version is not specified, the usual assumption is that the IIIrd is used. In the clavichord world Miklos Spanyi has been making a lot of use of Kirnberger II, very effectively.

 

Recently I heard David Breitman perform Mozart, CPE Bach, Haydn and early Beethoven on a Paul McNulty fortepiano, using this temperament, and it sounded wonderful, far better to my ears than KIII. Of course one of the issues is how far you are prepared to be restricted in the range of keys that you can use.

Dear David

 

Thanks

 

I'm going to have to check the tuning meter to see which its Kirnberger matches. It's the Korg OTwhatever that does multitemperaments, if anyone happens to know the machine. I'd assume KIII.

 

The reason for raising the temperament issue in its own right is to canvass experience of how far one can push the intervals to produce a strain without being recognisably out of tune, so still being able to make music in all keys very happily, but achieving that experience of key character. Does any temperament achieve this better than Kellner whilst still retaining universality?

 

How many of us were brought up on the legend that all keys sound different but found it curious that we couldn't hear it? Until starting to play with UT?

 

Bearing in mind that one expects some discordances in stringed instruments, are the strained intervals on UT organs more unpleasant than the equivalent tunings applied to strings?

 

Best wishes

 

Spot

 

PS On the practicalities of electronic tuning assistance, on pianos I used to produce frequencies on a Sinclair ZX Spectrum and then use a double-beam scope with a mic into the other channel and this used to guarantee laser sharp unisons on the three strings. Some machines have a series of squares which run across showing the phase difference and this is a helpful analogue. More recently software on a laptop http://www.tunelab-world.com/ does a similar job and is excellent if one wants that pinpoint accuracy, although aspects are complex to control.

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Guest Nigel ALLCOAT
Does any temperament achieve this better than Kellner whilst still retaining universality?

 

Young has similar characteristics and favours the more # keys whilst Kellner could be said to be more inclined towards the b's (up to 2 a-piece). As D is a favorite baroque keyboard key (both in minor and major), I tend to veer more towards the genius of Thomas Young (1773-1829). But instrument, acoustic and mood plays quite a part!

All the best,

N

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Young has similar characteristics and favours the more # keys whilst Kellner could be said to be more inclined towards the b's (up to 2 a-piece). As D is a favorite baroque keyboard key (both in minor and major), I tend to veer more towards the genius of Thomas Young (1773-1829). But instrument, acoustic and mood plays quite a part!

All the best,

N

And, yet again, there are two different versions of Young's temperament !!!

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On the practicalities of electronic tuning assistance, on pianos I used to produce frequencies on a Sinclair ZX Spectrum and then use a double-beam scope with a mic into the other channel and this used to guarantee laser sharp unisons on the three strings.

 

There's an excellent piece of software called WinTemper which is free to download. As well as mic input with a cent scale flat or sharp, it generates tones and has the facility to enter new tunings in a variety of different ways or experiment with your own. It plays minor or major thirds, fourths, triads etc back at you.

 

There are several good tunings not featured in any books - for instance, Hamburg and Grosvenor on the Drake website.

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I have quite a library of books, papers and websites about tuning and temperaments. Of these, the most useful for practical tuning are:

 

A Guide to Musical Temperament, by Thomas Donahue, Scarecrow Press, 2005, ISBN 0-8108-5438-4

and

Clavichord Tuning and Maintenance, by Peter Bavington, Keyword Press 2007, ISBN 978-0-9555590-0-6

 

For computer tuning programs, see

http://wintemper.com/

and

http://www.fmjsoft.com/chromatia.html

 

For information on tuning and temperaments, see

http://www.dolmetsch.com/musictheory27.htm

which (a long way down the page) includes a "Temperament/Tuning and Pitch Calculator" with data on about 300 different temperaments.

 

Note that different keyboard instruments are affected by temperament in different ways.

