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another tuning question: unequal temperaments and mixtures/mutations

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  • another tuning question: unequal temperaments and mixtures/mutations



    I have been away from the forum a bit having the pleasure of taking apart a small organ and moving it to my home :D Just read the thread about tuning and this brings me to my related but different question about tuning.



    While moving my organ and thinking about what needs to be done bofore it will be usable, one of the things will be a good tuning. Now as I'm only interested in baroque music and have no intention of playing with other instruments I would like to set it to an unequal temperament like Werckmeister or Kirnberger (Valotti?).



    I do not see a problem with 8', 4' and 2'. But how do you tune a Mixture III (1' based with repeats)? Do you tune each pipe to its pitch in the series? Same for a mutation, suppose you have Kirnberger III, then G is -2.39 cents off compared to equal. Now what do you tune the 2'2/3 to? Do you tune it as a correct quint to the C or as a octave to the G?


  • #2
    Re: another tuning question: unequal temperaments and mixtures/mutations



    Understand the three temperaments you mentioned are actually "Well" temperaments, and are not "unequal" per se.  Unless your pipe organ is exceptionally stable, a differential of 2 cents will barely be noticed in the far reaches of the compass.



     When tuning mutations, or the notes in a mixture, you must tune any non-unison intervals "straight" to your tuning reference.  Whatever temperament you use, I recommend you set the bearing in your 4' principal and use that as the reference for everything else.  You'll have fewer gray hairs when you're done.

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    • #3
      Re: another tuning question: unequal temperaments and mixtures/mutations



      Maybe I'm misunderstanding what you wrote, but I would have thought that the mutations (and mixtures containing them) would need to be tuned to the proper harmonics of the notes that invoke them. That is, a 2 2/3' pipe would need to be exactly 3 times the frequency of the 8' actuated by the same key. Is that what you meant?




      David[*-)]

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      • #4
        Re: another tuning question: unequal temperaments and mixtures/mutations

        Yes David, that's what I wanted to know. But if I understand Odelorgans correctly, then you do not do that. I understood that you tune the 2'2/3 not to the harmonic of the C but to the g above that C.

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        • #5
          Re: another tuning question: unequal temperaments and mixtures/mutations



          [quote user="davidecasteel"]Maybe I'm misunderstanding what you wrote, but I would have thought that the mutations (and mixtures containing them) would need to be tuned to the proper harmonics of the notes that invoke them. That is, a 2 2/3' pipe would need to be exactly 3 times the frequency of the 8' actuated by the same key. Is that what you meant?[/quote]If I may answer ...there are a couple issues in your post I think I can clear up.




          Three times the frequency of an 8' stop would make it a 2' stop, not a 2 2/3' stop.




          Mixtures don't contain mutations...exactly. A mutation is a single stop comprised of an off-unison pitch and it is usually non-breaking (or breaks towards the top). While mixtures do contain off-unison pitches, these are relatively high-pitched and they break several times throughout the gamut. They are usually not able to be played in isolation as a true mutation would be.




          Regardingyour tuning question: all mixtures and mutations must be tuned true (with no beats) to the 4' reference pitch. The 4' pitch itself can be in any number of temperaments, including meantone. FYI ... 4' stops are usually the tuning references, which is why I don't specifically mention the 8' in relation to tuning.




          [quote user="Havoc"]Yes David, that's what I wanted to know. But if I understand Odelorgans correctly, then you do not do that. I understood that you tune the 2'2/3 not to the harmonic of the C but to the g above that C.[/quote]No, that is not correct; you do tune a mutationas a harmonic of the 8' unison played from the same key. That's one way of thinking of it - but practically speaking, you will have an easier time tuning the mutation to the 4', not the 8'.




          Here is tuning/temperament in a nutshell: You first set a temperament using the 4' Octave. You set the temperament for one or two octaves of pipes; once that is set, then the entire 4' rank is tuned to that temperament.




