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#1 JohnDubery

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Posted 28 August 2014 - 06:24 PM

Hi, can anyone enlighten me on how Thomas Casson built up his mixtures?

 

I find the organs of Thomas Casson quite fascinating for their ideas and inginuity - about which a fair amount can be found from various sources. However there are a couple of areas in which information is rather thin on the ground, and his mixtures is one.

 

In some cases I can find the combination of pitches at the start of the mixture (e.g. the Omagh Great had "Harmonics 15.17.19.21.22 V" and Swell had "Mixture 15.17.19.22  IV") but that is all. I can find no reference to the types of ranks used, or the relative power or scaling; nor can I find any reference to how his mixtures break beyond a comment somewhere about only breaking one rank at a time.

 

Any information or references gratefully received, thanks.



#2 Colin Pykett

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Posted 29 August 2014 - 03:36 PM

I've never been able to find out much at the level of detail you are seeking.  The main reason is that he didn't actually build much.  Relf Clark wrote an article about Casson ('Thomas Casson: A Mere Introduction', JBIOS 26, 2002) in which he confirmed this.  Quoting:

 

"... Casson - though he appears to have sold a great many Positive Organs - built very few organs upon his system, and those he did build were mostly small and in little-known locations.  Indeed, for all his Positive Organs, Casson is today an obscure figure ... "

 

Nor does Clark in this essay speak much of Casson's output in terms of his organs, though he does describe his 'system' to some extent.  But there is nothing relating to the detail you require regarding his mixtures, though one or two references are given.  There is virtually nothing about him even in works by contemporary authors such as Hopkins & Rimbault and Audsley (he does not appear in the index of either, at least those of the editions I possess), though Elliston's 'Organs and Tuning' has a little.  He just didn't seem to cut much ice in his day compared to, say, the phenomenally successful Hope-Jones (with whom relations could scarcely be called friendly - envy?).  One problem might have been that Casson does not seem to have been a particularly nice man who did not endear himself to potential customers.  Oftentimes Hope-Jones wasn't particularly nice either, but he did know when and how to switch on the charm.

 

Even with well known organ builders it is often difficult to find more than the starting compositions of their mixtures, and issues such as relative power, scaling and breaks will all usually demand access to particular instruments unless one is exceptionally fortunate to find such detailed material documented somewhere.

 

It is possible that you might glean something from the organ builders who gave Casson a kick-start into the craft when he retired from his banking day job, because he was of course an amateur.  One was John Bellamy, so perhaps his ideas on mixture work influenced Casson's also.

 

CEP


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#3 JohnDubery

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Posted 29 August 2014 - 06:44 PM

Colin, thanks. Yes, there is not a lot; apart from Casson's own writing there is material by Elliston, Matthews, Dixon, Bewerunge, plus a few small articles here and there.

The idea of looking at those who influenced him is interesting; that makes me think to look more at those he influenced too (e.g. the early Harrison Harmonics mixtures).

Thanks, John



#4 Colin Pykett

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Posted 30 August 2014 - 09:18 AM

Casson worked at the time when the subject of acoustics was burgeoning as a result of the combined work of people such as Fourier, Toepfer, von Helmholtz and Rayleigh.  Among other things, it led to that late-Victorian zeitgeist in music, and particularly organ building, which seemed to say that 'science' was somehow 'better'.  For example, a knowledgeable organ builder who was noddingly familiar with these topics could point to his pipe scales as being better than somebody else's because they were 'scientifically' devised.  The same would have applied to mixtures.  To my mind it was this which led to the contemporary fascination with 'harmonics'-type mixtures, because these contained more pitches of the natural harmonic series than did more conventional quint mixtures (octave and fifth sounding ranks only).  Therefore, because they were nearer to 'Nature' as revealed by 'science', they were 'better' mixtures.