 

Clavichords are affected by the precise pressure of the player's finger on the key, so small differences between different temperaments aren't important, and a player can "bend" a note by exerting more pressure. Clavichords have little sustaining power, so tuning errors aren't easily heard in terms of beats, except by the very careful listener very close to the instrument.

 

The basic harpsichord has one string to each key (more elaborate ones allow different strings to be chosen, or several strings to be sounded). The strings are thin, light, and under low tension compared with a piano, so the harmonics are pure, and tuning needs to be very precise.

 

Pianos are more complicated. From the bass which uses single strings, higher notes have two strings and the highest have three. The multiple strings are usually tuned to slightly different notes to achieve richness of sound, and so the "pitch" of a note is not clearly defined. The heavy strings necessary to permit high tensions are quite stiff, compared with those of a harpsichord or clavichord, and they therefore suffer from "inharmonicity" - in theory the harmonics should be exact multiples of the fundamental note, but on the piano each overtone is just a little bit higher than the true harmonic, which is why tuners "stretch" the octaves.

 

Organs are the most demanding, as long sustained tones are possible and beats are easily heard. Unlike harpsichords and clavichords, they are rarely retuned by their owners to different temperaments. (The exceptions are "chest" or "continuo" organs which may have only one or two stops, and are designed so that pitch and temperament are easy to change).

 

Both mixture and mutation stops create problems, as they have to be tuned to the pure harmonics of the fundamental, a C will have pure harmonics at octaves (no problem) but also at fifths, etc, and the corresponding keys on a tempered instrument produce notes which are not exactly tuned to the harmonics. This is why the change from mean tone tuning, with its emphasis on pure thirds, to equal temperament created problems with third-sounding ranks of mixtures, and why the old cornets with their prominent thirds fell out of favour.

 

To hear a number of pieces, each played in several different temperaments for comparison, try

http://www.frogmusic.com/bt.html

where you can buy CDs of music by Bach, de Grigny and Purcell played in several different temperaments on a Rodgers toaster.

 

See

http://www.larips.com/

for Bradley Lehman's website about how he "decoded" information on a Bach manuscript to find "Bach's tuning", and to buy CDs comparing his version with others. His theory has generated a lot of controversy, but many professionals who have tried it have found that it works well for them.

 

There are many CDs of historic and modern organs tuned in different temperaments. Kenneth Ryder at St Peter Mancroft, Norwich using Vallotti,is one example. An interesting example can be found at

http://www.gothic-catalog.com/product_p/lrcd-1090-91.htm

of Hans Davidsson playing Buxtehude on the mean-tone organ at Goteborg.

 

The whole subject of temperament is highly controversial. There's a vast amount of historical and theoretical material out there, and both experts and the ignorant debate the issues quite fiercely (including who they decide are the "experts" and who are the "ignorant").

 

Let the performer use his or her ears.

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Guest Nigel ALLCOAT

The Well-Tempered Organ by Charles A. Padgham is a fine little publication that should lie next to your music - certainly in those libraries of folk who get asked to provide programmes for tempered instruments. It is so well written with many hints and helps for tuning too as well as giving at a glace the excellent keys, the good keys, the poor keys and those you should avoid!

Positif Press, Oxford. ISBN 0 906894 13 1

 

All the best.

Nigel

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The Well-Tempered Organ by Charles A. Padgham is a fine little publication that should lie next to your music - certainly in those libraries of folk who get asked to provide programmes for tempered instruments. It is so well written with many hints and helps for tuning too as well as giving at a glace the excellent keys, the good keys, the poor keys and those you should avoid!

Positif Press, Oxford. ISBN 0 906894 13 1

 

All the best.

Nigel

Unfortunately it has been "temporarily out of print" for quite a while. I asked Positif Press about this, and they couldn't say when it is likely to be reprinted.

