Just intonation, Equal temperament, and Irish flutes...

[Cork]

Let's get to the bottom of this.

Well, it's my education, too, please!

;-)

[Doug_Tipple]

I think that there has been a fairly good discusion of this at the thread, 8-key vs. Boehm, at least, I learned quite a bit.

I don't propose to get to the bottom of the topic, but I have written the following, which is on a page at my website.

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.

[Jack Bradshaw]

Whaaa.......it's easy ......when you are playing with a flute or a fiddle and you match perfect 5ths, 3rds etc.......you are playing just......if you are stuck w/ an instrument that is equal tempered you can't do it......

Edit: Hey Doug......we crossed in posting.....good points!

[Cork]

I think that there has been a fairly good discusion of this at the thread, 8-key vs. Boehm, at least, I learned quite a bit.

I don't propose to get to the bottom of the topic, but I have written the following, which is on a page at my website.

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.

For what you have just said, I am tempted to from here on refer to you as Doc_Tipple. You said it very well!

Just intonation is what one's ear hears as musical truth, no less than that!

[Cork]

Whaaa.......it's easy ......when you are playing with a flute or a fiddle and you match perfect 5ths, 3rds etc.......you are playing just......if you are stuck w/ an instrument that is equal tempered you can't do it......

Edit: Hey Doug......we crossed in posting.....good points!

Yes, we agree.

Thanks, Jack.

[Cork]

Doc_Tipple, Jack, and I appear to agree, yet what of the Irish flute?

[Jack Bradshaw]

The "Irish" flute is a little easier to play just, as the Boehm, w/ larger holes, can't adjust quite as easily.........

Of course, if by "Irish" playing, you mean all played monotonically (assuming that's the right word), it makes no difference.......

[sbfluter]

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...

First of all, brilliant post, Doug. It actually made sense to me.

But I think the above quote is sad. Another example of how we bowed down to the electronic gadgetry that's taking over our lives.

--Sincerely, a computer working trapped forever behind a screen...

[Cork]

...monotonically...

I believe you have just coined a new word, but I am convinced that you know whereof you speak.

But where could the modern Irish flute fit in?

Anybody?

[s1m0n]

Also, as an orchestra tunes by ear to an A440 pitch on the oboe..

Why oboe?

[Denny]

'cause it doesn't tune as well as anything else...

[Cork]

Also, as an orchestra tunes by ear to an A440 pitch on the oboe..

Why oboe?

Because, because, because, because, becaaause (to the Wizard of Oz tune).

[Jack Bradshaw]

Apparantly, oboes have a very stable pitch response..ie. they probably can't be retuned.....I remember my roommate in the early 60's, making a xtal controlled oscillator just so he could show his critics in the orchestra that the oboe realy was a pitch standard.......

[Cork]

Apparently there is some agreement, that just intonation and equal temperament are not the same, yet, the question remains, as just where the Irish flute could be tuned.

Just intonation, equal temperament, or both?

[Jack Bradshaw]

Well both, of course ! The "Irish" flute, like the fiddle is capable of both......it's amazing to me that so many flute players have never, NEVER, ever tried pulling the flute into pitch ! I think it's a result of them being taught that it's a fixed pitch instrument..ala Boehm...