          Next, I usually tune all the 8' flue stops in that division to that 4' stop; if there is another 4' stop in the division I will tune it to one of the keener 8' stops after it has been tuned. Then I tune the 2' stops andthe 16' stops. Everything in the division is tuned to the 4' reference stop, with the exception of some chorus reeds, which I like to tune to themselves after an octave or so has been tuned to the 4' flue reference. Quieter reeds can be entirely tuned to the 4', perhaps the top octave I might tune the reed to itself if it gets hard to hear the reference.




          When you get to the mutations (usually the 2 2/3' is the first one) you tune that to the 4' Octave. In other words, draw the 4' Octave and the 2 2/3'stoptogether. You will hear a C and a G playing together as a fifth. Starting at low C, you tune these so they are perfectly in tune (beatless). Proceed up the scale to the very top note.If it gets hard to hear, I drop the 4' stop and will play the 2 2/3' with its own octave below (the lowernote will just have been tuned, the upper note is what you are tuning).




          When it comes time to tune the Tierce you can either tune it to the 4' reference or tothe 2', if that is easier to hear.




          A colleague tunes all the mutations to the 8' Trumpet (which itself must be in perfect tune to the reference). It works extremely well, but I have found that it is a very good idea to double check with the 4' so that mistakes don't creep in.




          Mixtures are the last flues to be tuned, then I tune the reeds. Bear in mind that this is all within one division. After all the pipes are tuned in one division I then transfer the temperament from the tuned 4' Octave to the 4' Octave (or string) in the division to be tuned next (the secondary reference). Even though you have transferred the temperament sometimesit has to be modified - a very tiny bit - in order to sound well on that secondary reference stop. Then the entire process repeats for that division.




          This is the usual process, but all organs are different and some may require a slightly different approach.

          Comment


          • #6
            Re: another tuning question: unequal temperaments and mixtures/mutations



            Feel I'm getting it allmixed up now.



            When you get to the mutations (usually the 2 2/3' is the first one) you tune that to the 4' Octave. In other words, draw the 4' Octave and the 2 2/3' stop together. You will hear a C and a G playing together as a fifth. Starting at low C, you tune these so they are perfectly in tune (beatless). Proceed up the scale to the very top note. If it gets hard to hear, I drop the 4' stop and will play the 2 2/3' with its own octave below (the lower note will just have been tuned, the upper note is what you are tuning).



            That would mean that you put the 4' and 2'2/3 in tune. But also that if you then play with 8', 4' and 2'2/3 and you do play a fith that you get 2 different 2'2/3 pitches. One from the G and one from the 2'2/3 on the C that can be far off each other if you're into mean temperament. OTOH, this is probably what this whole temperament business is all about...

            Comment


            • #7
              Re: another tuning question: unequal temperaments and mixtures/mutations

              [quote user="soubasse32"]


              Three times the frequency of an 8' stop would make it a 2' stop, not a 2 2/3' stop.[/quote]I'm sorry, SB32, because I find it very difficult to have to disagree with you, but a 2' is 4 times the frequency of an 8' and twice the frequency of a 4'. A Tierce (1 3/5') is 5 times the frequency of an 8'. I am positive that this is correct.




              If tuning a 2 2/3' to a 4' is done to produce zero beats, the 2 2/3' must be an open pipe and the zero beats would have to be between the 2nd harmonic of the 2 2/3' (1 1/3') and the 3rd harmonic of the 4' (also 1 1/3'). I've no doubt this would work because beats in that range are probably easier to hear. (Because I'm not an organ tuner, I'm on much shakier ground here, but I believe I have the theory right.)




              Please forgive me for disagreeing.




              David

              Comment


              • #8
                Re: another tuning question: unequal temperaments and mixtures/mutations

                [quote user="davidecasteel"][quote user="soubasse32"]Three times the frequency of an 8' stop would make it a 2' stop, not a 2 2/3' stop.[/quote]I'm sorry, SB32, because I find it very difficult to have to disagree with you, but a 2' is 4 times the frequency of an 8' and twice the frequency of a 4'. A Tierce (1 3/5') is 5 times the frequency of an 8'. I am positive that this is correct.