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Guest spottedmetal
The Well-Tempered Organ by Charles A. Padgham is a fine little publication . . . so well written with many hints and helps for tuning too
Yes - a pink sqare book, if I remember correctly - brilliant. Possibly after a BIOS article first excited interest, the Padgham book was really the publication that ignited my enthusiasm. Unfortunately I lent mine to someone . . . :( So hope the Positif Press comtemplate a reprint seriously.
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In the past, about each town had its own musical temperament

and pitch.

Accordingly, all ancient organs were build after those quite

varied standards.

And as all of us know, to modify this equals to modify the

scaling of the pipes.

As a result, if we now allow us to play god, deciding which of

these pure conventions is/ are "good", we shall again commence

to destroy our heritage.

Are we willing to be a civilisation, or something else ?

 

Pierre

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Guest spottedmetal
To hear a number of pieces, each played in several different temperaments for comparison, try

http://www.frogmusic.com/bt.html

where you can buy CDs of music by Bach, de Grigny and Purcell played in several different temperaments on a Rodgers toaster.

. . . . . .

Pianos are more complicated. From the bass which uses single strings, higher notes have two strings and the highest have three. The multiple strings are usually tuned to slightly different notes to achieve richness of sound, and so the "pitch" of a note is not clearly defined.

Thanks! That CD sounds most helpful. The question that I'm driving at is, were you to be tuning an instrument for general purpose use for unlimited repertoire wanting to get away from equal but wanting the musicians playing it not to scream and tell you, or worse everyone else, how bad you are :( which temperament would you use?

 

I think all of Lehman, Kellner and Charles Francis have made reference to the Bach squiggle and the thought that that squiggle on the Well Tempered Klavier manuscript has relevance makes a lot of sense. Francis came up with results not dissimilar to Kellner.

 

Not wanting to divert this thread away from organs, on piano tuning I'm intrigued at the reference to the three strings being detuned. Perhaps this is necessary on the (music interrupting) brilliance of Steinway and Yamaha to soften them up, but on a softer Bechstein for chamber use, the tuning of the three strings to be not just in tune but to respond in phase, brings a laser-like definition to the sound.

 

Best wishes

 

Spot

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Guest spottedmetal
In the past, about each town had its own musical temperament

and pitch.

Accordingly, all ancient organs were build after those quite

varied standards.

And as all of us know, to modify this equals to modify the

scaling of the pipes.

As a result, if we now allow us to play god, deciding which of

these pure conventions is/ are "good", we shall again commence

to destroy our heritage.

Are we willing to be a civilisation, or something else ?

Dear Pierre

 

This raises a couple of very interesting points - firstly that our music has lost its flavour as a result of equal temperament - harmonisation has played God here as an early form of globalisation and universalisation - so trying to enable the music to regain some shadow of colour, without going to technicolor of course, is possible a worthy goal of civilisation.

 

The second is that of localisation: I think that it's a traversty that the Frenchness and freshness of design of Citroen dashboards and controls has been lost to virtually universal standards. The reality is that in order to sell cars the company thinks that any driver should be able to get into the driving seat and drive, without having to learn about their car. As soon as transport became easy, the same happened to musicians on tour. They required universal standards. Now an organist has to go a long way to understand the problem - and for this reason it's worth going to the Bazzani organ at Madonna del'Orto in Venice - Giovanni Ferrari knows how to play it and gets it to whisper, sing and roar most beautifully but any visiting uninitiated organist would say how terrible the instrument is and make a terrible clamour.

 

So perhaps players should be introduced to a little variety in their travels, even if only the 1/2 inch between keys! That's not to say that every 1920s Harrison and Harrison should be tuned unequally. Oh the din of discordant Tubas!

 

Best wishes

 

David P

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Not wanting to divert this thread away from organs, on piano tuning I'm intrigued at the reference to the three strings being detuned. Perhaps this is necessary on the (music interrupting) brilliance of Steinway and Yamaha to soften them up, but on a softer Bechstein for chamber use, the tuning of the three strings to be not just in tune but to respond in phase, brings a laser-like definition to the sound.

I think you have just defined the difference between science and art. In a cultured civilisation, each has its place.