 

The problematic, nay, unfortunate aspect of a harmonics-type mixture is that it must perforce include ranks such as the 17th and flat 21st (the 5th and 7th natural harmonics).  Quint mixtures do not have these.  When combined with equal temperament tuning (another 'scientific' and therefore 'better' idea, near-universal at the turn of the 19th century) there are hideous dissonances caused by the out-of-tune beats which occur when these additional ranks (tuned true to unison pitch) sound simultaneously with the other (ET) ranks of the organ.  Consequently these ranks have to be scaled and regulated very carefully if the mixture which contains them is to be useable.  I have no idea how Casson would have approached this problem, but their power would surely have needed to be significantly less than that of the other ranks.  It is quite possible that the immediately-identifiable sound of an organ which employed such mixtures would have been deemed attractive at the time, even though today enthusiasm has since waned.  Given the zeitgeist effect alluded to above, it could well have been little more than an Emperor's New Clothes type of issue.

 

As to breaks, there are no established rules for any type of mixture.  I have alluded previously on this forum to an excellent summary by Paul Hale in his editorial to Organists' Review of May 1996.  To my mind that is as good as one can find anywhere as an introduction to the subject.

 

CEP


"You can never know everything about something. But you can always know something about everything" - Amit Kumar

 

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#5 David Drinkell

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Posted 30 August 2014 - 04:16 PM

Although few large Casson organs were built and his magnum opus, at Omagh in Co. Tyrone,  has been greatly altered, his ideas about mixtures were realised, through the influence of George Dixon, in the Harmonics stops which were common on Arthur Harrison Greats.  I would not be surprised to find that his mixtures did not break until quite high in the compass, as was common with the more normal tierce mixtures of the time.

 

Casson's influence, as far as large organs was concerned, was much more than his actual output.  Relf Clark's article in the BIOS Journal, while interesting, had the disadvantage that the author, by his own admission, had virtually no experience of Casson's organs.  While this has little to do with the question of mixtures, since so few Casson organs were of a size to contain them, I think that a little seeking-out would have improved the article by giving an impression of what the small instruments, of which there are hundreds dotted around the place, actually sounded like or what they were like to play.  Relf Clark's home turf is relatively sparsely populated with Cassons (unlike mine - Essex, Suffolk and Norfolk, where money was scarce) but there are several within a short drive.



#6 Contrabombarde

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Posted 01 September 2014 - 06:55 PM

The only Casson I'm familiar with that has a Mixture is that in Namirembe Cathedral, Kampala, Uganda. It is a modest two manual with one mixture, a 15-19 to 12-15 composition and was restored a few years ago by Peter Wells. I have no idea whether it's original or a subsequent addition. But I always thought the organ was an unexpected treasure when I was living out there, whether because I wasn't expecting to find a pipe organ at all, or whether because the cathedral's souring brickwork create a magnificent acoustic that would make a dog of an organ sing, I couldn't say. I was just glad to be able to practice on it from time to time and must admit I rather liked it.

 

http://en.wikipedia....edral#The_organ



#7 innate

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Posted 02 September 2014 - 05:12 PM

The problematic, nay, unfortunate aspect of a harmonics-type mixture is that it must perforce include ranks such as the 17th and flat 21st (the 5th and 7th natural harmonics).  Quint mixtures do not have these.  When combined with equal temperament tuning (another 'scientific' and therefore 'better' idea, near-universal at the turn of the 19th century) there are hideous dissonances caused by the out-of-tune beats which occur when these additional ranks (tuned true to unison pitch) sound simultaneously with the other (ET) ranks of the organ. 

I've been aware of this issue for years, and it should apply pretty much to any non-unison mixture rank or mutation when combined with chords in Equal Temperament. What I don’t understand is why the "naturally tuned" mutations and mixtures in organs clash with ET and the naturally occurring harmonics in, say, orchestral clarinets don’t cause such a problem. I know orchestras don't play in exact ET but it must be quite close. Also clarinets play chamber music with ET pianos. I appreciate that a skilled clarinettist may adjust the tuning of individual notes to "fit" the tuning of other instruments but they can’t, surely, adjust the tuning of the (prominent) partials sounding the 12th and 17th independently of the fundamental, can they?



#8 JohnDubery

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Posted 02 September 2014 - 07:21 PM

"Namirembe Cathedral, Kampala" - thanks for that I'd never have thought to look. It seems, though, that the instrument dates from a couple of decades after Thomas Casson died, and has since been rebuilt a bit. Are any other Casson organs hiding in unlikely-seeming places?



