[Harp-L] tuning/temperaments



First, anyone interested in tuning and temperaments for the harmonica should go here and read the relevant pages:

http://www.patmissin.com

Start there, read that and then go forward. The simple answer to Jimmy's question is, not really.

Now to some specficis.

Michelle Le Free writes:


"My take, and Richard please jump in here if I've got this wrong, is that Just Intonation (JI) tunes certain notes sharp and others flat relative to pure Equal Temperament (ET)"



This may seem like semantics, but it can be vitally important: never use the term "pure Equal Temperament". The problem is that the term "pure" is often used to describe beatless intervals in musical terms, so using it to describe the commonly found equal temperament is begging confusion. Also, there is no such thing as an "impure" Equal Temperament--it's either an equal temperament or it isn't. This is like the term "compromised just intonation", it's meaningless--it's either JI or it isn't.


Personally I prefer 12-Tone Equal Temperament (12TET) to just ET, because it is more specific (you never know, you could be talking about "equal temperament" to an Arabic musician and he's meaning 24TET and you're meaning 12TET).


Vern writes:


"All instruments with fixed notes (harmonica, keyboard, etc.) must use equal temperament if they play in different keys without retuning."


No, as I have said on the many other occasions this has been posted, they may use 12TET, but they may also use many other systems. It just depends on what compromises the musician wants. I certainly find 12TET the most useful for the widest range of written music in many cases, but it is by no means the only nor the ideal solution for every situation. For example, I would guess that most harpsichordists rarely use 12TET, in part because the music written for harpsichord was rarely composed for 12TET. It depends entirely on usage and the instrument in question. Listen to some Handel stuff in 1/4 comma or 1/6 comma meantone sometime--it becomes obvious that he was not writing in 12TET. Certainly not when he wrote for English organs he wasn't (one prominent English organbuilder didn't switch to 12TET from meantone until the 1870's).



fjm writes:



"12T ET can sound wonderful given the right tuning. Harmonic minors are not nearly as jarring chorded in 12T ET as they are in a major key."



For some odd reason, despite being farther out in absolute terms from the typical beatless minor third, 12TET minor thirds are not nearly as grating as 12TET major thirds. It's a bit of weirdness about how the ear perceives things.



Iceman writes:



"when creating all 12 notes through that cycle of upward 5ths and inverted
intervals of downward 4ths, these perfect intervals were SQUEEZED smaller by 2
cents each - perfect 5ths were contracted by 2 cents and perfect fourths, being
inversions, were expanded by 2 cents each. The result was that your ending note
now matched perfectly your starting one. The intervals used became PERFECT
IMPERFECT intervals.


Since the human hear can't really hear a difference until 3 or more cents, this
2 cent shaving was not really apparent and did solve the problem of weird ugly
intervals and the inability to freely transpose music into any key. It equalized
the playing field in a compromise with Mother Nature."



Yes and no. Perhaps the human ear can't hear a difference of 2 cents shaving, but it can most certainly hear the beat frequencies created by this shaving. Indeed, it can hear significantly more subtle variations than 1 cent. Calling the intervals in 12TET "perfectly imperfect" is a nice bit of propaganda, but what they really are is uniform. All keys sound equally bad, with no one key (out of a subset of 12) sounding worse than any other. This was the difference between 12TET and the other various temperaments used, which tended to weigh more heavily towards various keys or certain intervals.


The reason I said "not really" in answer to Jimmy's question is because it depends on so many other factors. I'd bet people are more likely to notice if the tonal center of the harmonica (the A=440 setting of where you begin your root note) is off than between something like 12TET and one of the many compromise tunings proposed, for instance. Also, it depends on how you use it. If you're playing a lot of chords people may hear the dissonance in the 12TET chords more than they hear the variance between the harmonica and the backing instruments even if the harp was in something like 7-limit JI. Also, playing bends and overblows will add another layer of potential pitch relationships into the equation.

Basically, the best advice I can think of is to try a few temperaments and intonations out if possible and see what feels best to you and your bandmates (more the former, less the later) by listening, and then choose one system for a while and really learn how to use it (again by ear). If you want to stick with whatever is off the shelf in your favorite harp (12TET for LOs, for instance), then hope for consistent tuning and learn how to use that for best effect.




JR Ross





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