Even though I am no expert on music theory, I can offer some comments about the tuning of flutes. For the pvc simple-system flutes that I make, before I had an electronic tuner, I referenced the fundamental pitch of the flute to a Yamaha keyboard , and the remaining notes of the scale I pitched by ear (Just intonation). People kept writing me that my flutes didn’t agree with their tuners, so I decided to be more conventional and use a tuner, even though the equal-temperment didn’t sound as good to me.
I have no experience in tuning conical-bore flutes. However, I did do an experiment this last weekend. I listened to the four CD’s of “Wooden Flute Obsession 1 & 2”, which, as most of you know, contains the playing of many of the best Irish flute musicians in the world. With regard to pitch, however, without singling out any musicians in particular, to my ears a number of the tunes sounded “off” to me. I am not saying that the playing is, in fact, “out of tune”; it merely sounds that way to me, that’s all. I also make the assumption that the same players that are a problem for me will most likely please a majority of listeners, and that for traditional music, especially music played very fast, some lattitude can be given to the performers with regard to pitch accuracy. The following paragraphs are from my “Flute Buyer’s Guide”. Again, I know that I am not an authority on this subject. I offer it to stimulate discussion.
A Word About Tuning: In western music (as opposed to world music) the octave is divided into twelve notes or half tones. Although it is contrary to what a musically sensitive person hears, to simplify the tuning of instruments (especially keyboard instruments) it was decided to make the interval between these twelve half-tone notes exactly the same size, with each of the half-tone intervals being further broken down into 100 units or cents. Therefore, the octave is divided into 1200 cents, with half-tone intervals being 100 cents and whole-tone intervals being 200 cents. This system of intonation is called equal-temperment, and it is the standard for all electronic tuners, except for the more expensive tuners that allow tuning to the exact frequency.
Human beings have an innate sense of relationship, both visually and aurally. For example, without using any measuring devices we are able to divide a pie into eight equal pieces. Similarly, with regard to music we can sense certain basic musical intervals in the octave. It turns out that the basic intervals that we sense are related to rational numbers or fractions. The simplest relationship is the octave interval (twice the frequency) or 2:1 ratio. The perfect fifth interval has a ratio of 3:2, and the fourth interval has a ration of 4:3. As the integers become larger, it becomes more difficult to sense the interval. For example, the interval of a seventh is 15:8. A system of intonation for intervals arrived at in this fashion is called Just intonation. However, with Just intonation the intervals are not all the same size, and in the past this caused many technical problems in tuning, so this system was abandoned in favor of equal-temperment.
Our current equal-temperment system of intonation is obviously convenient, but this convenience has been bought at a price. The price is that the scale doesn’t sound right to a musically sensitive person. For example, it is nearly impossible for a musician to tune a piano, because the “correct” notes don’t sound exactly right. In fact, three of the eight notes in a one-octave diatonic, equal-temperment scale vary between 14 and 19 cents from the same notes in the musician’s scale of Just intonation. Also, as an orchestra tunes by ear to an A440 pitch on the oboe, the string section tunes their instruments by ear (no tuners) by listening for perfect fifths between the strings, and somehow the whole orchestra comes together and sounds in-tune to the listener. But actually there are many variations in pitch that are not perceived by the listener. Because of variations in attack strength and embouchure, the side-blown flute is especially vulnerable to frequency fluctuations, and frequency fluctuations up to 4 per cent have been observed, even among concert musicians. I can play my Irish flute in front of an electronic tuner and have the needle swing from 20 cents below to 20 cents above standard pitch just by the way I blow and the way I shape my lips (embouchure).
And lastly, quoting from the classic book “Music, Sound, and Sensation” by Fritz Winckel: “Although completely pure intonation is most difficult on the flute, it is also of least importance, for the (flute) tone is poor in overtone content, and a slight distuning can have a positive equalizing effect.” In other words it may be a good thing to be slightly off-pitch. And that is my main thesis and purpose for writing the above comments about tuning. I believe that some people have unreasonable expectations about pitch and intonation. They think that their $20 electronic tuner set to equal-temperment is the gold standard and that any variation from “dead-on” pitch accuracy is not acceptable. To the contrary, my attitude with regard to flute performance is to lay perfectionism aside and accept some variations in intonation as inescapable and perhaps even a good thing.
I have not seen anything you wrote or I wrote that would indicate that you attacked me or that I felt attacked by you.