#9 DouglasCorr

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Posted 02 September 2014 - 08:20 PM

I've been aware of this issue for years, and it should apply pretty much to any non-unison mixture rank or mutation when combined with chords in Equal Temperament. What I don’t understand is why the "naturally tuned" mutations and mixtures in organs clash with ET and the naturally occurring harmonics in, say, orchestral clarinets don’t cause such a problem. I know orchestras don't play in exact ET but it must be quite close. Also clarinets play chamber music with ET pianos. I appreciate that a skilled clarinettist may adjust the tuning of individual notes to "fit" the tuning of other instruments but they can’t, surely, adjust the tuning of the (prominent) partials sounding the 12th and 17th independently of the fundamental, can they?

This is an interesting point- and leads to questions like should chords played on a Quintadena (which has a prominant 12th) sound conspicuously out of tune in ET??  I don't think they do in my experience!



#10 Colin Pykett

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Posted 03 September 2014 - 09:36 AM

I've been aware of this issue for years, and it should apply pretty much to any non-unison mixture rank or mutation when combined with chords in Equal Temperament. What I don’t understand is why the "naturally tuned" mutations and mixtures in organs clash with ET and the naturally occurring harmonics in, say, orchestral clarinets don’t cause such a problem. I know orchestras don't play in exact ET but it must be quite close. Also clarinets play chamber music with ET pianos. I appreciate that a skilled clarinettist may adjust the tuning of individual notes to "fit" the tuning of other instruments but they can’t, surely, adjust the tuning of the (prominent) partials sounding the 12th and 17th independently of the fundamental, can they?

 

In theory the problem arises with all instruments.  However it is writ large with mixtures because they are so loud.  Mixtures were invented to make the organ loud at a time when wind pressures, and therefore the power of unison stops, were perforce so low.  The perception of subjective loudness which mixtures endow is to some extent an aural illusion because the ear/brain assigns greater loudness to a sound whose acoustic power is spread over a large part of the audio spectrum, compared to a sound of the same power which is concentrated in fewer frequencies.

 

The amplitude of the beats which occur between mixtures and corresponding notes of the tempered scale is related to the power of the frequencies which generate those beats, therefore they tend to be more noticeable with mixtures (and mutations) because of their relatively high amplitudes.

 

In practice the beat frequencies are fairly low between the perfectly tuned quint ranks in a mixture and the corresponding tempered notes elsewhere in the compass of the stops which are drawn with them.  The deviation is only 1.97 cents (100 cents equals one semitone) with ET.  Thus the beat rate between the 3rd natural harmonic of A440 and top E on an 8 foot stop - a twelfth above A - which should ideally speak the same note, is 3 beats in 2 seconds.  If anything, this tends to add richness and 'shimmer' to a quint mixture rather than an impression of dissonance.

 

With tierce mixtures containing 17th ranks and harmonics mixtures containing 21st ranks as well, the beats are very much faster and (to my ears) intolerable with ET.  They are better with the 'best' keys in certain unequal temperaments, but by definition, they will be even worse than with ET in the 'poorer' keys in those temperaments.

 

It can be argued that mixtures are ultimately irrational, they defy logic, in that they are an attempt to tune an organ to two temperaments at once - the perfect intervals of the natural harmonic series which are also reflected in the mixture, with the temperament to which the other stops are tuned. 

 

This is an interesting point- and leads to questions like should chords played on a Quintadena (which has a prominant 12th) sound conspicuously out of tune in ET??  I don't think they do in my experience!

 

No, the chords don't sound conspicuously out of tune because a quintadena is effectively a 2 rank quint mixture, and with quint ranks the beat rates are tolerably slow and not particularly dissonant, as explained above.  Also the amplitude of the quint in a quintadena, although subjectively obvious, is nevertheless lower than that of the fundamental (usually).  It is certainly much lower than that of an average separate 12th mutation stop, unless its power had been deliberately attenuated by an unusually large amount.  Because of the low power of the quint, any beats generated will also be of lower amplitudes than if a separate quint rank was in use.  I like quintadenas very much myself, and if it's of any interest I did an analysis of how Hope-Jones might have viewed them as an ersatz mixture-substitute.  See:

 

http://www.pykett.or...quintadenas.htm

 

But in the end people have different views, and it boils down to horses for courses.  I don't think one can be too prescriptive.