                If tuning a 2 2/3' to a 4' is done to produce zero beats, the 2 2/3' must be an open pipe and the zero beats would have to be between the 2nd harmonic of the 2 2/3' (1 1/3') and the 3rd harmonic of the 4' (also 1 1/3'). I've no doubt this would work because beats in that range are probably easier to hear. (Because I'm not an organ tuner, I'm on much shakier ground here, but I believe I have the theory right.)




                Please forgive me for disagreeing.[/quote]No worries - you are correct. I posted this when I was running quite late for church [:$] so I did make an error there; I was thinking of straight octave doublings rather than adding frequencies together.




                As far as the 2 2/3' being an open pipe - that is irrelevant. The point is that you tune two organ pipes so they do not beat, no matter if they are closed, open, tapered, partially closed, whatever. This is what must be done for all pipes - unisons and mutations - in order for a pipe organ to be in tune.




                A 4' stop is used as a reference, but sometimes it is too loud, too large scaled, etc. For this reason sometimes another pitch (such as a 2') will be used to tune a mutation. It is all about the tuner being able to hear the beats, which sometimes results in some unusual approaches.




                If we analyzethe harmonics and mathematics too muchit getsinto a sort of 'analysis paralysis'- I know engineers like to have these discussions [;)] but in practice it is much more prosaic: you tune the pipe to the reference stop until you hear no beats.

                Comment


                • #9
                  Re: another tuning question: unequal temperaments and mixtures/mutations

                  [quote user="Havoc"]Feel I'm getting it allmixed up now.[/quote]It can be a very confusing subject - especiallyto put into writing.


                  [quote user="Havoc"][quote user="Soubasse32"]When you get to the mutations (usually the 2 2/3' is the first one) you tune that to the 4' Octave. In other words, draw the 4' Octave and the 2 2/3' stop together. You will hear a C and a G playing together as a fifth. Starting at low C, you tune these so they are perfectly in tune (beatless). Proceed up the scale to the very top note. If it gets hard to hear, I drop the 4' stop and will play the 2 2/3' with its own octave below (the lower note will just have been tuned, the upper note is what you are tuning).[/quote]




                  That would mean that you put the 4' and 2'2/3 in tune. But also that if you then play with 8', 4' and 2'2/3 and you do play a fith that you get 2 different 2'2/3 pitches. One from the G and one from the 2'2/3 on the C that can be far off each other if you're into mean temperament. OTOH, this is probably what this whole temperament business is all about...[/quote]Yes, exactly.




                  If I play a C-major chord on an 8' Principal I will hear the notes C, E, and G. If I add a Nasard to the registration I will hear G, B, and D. If you are in equal temperament, those two notes 'G' will be out of tune with each other. Some temperaments will make that effect sound worse, some will sound better (depending on the key you are playing).




                  But that is the nature of the organ; if you were to play only octaves, any freshly-tuned organshould sound absolutelyperfect. When you start adding mutations and mixtures the harmonics will clash a bit, depending on the temperament. Since organ registrations usually favor the unison pitch, the ear will tend to hear that more prominently. If that weren't the case, nobody would be able to tolerate mutations and mixtures played in chords (which is true for some very sensitive people).




                  One other comment re: quints and tierces: of the two, quints tend to be less 'irritating' in chords when played on an equal-tempered instrument. If you play a Quint or Nasard on low C and then listen to the same note "G" played on an 8' or 4' stop you will see they are not too far out of tune with each other.




                  On the other hand, if you were to do the same thing with a Tierce, you'll notice the two notes "E" tend to be much further apart, tuning-wise. That's one reason I like to play a Cornet or Sesquialteraon a solo melodyrather than in block chords.

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