Sax on the Web Portal - Re: Thirds
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  • Thirds

    Intervals sound in tune when their ratios are locked at the simplest ration. So, an in-tune octave has a 2:1 ration (i.e. A=440/A=880), a P5 should have 3:2, a P4 4:3, M3 5:4, m3 6:5, etc. Singers and string players do this automatically, making the interval sound 'in tune' is simply removing the beats (difference between the in-tune ratio and the ratio actually being played). For example, if two players are playing a P5 at 660 and 440 hz, then the beats will be absent. If one player is 2 hz in either direction, then 2 "waves" will be heard each second. As Pete points out, if you are playing with piano or another fixed-pitch instrument, then you have to play with equal-tempered tuning. However, in a chamber group of only saxophones, string players, trombones, or other flexible-pitch instrument, we have the option of playing with "just intonation," which pretty much any skilled player will automatically do, whether they realize it or not.

    The piano is a compromise--it sound pretty good in all 12 keys, not great in any. Earlier keyboard instruments were tuned to play beautifully in the key of the piece being played (harpsichord, clavichord). When I play the M3 in quartet, I drop it around 15 cents, and my students are learning to do the same. The minor 3rd needs to be raised by the same amount. If you doubt, here's an experiment. Set your tuner to play 'A-440'. If you're playing tenor, that's your B. Now, play your F#, the P5 above the B. Lock it into tune, and hold it. Now, change your tuner (or tuning CD) to play a concert C (your D). You're now playing a M3--listen and decide for yourself it it sound in tune at that pitch level. Then, drop until the beats disappear. Hold it there. Now, use the needle on your tuner to see where you are playing--it will likely be about 15 cents 'flat'--which in this context means 'in tune'! Then, change the sounding pitch of the tuner, raising it by a half-step. You are now playing the minor 3rd--see what you need to do to sound 'in tune,' which will likely mean moving the pitch up by about 30 cents from where it was in tune as a M3.

    Further details here.
    This article was originally published in forum thread: Thirds started by stradivarius151 View original post
    Comments 9 Comments
    1. SongsMadeForYou's Avatar
      SongsMadeForYou -
      sweet, i used to play mostly piano but i'm into sax right now - yet another reason to be stoked about the saxophone
    1. click's Avatar
      click -
      "I hate and detest pianos. They are mechanical blunderbusses!"
      Professor Theodore von Schwarzenhoffen
    1. nitrosax's Avatar
      nitrosax -
      Yes...the infamous 13.7 cent flat M3...good stuff!

      Rumor has it that much destruction used to happen in the Sinta studio because of trying to tune those intervals back in the day...

      Hope you are well...

      Ryan Knight
    1. furlongjw's Avatar
      furlongjw -
      I was actually going to start researching a reference tonight that I can use for intonation. Any recommendations? I would be interested in reading more about it, but wanted to find a credible reference.
    1. furlongjw's Avatar
      furlongjw -
      I just ordered the JI book. Thanks, I didn't see the link at the bottom until just now.
    1. dougoconnor's Avatar
      dougoconnor -
      Some thoughts on this topic, just to share, I hope it illuminates the subject further for the readers and invites discourse:

      In my experience in school, I've found that brass and wind players tend to hear according to the just intonation system, and that string players tend to hear according to the Pythagorean intonation system. Singers go every which way (a good thing), I find, they are devoting so much thought to spirit, color, imagination, etc.

      Just intonation for strings, it seems from my research, has gone out of favor since its heyday with the Tartini string method (painstaking tuning of thirds and sixths in unison up and down scales). What's interesting to me about Pythagorean tuning, where the M3 is 8 cents HIGH, in fact (to equal temp), is that it works better from a melodic point of view.

      Consider a dominant G7 chord in the final cadence of a C major piece. The B natural is the M3, so the desire for us wind players is to drop that sucker so that it gives us "beatless" smooth tone lock. This is harmonically driven intonation. I still find it hard to let that sound go. Yet that produces an awkward melodic interval going from leading tone B to C, one that singers would typically raise, thereby intensifying the desire for the tonic. This is melodically driven intonation.

      Try it some time and post your observations here. I think equal temperament is just poor for color intervals, but that a WIDE M3 also sounds good, though not as relaxed and smooth as a "just" M3. It's a different function.

      Despite the fact that the two systems have almost directly opposite tendencies (just vs. Pythagorean), my life as a player has gotten much easier having become aware of the way they both surface in music. My current point of view, therefore, is that intonation becomes an artistic choice, understanding that particular placement of a pitch usually favors either harmony OR melody.

      I believe this may be part of what is at the root of the age old, forever incessant arguments about who is in tune and who it out of tune. We wind players play with less vibrato, we love tone, pure unadulterated sound. Just intonation is also seductive in that it offers scientifically "correct" and absolute places to put the pitches. We also have an "unstretched" overtone series. When strings are under tension, it stretches the overtone series wide in a phenomenon called enharmonicity. This is why pianos are not tuned "in tune," and why a tuner with excellent ears is necessary over a machine (because each piano has a different enharmonicity). Because string instruments have this enharmonicity, and because the bowed ones often use a lot of vibrato (instead of pure tone), I'm theorizing that this takes importance away from the harmonic aspect of tuning for them, and also favors intervals that are sharper than we wind dudes are used to.

      Many of my ideas here are inspired by a book called "Exquisite Intonation for Winds, Strings, and Singers: a six-month course" by Theodore Podnor (a violinist). His ideas are often a little radical in this regard, I think, he strongly disfavors the just system which I still find very useful in many places. But as saxophonists, I don't think we hear radically different viewpoints on intonation very often, so this is a fun read.

      At the end of the day, many of the violin and string faculty I've asked about intonation cut right to the chase, "Just play it where it sounds good!" So ends the hunt for an absolute
    1. hanksax's Avatar
      hanksax -
      Thanks to dougoconnor for a very lucid and well written comment. The direction of the phrase/melody is crucial for intonation. Not acknowledged enough, I think.
    1. Ed Geddes's Avatar
      Ed Geddes -
      So this is why experienced, good players say " throw away the tuner". Always wondered.
    1. stevetres's Avatar
      stevetres -
      I think Harmonic Experience by W.A. Mathieu is the best resource for musicians to explore pure tunings. It guides you through the musical and emotional significance of pure tunings rather than just presenting the science.

      http://www.amazon.com/Harmonic-Exper.../dp/0892815604

      Steve T
      www.stevetres.com

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