 

CEP


"You can never know everything about something. But you can always know something about everything" - Amit Kumar

 

www.pykett.org.uk


#11 innate

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Posted 03 September 2014 - 06:21 PM

Thanks for the detailed response, Colin. I'm aware that there is a conjecture that one of the reasons mixtures and mutations almost disappeared from new organs at the start of the C20 was because of their perceived incompatibility with ET. And also that incompatibility between mixtures and *any* chromatic tuning will be less noticeable with traditional "flexible" winding. But in the last 50 years in the UK there has been a general tendency to have as many mixtures and mutations as there have ever been on British organs and a great reluctance to use any temperament other than ET. Taking into account Colin’s assertion that there is only a problem when mixtures (and mutations) include thirds and sevenths, do you suppose that we are just inured to the clashes? Our hosts are proud, for example, of their tierce mixture on the Pedal at St Ignatius, NYC; in a C major chord with a C in the pedal, that mixture will contain an alto or tenor E that is going to clash with any E at unison pitch played on the manuals.



#12 DouglasCorr

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Posted 03 September 2014 - 06:30 PM

Many thanks, Colin, for your detailed reply and interesting measurements in 10 above.



#13 Colin Pykett

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Posted 04 September 2014 - 09:05 AM

 that mixture will contain an alto or tenor E that is going to clash with any E at unison pitch played on the manuals.

 

The beat frequency between a tierce rank (3 1/5') on the pedals at bottom C and tenor E on the manuals would be 1.3 Hz.  The beat frequencies get higher as you go higher up the compass and soon become very rough on the ear with a tierce/17th rank.

 

How about the Septieme (4 4/7') at one time on the pedal organ at Notre Dame? (I haven't checked whether it's still there).  This is the 7th harmonic (flat 21st interval) relative to 32 foot pitch.  It would produce a beat frequency of 9 Hz between bottom C on the pedals and bottom B at unison pitch on the manuals.  Because the flat 21st is so flat, it actually lies much closer to A#, with which there would be a beat of 2 Hz.  Apparently Vierne said it gave the pedal organ "the richness of a muster of double basses".

 

All these figures relate to an organ tuned to A = 440 Hz in Equal Temperament.

 

It's the organ builders whom I take my hat off to.  How the deuce do they ever tune the things (i.e. mixtures and mutations of any type and pitch) and remain sane?  I've watched them at work and have wondered whether they suffer from more rapid age-related hearing loss than the general population who aren't exposed to (say) a five rank mixture shrieking away at close quarters?  I'm not being disrespectful - it must be a real issue for them.

 

CEP


"You can never know everything about something. But you can always know something about everything" - Amit Kumar

 

www.pykett.org.uk


#14 JohnDubery

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Posted 18 October 2014 - 12:14 PM

Some things I have discovered since posting the question - in case of interest to anyone else:

 

Details of the Great Mixture V on the London Organ School organ can be found in Wedgwood here -

https://archive.org/...e/n131/mode/2up

- with the curiosity that this article speaks there being independent 12th and 15th stops, but the stop-lists I have found (NPOR and Dixon's article about Casson) omit these. Somewhat furthering the curiosity is that both Audsley and Wegdwood list the organ school organ as containing an example of the stopped harmonic 12th.

 

Details of the Great Mixture III at Dyserth can be found in the NPOR (D017178)

 

Wedgwood suggests that Casson used the principle that only one rank should break at a time -

https://archive.org/...e/n129/mode/2up

- both of the above mixture compositions conform to this.

 

John



#15 Colin Pykett

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Posted 21 October 2014 - 10:20 AM

That's interesting John, especially the introduction of sub-harmonics of unison (8') pitch.  Although used in earlier times, they were found increasingly frequently in the 19th century when organ builders suddenly decided they 'understood' the then-burgeoning science of acoustics (see #4 above). But they make no acoustical sense unless they are used with the respective ground tone (16' or 32' as the case may be) because only then can they reinforce the natural harmonics of the ground tone.  Even someone of the stature of Cavaille-Coll fell into this trap (and he was pretty well clued up scientifically for his day), thus making the designs of some of his mixtures rather bizarre and akin to those of Casson.

