source file: m1443.txt Date: Wed, 10 Jun 1998 16:59:19 EDT Subject: Goofed instructions to piano tuner yield instructive demonstration From: I asked my piano tuner to give me a mathematically accurate quarter comma mean tone E5 above A 440 to record for demonstration purposes before tuning it to a just fifth E 660, as I wanted to demonstrate the contrast between a just fifth and a tempered fifth. My thought was that the demonstration would substantiate the idea that tempering the fifth 5.4 cents flat would leave its character essentially intact. He was working with his frequency meter and I said: "The E is 5.4 cents flat". He set his meter to minus 5.4 cents and was working his tuning hammer this way and that as strobe lights on his meter would rotate first clockwise and then counterclockwise. Finally he got the E pretty well at the -5.4 cent point and played the A 440 - tempered E 660 fifth. As I heard it - with its disappointingly off sound - I felt a wave of discomfort. I hadn't thought a quarter comma mean tone fifth sounded that bad. My piano tuner, a twelve equal temperament fan, said: "Whew!". Then I began speculating as to why, in this situation, the tempered fifth sounded so bad. Perhaps it was because not all three unisons were being used. So he tuned the other E 660 unisons and the fifth continued to sound "off". I'd heard this "off" sound quite a lot with my quarter comma mean tone tuned piano, and I'd felt that when strings went slightly out-of-tune in such a direction as to make a tempered fifth even flatter, it didn't take much to make it sound "off". But if the tuning was accurate, the 5.4 cent flat fifths sounded to me like acceptable fifths as long as I didn't listen too critically to them. I thought: "Well, I guess they sound worse than I'd thought. If that's the way they sound, that's the way they sound, and that's what I'll demonstrate to the music students." Then the thought hit me - "The frequency meter reads minus 5.4 cents, but that's 5.4 cents less than the EQUAL TEMPERAMENT frequency for the E5, which is ALREADY tempered close to 2.0 cents flat! I felt a sense of relief and asked him to set the E to minus 3.4 cents, which he did. He played the less tempered fifth again and it sounded "right" for a quarter comma fifth to me - just barely OK. By that I mean that when I hear it, it has that feel of a musical, significant fifth with some kind of emotional impact. One knows it's "tempered", but it doesn't seem to have lost too much of its character. The 7.4 cent flat fifth, on the other hand, sounded immediately recognizable to my ears - and my piano tuner's - to be "off". What this inadvertent lesson brought home to me was something I'd already come to believe - that pitch differences as small as 2 cents on an instrument such as the piano can make a significant difference to the character of a musical interval's sound. When he tuned the E5 to a pure fifth above A 440, setting his frequency meter to plus 1.9 cents, the pure fifth on the piano really sounded good. As he was getting close, I found myself wanting to hear the E sharper and just a bit sharper, etc. Then it sounded really good. I didn't place that fifth next to an equal tempered fifth, but will do so when I prepare the demonstrations in my computer. I'm pretty sure, though, that the just fifth really does sound different than a fifth which is only two cents flat. He also tuned the C sharp 5 to both an equal tempered third above the A4 and to a Pythagorean third +7.8 cents on his meter while the E was a just fifth above A4. On the piano, the Pythagorean third sounded stranger and more inharmonious than an equal tempered third. The just triad on A4 which I played and recorded (other piano strings damped) sounded really good - sweet and high and bright. The Pythagorean triad on A4 sounded - to me - really strange - not terrible, but quite strange. What I'm learning with the piano is that in some cases, quite small changes in pitch can appreciably affect a chord's character. Note: I've had the piano in quarter comma mean tone temperament for about six months and have been playing it a lot, practicing and improving my piano technique. Yesterday, after setting the demonstration fifths and thirds to be recorded then, my piano tuner put the piano into sixth comma mean tone temperament. It will be in that tuning for a week while I make comparison recordings of pieces I've already recorded in 1/4 comma mean tone temperament. Then next week he'll tune the piano to equal temperament so that I can make comparison recordings of these numbers in equal temperament. Soon after that, he'll return the piano to 1/4 comma mean tone temperament, which I find very enjoyable to play. Dave Hill, La Mesa, CA