> I recall my instructor at the Chatauqua Institution stating that if you >tune beatless octaves above the temperament octave you will automatically >stretch these octaves. >From one who still uses the "human computer" I'm curious. I'm ashamed to >admit I haven't spent much time studying these matters but do you electronic >folks impart a beat to these octaves to stretch them? > >Bob Sadowski >Erie, PA Bob, You're confusing two differerent meanings of "stretch." I like to separate them into "natural stretch" and "artificial stretch." Natural stretch is what happens naturally (!) when tuning beatless octaves. Because piano strings have inharmonicity, the frequency of an upper partial is (usually!) a tiny bit greater than an exact multiple of the fundamental's frequency.. Therefore you "naturally stretch" a coincident partial of another note to meet it. For example, if we tune A4 at the first partial to 440 Hz, its second partial is higher than a simple doubling (880 Hz). Due to inharmonicity, it's maybe at 881. If you tune A3 to A4 using the 3rd:10th test, you're tuning a 4:2 octave (the 4th partial of A3 to the 2nd partial of A4). But the 4th partial of A3 also has inharmonicity, and because it's a higher-order partial it's probably more "off-line" than A4's second partial. Therefore A3 is pushed downwards, even though A4's second partial is pushed slightly upwards. But when we tune the piano we don't have to worry about any of this! If we just tune the octave beatless, it all takes care of itself. This is what your instructor meant. (By far the best demonstrations I've ever seen of this are Daniel Levitan's tuning classes, and the best written explanation is Daniel's series of articles in the Journal a few years back. He writes very clearly and the prop he uses in his class is simply brilliant. As you can tell, I think he's one damn smart guy.) Then there's a second kind of stretch I like to call "artificial" stretch. If you make any interval wider or narrower than its "natural" stretch, you're creating "artificial" stretch. This is what we do when we tune A3-A4 a half beat wide by using the 3rd:10th test and making the 10 a half beat faster than the 3rd. All modern ETDs incorporate both kinds of stretch, albeit in different ways. Reyburn CyberTuner takes care of natural stretch the same way aural tuners do: by matching partials. When RCT takes samples, it records many partials of many notes. For example, it records partials 1, 2, 3, and 4 of A3 and of A4. So when it computes the A3-A4 octave, it simply matches the 4th partial of A3 to the 2nd partial of A4. Bingo au naturelle! To add artificial stretch, RCT gives you several choices. You can click an on-screen button to choose any of ten pre-set overall stretches. For example, if you choose Octave Tuning Style #1 then the A3-A4 4:2 octave will be .20 bps wide, and if you choose Octave Tuning Style #9 then A3-A4 will be .72 bps wide (and the overall stretch will increase proportiionately automatically). If you want even more control of the artificial stretch, you can use RCT's Custom Equalizer, which lets you micro-adjust the stretch of every octave of any Octave Tuning Style by raising or lowering a slider located above A0, A1, A2, A3, A5, A6, or A7 in increments as little as 0.02 bps. For example, in Custom EQ you might first select Octave Tuning Style #5 but want an eensy bit more stretch at A7 and a itty bit less stretch at A3. So you click on the OTS #5 button, then click and raise the slider over A7 till the graph or numbers make you happy, and then click and lower the slider over A3 likewise. Custom EQ's graph can show you the changes you made to OTS #5 and predict interval widths in beats and cents! for various octaves, double octaves, fifths, twelfths, etc. When you're happy, you click the Calculate button and, in less than a half second, RCT calculates an 88 note tuning with the exact stretch you want. Mitch ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Mitch Kiel, RPT authorized Reyburn CyberTuner sales and support 1-888-I-LUV-RCT (1-888-458-8728) 11326 Patsy Drive SE Olympia, Washington 98501 USA email: mitchkiel@olywa.net Visit the RCT Web site at www.reyburn.com
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