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Hi Alfredo,

I read the paper cited above and agree with Robert Scott's assessment.

Tuning an organ pipe is accomplished during the stabilized sound after the initial pulse of air which starts the oscillation. This sound is effectively mode-locked and therefore harmonic.

Interesting paper, thanks for sharing.

The resonances of the system do not necessarily line up with the harmonics being produced when driven although obviously some of them must or it wouldn't work.

The trombone is a good example, poorly understood by players. It has a set of resonances we call partials; when playing a steady note that note has a set of harmonics we call overtones. Most assume the partials and overtones line up, but they don't. The overtones are forced to be integer related frequencies by mode locking, but the partials vary depending on the design choices of the manufacturer.

The input frequency can be varied slightly for any given tube length, because that resonance extends over a small range. That means potentially different resonances may be excited for the same note, and the timbre can vary. Instruments designed for symphonic use where great tone consistency is required try to line the resonances up and avoid this effect, while jazz players who use more color changes want a horn where the resonances allow more flexibility. This is what I understand voicing to mean with respect to organ pipes.

A quick, dirty way of looking at organ pipe timbre characteristics is this:

A fat, short organ pipe tends to sounds flutey. A medium width pipe tends to sound like an organ (principal stop), A long, thin pipe tends to sound stringy.

There are a lot of other factors that go into pipe timbre - type of wood or metal used, stopped or open ended pipe, reed or no reed, and so on, but the basic quality of timbre is the ratio of length to width.

I assume that trombones, being an open pipe most of the time, have their timbre constrained by same ratio (with some flexibility as you mentioned).

Edit: I should also mention that, unlike trombones, trumpets, etc., organ pipes are rarely overblown, that is to say, played at double or greater the fundamental resonant frequency of the pipe, since that effectively changes the timbre.

Yes. Tenor trombones basically come in small, medium, and large bore sizes, all the same length. (obviously, or they wouldn't be the right pitch)

In general the smaller bores are brighter sounding and the larger ones darker; also the tendency to become more bright and brassy as they are played louder is greater for the smaller bores.

Unlike an organ they are not cylindrical for the whole length. They are part cylindrical and part conical, and that ratio changes as the slide is extended.

Hi Prout, hi Robert and TimR,

Thank you for your addings.

I too understand what can be understood, according to the above paper, and to some other studies and observations conducted so far (limited to what I could find around), and here I needed to precise that there are other components, together with frequencies that might be understandably represented as integer multiples.

I haven't had a chance to assist a pipe organ tuner, Prout, although I would really like to ba able to. Until then, I cannot tell what the outcome would be on a pipe organ, if the octave was 2.0005.. to 1, instead of 2:1.

Please confirm, was that the issue your were pointing out?

Regards, a.c.

Edit: Robert, TimR, have you ever tuned a pipe organ? Would you be able to guess the outcomes, in case the octave is slightly wider than 2:1?

We clearly beats when two pitches are heard simultaneously if the beat rate is less than about 16bps. An organ pipe playing with the octave above will beat if the octave is not a perfect 2:1 ratio. Since organ ranks are often played simultaneously (that is an 8 foot will be played with a 4 foot and 2 foot rank) their harmonics, which are perfect integers, will beat with each other even when a single note is played. It will not be in tune.

..."We clearly beats when two pitches are heard simultaneously if the beat rate is less than about 16bps."...

I do not understand your first sentence, Prout.

..."An organ pipe playing with the octave above will beat if the octave is not a perfect 2:1 ratio."...

Yes, it 'will beat', or perhaps it 'might beat', depending on how_much the octave actually deviates from 2:1? (I am asking, please see my edit above)-

You see, Prout, in general (and numerically) if you tune 2:1 octaves and 12_root_of_two, you get 12ths that will get progressively narrower and narrower, and all SBI's and RBI's will double their beat-rates, octave after octave.

An anedocte, when I asked two organ tuners what they did with 12ths, how would they manage the 'temperament' expansion... they disappeard.

Edit: Prout, have you ever had a chance to tune a pipe organ?

Edit n.2.: you wrote: ...Since organ ranks are often played simultaneously (that is an 8 foot will be played with a 4 foot and 2 foot rank) their harmonics, which are perfect integers, will beat with each other even when a single note is played. It will not be in tune."...

Yes, you can anticipate that 'harmonics' would beat somehow, perhaps very very slowly (?); whether it would not sound 'in tune', this (IMO) needs to be verified. I hope you understand that 'intonation', for me, it is a question of beat-proportion.

Edit n.3: and you may see how clichés take shape, when you say ..."their harmonics, which are perfect integers, will beat with each other even when a single note is played. It will not be in tune."..., here it seems that "beat" translates 'will not be in tune'.

I have never tuned a pipe organ

I was hired to disassemble one many decades ago, as my church upgraded and somebody else bought our old one; it was fascinating but I no longer remember the details, just that they hired about a dozen of us and very quickly there were only two of us left

I also direct a handbell choir

Bells are theoretically designed to sound the fundamental and the 12th; but for whatever reason, many of them have beats when rung alone, and I have a couple of bells that sound out of tune in particular chords

Thank you, TimR, it is nice knowing that you play trombone, which one do you play, is it valves or coulisse? The latter is an instrument that really attracts me, perhaps one day I will go for the smallest one, we call it tromboncino, better proportioned with my height :-)





Hi Robert, hi Prout and All,

I would really like to make a distinction between a 'beat' that we may want to avoid, because 'that beat' would sound out of tune, and a beat that doesn't need to be avoided, (IMO) like the one that (for instance) a 2.0005:1 octave might produce.

