<div>Double octave, yes. But within this, check all the twelfths -- they should be as close to pure, beatless as possible and this will guarantee the right amount of stretch. The test for a perfect 12th is a sixth below the lower note. That is: to test C4-G5, use Eb3 against the C4 (a sixth that beats at the frequency of G5) and Eb against G5 - should beat the same. This will almost always give you an octave stretch that is the sweet spot between 4:2 and 6:3.
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<div>Note - mathematically perfect ET twelfths in a world without inharmonicity would be narrow. Inharmonicity stretches them. The spot of the perfect 12th turns out to be a great choice for the stretch because the 3rd partial is usually very strong.
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<div>Perfect twelfths are also an excellent test up into the high treble.<br><br> </div>
<div><span class="gmail_quote">On 8/22/07, <b class="gmail_sendername">John Formsma</b> <<a href="mailto:formsma@gmail.com">formsma@gmail.com</a>> wrote:</span>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">Comments interspersed.<br><br>On 8/21/07, Matthew Todd <<a href="mailto:toddpianoworks@yahoo.com">toddpianoworks@yahoo.com
</a>> wrote:<br>> I have been really, really studying tonight.<br><br>Good! You will eventually get it if you keep studying the right stuff<br>and apply yourself. I promise.<br><br>> Can someone please explain the system they use to tune 2:1, 4:2 and 6:3
<br>> octaves. I am so close to grasping this concept, but I think I need another<br>> tech to explain it to me besides Reblitz.<br><br>Get someone else besides Reblitz. As was mentioned, Baldassin's On<br>Pitch, the newly revised version, and the PTG Tuning Exam Source Book
<br>were great for helping me understand all this.<br><br>> In the octave interval, if I were to tune a 4:2, the fourth partial of the<br>> lower note theoretically has the same frequency as the 2nd partial of the<br>
> upper note. Do those partials normally dominate each octave? How can I<br>> tell whether to tune a 4:2 or a 6:3?<br><br>Yes, you have a dominant partial pair. Which is why you "normally"<br>tune certain octave sizes in certain places in the piano. The
<br>Baldassin book has a chart that tells which octave size generally fits<br>best.<br><br>However, you must get the best fit for each piano. You can't just<br>begin by tuning a 4:2 plus a little bit in the A3-A4 octave in every
<br>piano, and expect it to be the best. Some pianos will require in<br>between a 2:1 and 4:2, and some pianos might allow for 6:3.<br><br>To help you know what octaves will work with the piano, I find it<br>immensely helpful to start by working within a double octave. You tune
<br>A3-A4 first, then tune A2 from A3. This will help you establish the<br>correct octave width b/c you are using two octaves rather than one.<br>(Otherwise, if you begin with a A3-A4 octave that is too wide, you<br>will end up with bass and treble octaves that beat too much. Working
<br>with a double octave prevents this.)<br><br>What I do is this: Tune A4, then A3. Make it sound the best (you can<br>change it later). Check to make sure it's close to a 4:2 octave with<br>the M3-M10 test (because usually that fits most pianos well). Then
<br>tune A2 from A3, and make it a 6:3 octave using the m3-M6 test. Then<br>you want to use F2 with A2, A3, and A4 to see if those octaves will<br>work for that piano.<br><br>You want to first make sure that A2-A4 is not more than 1 bps. This
<br>is *very* important. Play F2-A2, then compare it with F2-A4. (Listen<br>at A4.)<br><br>Now use F2 to check A4 and A3. F2-A4 will probably be a tiny bit<br>faster than F2-A3. And F2-A3 will probably be a tiny bit faster than
<br>F2-A2. If you have correctly set these octaves, the tuning will fit<br>that piano very well. There may be some strings in lesser pianos that<br>don't fit well, but they will be minimized if you get octaves right
<br>from the first. If you do this on a well-scaled piano, you will be<br>astonished at how good it can sound when you're done. Octaves<br>complement each other, and it is just delightful.<br><br>Clear as mud? Probably. <Grin> Get the books, do the requisite
<br>head-scratching and pulling out. You'll get it sooner or later if you<br>don't give up.<br><br>You will also find there are multiple checks for octaves. The M3-M10<br>is a check for a 4:2 octave. But also another good one is the
<br>"shared" P4/P5 test. Say you're checking A3-A4 to see if it's 4:2. If<br>A3-D4 beats the same as D4-A4, it's a 4:2. HOWEVER, the 4th must be<br>expanded, and the 5th must be contracted for this test to be valid.
<br>So, it would go like this: Expand D4 to get a 4th beating to whatever<br>you can hear well. Then check D4-A4 to see if it's the same. If it's<br>the same, it's a 4:2. If it's faster, you have an octave smaller than
<br>4:2. If it's slower, you have an octave larger than 4:2.<br><br>I like to use this test because it's relatively easy to hear. I find<br>it tricky to know if the M3-M10 beats are the same because of<br>competing higher partials that can fool the ear.
<br><br>Wish we were able to sit down at a piano while explaining this. It<br>would be much more understandable.<br><br>JF<br></blockquote></div><br><br clear="all"><br>-- <br>| || ||| || ||| || ||| || ||| || ||| || ||| || |||
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