JC

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Not wanting to divert this thread away from organs, on piano tuning I'm intrigued at the reference to the three strings being detuned. Perhaps this is necessary on the (music interrupting) brilliance of Steinway and Yamaha to soften them up, but on a softer Bechstein for chamber use, the tuning of the three strings to be not just in tune but to respond in phase, brings a laser-like definition to the sound.

See Wikipedia http://en.wikipedia.org/wiki/Piano_acoustics which reads:

"The three strings create a coupled oscillator with three normal modes. Since the strings are only weakly coupled, the normal modes have imperceptibly different frequencies. But they transfer their vibrational energy to the sounding-board at significantly different rates.

 

The normal mode in which the three strings oscillate together is most efficient at transferring energy since all three strings pull in the same direction at the same time. It sounds loud, but decays quickly. This normal mode is responsible for the rapid staccato "Attack" part of the note.

 

In the other two normal modes the strings do not all pull together, e.g., one will pull up while the other two pull down. There is slow transfer of energy to the sounding-board, generating a soft but near-constant "Sustain"."

 

Clavichords are normally strung in pairs, and part of the art of tuning is to make sure that the two strings of a pair are ONLY JUST not quite perfectly in tune. It's easy to verify that the tiniest tweak, not perceptible as a different in pitch, can change the balance of a note from loud and coarse with little sustain into a quieter longer sustained response. It was perhaps misleading when I wrote that multiple strings on the piano are tuned to slightly different notes, when I should have said that they are minutely detuned. The balance is a matter of taste.

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Guest spottedmetal
See Wikipedia http://en.wikipedia.org/wiki/Piano_acoustics which reads:

"The three strings create a coupled oscillator with three normal modes. Since the strings are only weakly coupled, the normal modes have imperceptibly different frequencies. But they transfer their vibrational energy to the sounding-board at significantly different rates. . . .

Clavichords are normally strung in pairs, and part of the art of tuning is to make sure that the two strings of a pair are ONLY JUST not quite perfectly in tune. It's easy to verify that the tiniest tweak, not perceptible as a different in pitch, can change the balance of a note from loud and coarse with little sustain into a quieter longer sustained response. It was perhaps misleading when I wrote that multiple strings on the piano are tuned to slightly different notes, when I should have said that they are minutely detuned. The balance is a matter of taste.

Thanks for taking the time to elaborate on these fascinating revelations!

 

For decades I've been obssessed by laser-like "in phase" accuracy and been frustrated by tuners who apparently haven't bothered but perhaps now understand the reason why. Possibly on a softer more naturally singing instrument of the late 19th Century, the multiplication in power improves the carrying of the sound. Perhaps it might be relevant to bear in mind that modern practice might have derived from tuning a virtually singular brand of instrument for recital purposes in acoustics for which often it's simply too powerful?

 

Doesn't this have an analogue with organs with closely adjacent pipes?

 

The subject of loose coupled oscillators and their effects is most interesting - and most probably the reason why toasters need at least triple the number of stops to sound as useful as a pipe-organ.

 

Best wishes

 

Spot

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Guest spottedmetal
I think you have just defined the difference between science and art. In a cultured civilisation, each has its place.
Dear John

 

:( Are you saying that soft-tuned Steinways are art and laser-phased Bechsteins are science? :blink: Can we apply this to hard percussive Germanic chiffs :P and nice creamy early 20th century Harrison and Harrisons :D ?

 

Before :angry: Pierre tells me that tuning an H&H to an unequal temperament would be uncivilised, don't worry, I wouldn't dream of suggesting it! :lol: Or perhaps . . . what's the mildest UT that we could get away with?

 

Best wishes

 

Spot

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Dear John

 

:( Are you saying that soft-tuned Steinways are art and laser-phased Bechsteins are science? :blink: Can we apply this to hard percussive Germanic chiffs :P and nice creamy early 20th century Harrison and Harrisons :D ?

