Tuning Of Enharmonics In Equal Temperament

[Bob Tedrow]

Pray tell,

 

 

Should not enharmonics be tuned to the same pitch in an english concertina tuned to an equal temperament? Is that not redundant?

[ocd]

Pray tell,

 

 

Should not enharmonics be tuned to the same pitch in an english concertina tuned to an equal temperament? Is that not redundant?

 

Yes, they are, but sometimes they are handy for easier fingerings. (Some people call them enharmonic substitutes.)

 

ocd

[Paul Groff]

Pray tell,

 

 

Should not enharmonics be tuned to the same pitch in an english concertina tuned to an equal temperament? Is that not redundant?

 

Hi Bob,

 

It is more or less true by definition.....

 

Although there are some fairly obscure variant uses of the term "equal temperament," (*) when most of us use the term these days we are referring to a system where the octaves are tuned "just" (each successive octave is a pitch twice the frequency of the one below), and each octave is subdivided into twelve pitches that are "equidistant on a logarithmic scale." Every note has the frequency of the next lower note, multiplied by a constant which is the 12th root of 2. (Here the "2" reflects the doubling of frequency with each octave and the "12" reflects the division of the octave into twelve parts). In other words, if the frequency of any note is "n" (Hz or cycles per second) then the frequency of the next highest note in this ET system is "(n) times the 12th root of 2." [Don't know how to bring up the correct math notation here]. By definition in this system, C# in any given octave has the identical frequency to Db; D# to Eb, and so on. There are only 12 different pitches per octave, if we count only (either) the upper *or* lower limiting pitch. In this system, enharmonics are merely different spellings to which the same pitch is assigned. When an english concertina is truly tuned to equal temperament, the duplicate buttons for Eb vs D# and Ab vs G# in each octave where they occur are only useful for alternate fingerings, as OCD noted, not to provide different pitches. That is why some english-system players have been known to substitute a low F natural for the low Ab or G# of a 48 key treble (or other substitutions). Sometimes the reeds for one of these duplicated pitches are pulled out of one of the high chambers to provide an air button when the instrument lacks one, showing their redundancy.

 

Though others on this forum have disputed me in the past, I have always felt that these duplicated notes in each octave were originally designed to be tuned differently from each other (as enharmonics in meantone should be) and I have seen several old original englishes in 1/4 comma meantone (or close to it) that bear this out. I was not the first person to write about this of course, and have never claimed this observation was original to me, but when I first alluded to this point on this forum about 8 years ago there were some longtime english-system players here who thought the original *intent/designed purpose* of those duplicates in the english layout was to provide duplicate fingerings! In my view their persistence in the button layout once equal temperament became dominant for the english system is like the appendix or other vestigial organs in our body that have hung around once their former use is no longer being served.

 

 

 

*Leaving aside the "stretching" of octaves in some tuning schemes for pianos etc., there are some exceptions we can note. Other scales for which the term equal temperament has been used include:

 

1. Some have described 1/4 meantone temperament as a sort of "equal tempered just intonation;" to me this statement is likely to confuse. In 1/4 comma meantone the major thirds are just and all of them are equal in size, also every key has the same internal relationships among the notes of its scale, but the octave itself is not divided into equal units.

 

2. Then, it is possible to equally-divide the octave (on a log scale) into more or fewer than 12 units. A division of the octave into 31 or more equal units gives many options for intervals that are very harmonious ....see:

http://en.wikipedia.org/wiki/31_equal_temperament

 

..... and I believe I have seen some Gamelan scales described as "equal tempered with 10 notes" -- i.e. the octave divided into 10 equal units (on a log scale).

Edited October 25, 2008 by Paul Groff