 

My belief is that, clued up or no, they apparently believed that the beats which occur between a sub-harmonic such as 5 1/3' and an 8' ground tone would result in a 16' difference tone being heard even when there was no 16' ground tone.  Even today this misunderstanding is widespread e.g. for resultant bass pedal stops as well as for mixtures and mutations.  In fact there is a major difference between beats and difference tones in that there is no acoustic energy in the air at a beat frequency.  Therefore no difference tone is presented to the ear.  The conversion of energy from beats to audible difference tones requires significant non-linearity, and this can only occur in the ear and/or brain as it does not occur in the atmosphere.  But in healthy ears the non-linearities are usually too small for us to hear difference tones unless the generating tones are unusually loud.

 

See my article for more detail at:

 

http://www.pykett.or...sultantbass.htm

 

CEP


"You can never know everything about something. But you can always know something about everything" - Amit Kumar

 

www.pykett.org.uk


#16 DouglasCorr

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Posted 21 October 2014 - 09:23 PM

Colin - I thought your paper about acoustic basses very interesting - at school we had an acoustic bass 32ft and I always thought that it only "worked" on the bottom few notes - anyway your analysis it very convincing.

 

I thought I would try out some of my own analysis using Fourier Transforms, but I no longer have the research software that MOD once provided me with- however I am pleased to find that in this day and age everything is already done for you on the computer - try adding your own mixtures of tones together e.g.   100Hz + 150Hz http://www.wolframal...e + 150Hz tone   in the power spectrum you can see that there is no power below 100Hz i.e. no "difference note" (although the speaker option didn't work for me). You can synthesise whatever you like!!!  Have fun folks!!! :lol:



#17 sprondel

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Posted 22 October 2014 - 10:19 AM

My belief is that, clued up or no, they apparently believed that the beats which occur between a sub-harmonic such as 5 1/3' and an 8' ground tone would result in a 16' difference tone being heard even when there was no 16' ground tone.  Even today this misunderstanding is widespread e.g. for resultant bass pedal stops as well as for mixtures and mutations.  In fact there is a major difference between beats and difference tones in that there is no acoustic energy in the air at a beat frequency.  Therefore no difference tone is presented to the ear.  The conversion of energy from beats to audible difference tones requires significant non-linearity, and this can only occur in the ear and/or brain as it does not occur in the atmosphere.  But in healthy ears the non-linearities are usually too small for us to hear difference tones unless the generating tones are unusually loud.

 

As far as I can see, you are correct except for the very last bit. From what I read in Daniel Levitin’s excellent book “This Is Your Brian on Music”, there is the fact that musical frequencies are represented in the brain as firing frequencies at the same rate. Fascinating as that may be in itself, it gets even more so when he writes that resultant tones, though they are not present as frequencies measurable to electronic equipment, are measurably present in the brain at exactly the frequency that results from the difference of the frequencies that are present and measurable.

 

So difference tones apparently are real to brains, if not to computers. They are a human phenomenon.

 

In organs, they work more or less well depending on voicing and scaling as well as acoustics. Eberhard Friedrich Walcker’s “monkey fifth” Violones are famous, in the bottom octave of which a stringy open 8’ pipe carries a “rucksack” stopped pipe sounding the fifth above its fundamental. Walcker and his voicers managed to make the transition from open pipes to “monkeyed” ones all but inaudible. This, as well as the numerous occurences of sub-unison harmonics in historic organbuilding, e. g. in Schnitger, Clicquot etc., all without the related 16’ or 32’, tells its own story as concerns difference tones and their use in certain styles of organ tone, doesn’t it?