I wonder if there is a word missing, a word that can describe an interval that is not 'pure' and yet it doesn't really beat, which is what I hear when I tune (I would call it) a 'tonic' octave, where the octave is only (say) 'open', and what I hear there is like vowels 'm' and 'u' that would perhaps make a beat (a loop) in something like ten seconds.

In Italian we also refer the word 'tonic' to muscles, and the prefix ipo and iper.

Robert, is TL intented for tuning organs too? If positive, does it address 12th root of two theoretical values?

Regards, a.c.
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Alfredo,

TuneLab could be used for tuning organs, but we have another app for iPhone called "Organ Tuner" that is better for that purpose. Yes, it does use exact 2:1 ratios for octaves (no stretch). Therefore the 12 notes in each octave do have a ratio of exactly the 12th root of two from note to note. We also have the option to modify the temperament to make the usual historical non-equal temperaments. But the octave ratio is always 2:1 exactly.

Hello all,

It is easy to try any type of octave/interval on the software scala, using sampled tones of organs, pianos, or even external samples if the ones of the computer are not satisfying.

AT the organ, seem to me that the fast beating intervals are very soon beating a lot. An open octave is possibly used by some organ tuners, but I do not really imagine how they do to verify aurally how is the tuning.
Triple octaves soon are sounding too much enlarged on such instruments.

If they tune as for harpsichords, the 2:1 ratio is wanted, and not the "open" octave we have naturally at the piano. That is a totally different way of listening, I think (without attention to the time/power relation.

I tuned small organs and find the octave by lining of the present partials, there is the hot spot clearly audible. not waiting for any evolving in time of that.

that is anyway the usual way of doing it , and the organ players do not like to perceive any enlarging.

Hi Prout,

You said "be candid" and I will, in any case take my words with a pinch of salt. The whole tuning is "irregular" and the heaviest approximations are at the extremities. Nevertheless, many times I happen to tune pianos that are worse than that, and the owner is perhaps a full time pianist.

Arpeggios (for me) are not that good for checking octaves, maybe because my ear ends up focusing onto the other intervals: in this case, M3, fourths and fifths become more 'significant', since they are actually forming the arpeggio.

If you want to check your ear on octaves, do record only octaves, two notes at the time, either chromatically or the way you prefer.

Regards, a.c.
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Thanks Robert,

It would be very interesting to check that tuning aurally, meaning a serious check of all beat progressions. I am convinced that M3 cannot be progressive, together with 'coherent' fourths and fifths, in that the 2:1 octave-ratio does not leave enough room. And I think that this would become even more noticeable on wider chromatic intervals, (read non-coherent 10ths, 12ths and 17ths) making the whole 12 root of two tuning sound as a sort of irregular temperament.

Please consider that I (and my beat perception) might be wrong, perhaps you have already done that check using a beat analyzer?

Regards, a.c.
.

Hi Isaac,

Thanks for your feedback. IMO, the point is 'how open' the octave is; like you, I think that the octave can easily get 'too open' and give raise to annoying beats, both on organs and pianos.

My feedback with harpsichords is different. I had three good opportunities to tune harpsichords, in quiet places and for days on a row, when some seminars and concerts where performed. My octave stretch was still under observation, but then, on a two-keyboards instrument, I could reconfirm the overall tuning to a surprising level, by playing the same notes on the two boards, like in a unison.

In a way, that made me think again about the influence of iH, how it was commonly understood some thirty years ago.

I am still looking forward to meeting you again, :-).

Regards, a.c.
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Hi Alfredo,

Thank you for listening and I very much appreciate your observations. I thought it would be helpful to listen to the octaves and how they beat against the other intervals. I think you are right, though, that I should post octaves only.

My own opinion of the tuning is that I don't like it. The bass is not stretched enough to my ear, the high treble is 'in tune' or slightly flat, depending on my mood, and while I like the sound of the finished arpeggios after they 'settle down' , I think the attack is not clear.

The temperament is clearly heard, I think, and is sensible from about C2 to C7, but is still not good enough.

Thanks again for your comments. I am beginning to think that a milder temperament will suit my particular piano better, and I must continue to improve my listening skills.

Hi Alfredo,

In theory, with no iH and 2:1 octaves, ET will have perfectly progressive M3s, P4s and P5s. The P4s and P5s will be exactly equal, though opposite in sign (P5 slightly narrow, P4 slightly wide).

Hi Prout,

Do you mention the above because you have tried to put the first 2:1 octaves ET theory into 'no iH' practice?
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Yes, when tuning an organ.

Alfredo, unlike in a piano where the irregularity of IH makes the calculations much more complicated, the mathematics of how pitches beat in a no-IH instrument like a pipe organ is simple. If you do observe any unevenness in the progression of tempered interval beat rates in a pipe organ tuned to 2:1 ET, it would be due to tuning error.

It is possible that the air pressure in the pipe chest might not be perfectly regulated, so the pitch of a single pipe could change slightly when another pipe is played along with it. This might give the appearance of imperfectly progressing intervals, but that would only be because of the imperfect control we have on the fundamental tuning. If the tuning could be guaranteed to stay at the pitches specified by 2:1 ET, the beat rates of the intervals can be guaranteed to be perfectly progressive in exactly the same ratios as the pitches are progressive.

Some pipe organ stops do have a small amount of inharmonicity - see Chimney Flute

Any non-perfect instrument will have a small degree of inharmonicity, even regular organ stops as there physical characteristics of the air which are not perfect - plus multiple path lengths (as in the chimney flute) - but the iH is much much less than in a string.

Paul.