 

Before :angry: Pierre tells me that tuning an H&H to an unequal temperament would be uncivilised, don't worry, I wouldn't dream of suggesting it! :lol: Or perhaps . . . what's the mildest UT that we could get away with?

 

Best wishes

 

Spot

I'm saying that great music has no need of laser phasing any more than a great photograph needs a Leica. The art comes from the user, not the engineering. Minor imperfections in an instrument often add rather than detract from its charm.

JC

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For decades I've been obssessed by laser-like "in phase" accuracy and been frustrated by tuners who apparently haven't bothered

Ask a toaster manufacturer how he feels about laser-perfect tuning. They actually go out of their way to build random mistuning into their instruments because perfection sounds too lifeless. At least, the better ones do - I can't speak for all.

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Guest Barry Williams

Yes, and the toaster people almost always overdo it, with grotesque results. The very worst is the so-called 'randomisation' common with the Bradford type systems. Years ago Makin Organs had rotating speakers ('rotafons', I think,) to try and achieve the same effect.

 

A few months ago I heard a small Allen where some stops had been put in tune for the purpose. It sounded far better than with the 'factory-fitted' de-tuning.

 

Nothing can match a pipe organ, though a bad one may not be as effective for church work as a synthetic instrument.

 

Barry Williams

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Guest spottedmetal
I'm saying that great music has no need of laser phasing any more than a great photograph needs a Leica. The art comes from the user, not the engineering. Minor imperfections in an instrument often add rather than detract from its charm.

. . . .

Ask a toaster manufacturer how he feels about laser-perfect tuning. They actually go out of their way to build random mistuning into their instruments because perfection sounds too lifeless. At least, the better ones do - I can't speak for all.

Um - yes - I'm disputing neither - to some extent it depends on the instrument. Don't we tune pipe organs as exactly as we can, imperfections of winding and pipe coupling providing enough randomness, whereas instruments that are too perfectly engineered as machines such as :( Steinways and toasters need their perfection brought into the levels of the real world?

 

I used the analogy with a laser in a particular scientific sense, where the effect of all the atoms being excited in unison and emitting their light in unison at the same frequency to the point of phase coherence, has an effect vastly different from the same basic source not arranged to do so. There is thus a vast difference between the output from a standard Light Emitting Diode, LED, with which we are familiar on most electronic devices nowadays and a Laser Diode which we see in pointers and in CD and DVD writers or "burners" and often used by teenagers for inappropriate destructions.

 

On a historic piano with a weak mid treble from tenor C upwards, the amplification akin to that of a laser which one achieves by attempted exactness of tuning is considerable and is an important contribution towards the upperwork brilliance for instance for Chopin, Liszt and Scriabin. Audiences do comment on the differences they hear as a result. If anyone is interested I can point to some recordings resulting. On modern concert instruments with which others might be familiar, the object is often to achieve the opposite, where for instance a Yamaha might be distractingly bell-bright.

 

Unfortunately, having tuned an instrument for a concert, it's all too easy to be distracted by a tuning imperfection during a performance listening for the something that might have slipped - how many people who tune share this problem?

 

With regard to toasters, one manufacturer with which I'm familiar uses two seperate main clocks, one for the Choir/Great and the other for Swell and Pedals. In adding Solo and Echo manuals to my own machine, it has been apparent that when all are coupled together, the slight mistunings or phase mismatching between the main toaster and the two extra units are particularly helpful, and I have even experimented with the main instrument in ET, and the subsidiary two units tuned to Kellner or Vallotti or even both! The effect is to introduce mistunings on certain almost random notes at a lower level than the main sound providing the richness that one hears on unmanageably large (or Spanish) organs. It's an interesting experiment and one on which visiting performers will be able to experiment and audiences will express preferences in due course.

 

So how late in terms of organ composers might we go in terms of performance on UT instruments? Mendelssohn? And any later? And if we go later with composers who expected ET, which temperament might one use to still preserve universality?