 

Best wishes

Friedrich



#18 Colin Pykett

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Posted 22 October 2014 - 11:06 AM

Friedrich, the issue is whether one can consciously perceive (i.e. actually hear) difference tones, regardless of what Levitin or anyone else might say about ear/brain function.  I cannot hear them under normal listening conditions and nobody I have ever met can either - even when I take them into a church or my studio and experiment on them!  I have only come across one person who claims he can hear them under normal listening conditions, and that was only on the basis of an email so I was not able to confirm it personally.  I do not know him otherwise.

 

Can you hear them?  If so, what does music sound like to you?  It must sound very different to how I perceive it, because you will hear (say) tenor C when you play middle C and the G above it simultaneously.

 

CEP


"You can never know everything about something. But you can always know something about everything" - Amit Kumar

 

www.pykett.org.uk


#19 sprondel

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Posted 22 October 2014 - 12:44 PM

Friedrich, the issue is whether one can consciously perceive (i.e. actually hear) difference tones, regardless of what Levitin or anyone else might say about ear/brain function.  I cannot hear them under normal listening conditions and nobody I have ever met can either - even when I take them into a church or my studio and experiment on them!  I have only come across one person who claims he can hear them under normal listening conditions, and that was only on the basis of an email so I was not able to confirm it personally.  I do not know him otherwise.

 

Can you hear them?  If so, what does music sound like to you?  It must sound very different to how I perceive it, because you will hear (say) tenor C when you play middle C and the G above it simultaneously.

 

If sounded as two notes at a time, I will probably hear them as such. The Sesquialtera phenomenon – play one note on a North-German Sesquialtera, consisting of a slightly sharp twelfth and a flat seventeenth, and you will hear those notes apart, as I do. Start playing lines and runs throughout the compass, and the separate notes will vanish, giving way to a glassy and nasal fundamental. According to Levitin, that is a product of our brain processing and ordering environmental sounds. Jehan Alain knew all that instinctively and made use of it in his compositions, e. g. towards the end of the Second Fantasy, where at least my brain struggles to shake off the illusion of hearing a harmonic that belongs to another fundamental, and to perceive the diminuendo line at the actual pitch.

 

As a violinist, I used to make use of difference tones when practicing double-stoppings. You can train yourself to perceive them quite quickly. If a major third “drones”, it will work in solo playing, but rarely in ensemble. When I practiced scales in thirds, I tried to get rid of the drone, sharpening the major thirds and narrowing the minor ones in order to arrive at something approaching equal temperament; when I practiced fourths, I sought the drone, because without it the fourth would sound foul. (I gave up that kind of practice, useful as it proved, because of lack of time, and after all, I did not make it my profession.)

 

I find the subject as fascinating as you do, and think it is one of special importance to the organ; in fact, it singles out the organ as the one instrument that extensively makes use of the effects of difference tones as perceived by the human brain, in order to give the music a special colour. In my ears, a Grand Plein Jeu with sub-harmonics in the order of 5 1/3’ and even 10 2/3’ sounds fascinating, even when no actual fundamental rank is present. 

 

At Lausanne cathedral, Fisk included blind features with the Great mixtures: The sub-unison ranks only come on if the respective fundamental rank is drawn (16’ or 32’ open). That’s smart, but I think it’s slightly beside the point in certain styles.

 

I even am tempted to say that the fundamental is grossly overestimated in organ sound.

 

Best wishes

Friedrich



#20 sprondel

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Posted 22 October 2014 - 01:01 PM

Can you hear them?  If so, what does music sound like to you?  It must sound very different to how I perceive it, because you will hear (say) tenor C when you play middle C and the G above it simultaneously.

 

Sorry, I went on and on without answering your actual questions. I believe I do hear the music very much as you do, in so far it concerns complex musical structures. Of course I do hear chords and not complexes of harmonics, and lines instead of rapidly changing fundamentals of irrational pitch. However, in compound stops and registrations that include strong harmonics, I usually hear the fundamental they relate to, even if it is only weakly present as a rank, or not present at all. Long-held chords may become awkward if they include loud thirds or higher-pitched odd harmonics.

 

I do hear, and much enjoy, longer chords locking-in with harmonic complexes, though, where unequal temperament uses near-pure thirds that fall in line with the harmonics of a reed in the bass and third-sounding ranks in the other voices.

 

Best wishes

Friedrich






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