 

And which composers continued to use certain keys for certain moods, simply based on the legend that a certain key was associated with certain moods, despite not being able to hear them for the universal adopton of ET?

 

Best wishes,

 

Spot

 

 

 

PS If anyone is scrapping an analogue toaster, I'd possibly be interested in the guts of the tone generators. There being no digital samples of which I'm aware of stops in the 1ft to 1/4ft range available for toasters, and in view of the near bat-relevant frequencies, harmonic content of these might be less important and so frequency multiplying some standard analogue generators might be a good way to experiment in these regions.

 

On the subject of toasters, is the one at Lancaster Priory

http://www.priory.lancs.ac.uk/orgspec.html

somewhat unique in its scale and age . . . ? Perhaps it's no coincidence that they are appealing for a pipe-organ

http://www.priory.lancs.ac.uk/organapp/organap2.html but as a toaster the console is audacious:

http://www.priory.lancs.ac.uk/organ.html

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Spot

PS If anyone is scrapping an analogue toaster, I'd possibly be interested in the guts of the tone generators. There being no digital samples of which I'm aware of stops in the 1ft to 1/4ft range available for toasters, and in view of the near bat-relevant frequencies, harmonic content of these might be less important and so frequency multiplying some standard analogue generators might be a good way to experiment in these regions.

 

On the subject of toasters, is the one at Lancaster Priory

http://www.priory.lancs.ac.uk/orgspec.html

somewhat unique in its scale and age . . . ? Perhaps it's no coincidence that they are appealing for a pipe-organ

http://www.priory.lancs.ac.uk/organapp/organap2.html but as a toaster the console is audacious:

http://www.priory.lancs.ac.uk/organ.html

 

Hi

 

Try Classic Organs at Boxhill - but it would probably be easier to build oscillators at the relevant frequencies than try to use frequency multipliers.

 

The Makin at Lancaster would probably have been custom built - the Makin company were successors to Comptons, who were the Rolls Royce of electronic organs in their day - although that may not still have been the case when the Lancast organ was built.

 

Every Blessing

 

Tony

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On the subject of toasters, is the one at Lancaster Priory

http://www.priory.lancs.ac.uk/orgspec.html

somewhat unique in its scale and age . . . ? Perhaps it's no coincidence that they are appealing for a pipe-organ

http://www.priory.lancs.ac.uk/organapp/organap2.html but as a toaster the console is audacious:

http://www.priory.lancs.ac.uk/organ.html

 

Appologies for a tangent, but for those wishing to see what was destroyed in the process of installing the above this seems to be on the NPOR as Lancaster St Mary at the following link. It was obviously controversial at the time as the faculty application went to a Consistory Court.

http://npor.emma.cam.ac.uk/cgi-bin/Rsearch...ec_index=N12830

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Um - yes - I'm disputing neither - to some extent it depends on the instrument. Don't we tune pipe organs as exactly as we can, imperfections of winding and pipe coupling providing enough randomness, whereas instruments that are too perfectly engineered as machines such as :( Steinways and toasters need their perfection brought into the levels of the real world?

The baroque trumpet is a good example of this. Although these had no valves (and almost certainly no finger holes) they could be played with great agility and in tune near the higher harmonics. After Bach's time the skills were lost, and a century ago people trying to perform his works substituted alto clarinets, played an octave lower, and even invented a small version of the modern trumpet which thye called the "Bach trumpet".

 

Eventually someone decided to make a copy of one of the original instruments. It was easy to adapt one of the modern machines to spin the metal to an acoustically perfect bore, but the instrument was useless. The perfect bore held the harmonics so tightly that they couldn't be "lipped" - and it is well known that some of the higher harmonics do not lie anywhere near the notes of the musical scale.

 

The next attempt used the traditional methods, of taking flat sheets and hammering them into shape. Inevitably there were many small deviations from acoustic perfection, but the instrument worked perfectly.

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