<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Hi Kent,<div><span class="Apple-tab-span" style="white-space:pre"> </span>Thanks for sharing this. Very interesting. I hadn't heard about this program, or only very vaguely.</div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>I don't think of a pure 12th as particularly wide as a basis for tuning. Take a 3:2 5th above a 2:1 octave. Tuning conservatively, the 3:2 5th will be about 2 cents narrow and the 2:1 octave will be about 2 cents wide. Result: pure 3:1 12th. Someone looking to increase stretch might shade the 3:2 5th a bit wider, say 1 cent narrow, and shade the 2:1 octave wider as well, say 3 cents wide (meaning the 10th/17th test would have the 17th beating just less than 1 bps in mid range). Not at all unusual, and the 12th will now be wide by 2 cents. With "pure 5ths" as Jim Coleman wrote about a few years back, the 12th will be wider than that. I would say that a tuning based on pure 3:1 12ths in the mid range would be fairly standard sounding, close to the original FAC or an RCT 5 or 6.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>If the 3:1 12ths are used consistently throughout the piano, top to bottom, I would expect the result to be rather more narrow than most of us tune, particularly in the bass. Your samples didn't sound that way in the bass, though I thought the high treble sounded a bit flatter than what I would want personally. I suspect the VTD does a 6:1 19th for the bottom couple octaves or so, based on what I heard.</div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Stopper sounds like he wants to be considered a mysterious magician. Fine, let him. I got to wondering how one might do a 3:1 tuning "on the fly," and came up with a very simple way. Whether it is the same as what he does, I have no way of knowing, but I know with certainty that it would work just fine, and would be easy to set up (for someone who knows how). This is not the easiest stuff to write about clearly, so I'll just do my best and hope it is intelligible.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Start with a spreadsheet of 88 cells (like RCT does, and SAT as well, in the background), one cell for each note. They are set up to have 3rd partial values, except for the top 19 notes, which have 1st partials. They are blank except for D3, which reads zero cents at A4 (the 3rd partial of D3). There are formulae in the background, but only the one actual entered value.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>The software is set up so that the ETD first reads the 1st and 3rd partials of the note played, and compares the two, similar to what we do to set up an FAC tuning on a SAT. 1st partial value is subtracted from 3rd partial value to come up with a difference value. </div><div><span class="Apple-tab-span" style="white-space:pre"> </span>The first note should be between D3 and A4 (it could be farther afield, but that would involve extrapolation, and would yield a less precise A4). For simplicity's sake, let's say we start at D3. The ETD reads the 1st and 3rd partials of D3, calculates the difference in value, and enters that difference as a negative value in the cell for G2 (a 12th below D3, whose value will correspond to the 1st partial of D3. D3's 3rd partial will, by default, be A4 at zero). It then calculates a curve between that number and zero, logarithmically even over 19 steps, and fills in those values in the cells between G2 and D3. We now have a total of 20 cells filled in with actual tuning values. In each case the value is both the 3rd partial of the note to be tuned and the 1st partial of the note a 12th above. This takes less than a second to occur (miracle of modern processor speed), and we proceed to tune the 3rd partial of D3 to A4 at 0 cents.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Tuning upward, play D#3. The difference between 1st and 3rd partials is calculated, added to the value in cell G#1 (which corresponds to the 1st partial of D#3), the result entered into the cell for D#3, and we tune to that value. And so forth up to F6. Above F6, 1st partial values are entered into each cell from the cell 20 notes below (ie, the 1st partial will correspond exactly to the 3rd partial of the note a 12th below. F#6 will correspond to B4, G6 to C5, and so forth up to C8).</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Tuning downward from D3, we already have values entered for 19 notes, so the ETD will be "calculating ahead" for the note a 12th below. Starting with C#3, 1st and 3rd partials are read and compared. The difference is subtracted from the value in the cell for C#3 and entered into the cell for F#1. And so on until A0 has been filled, at which point no more calculation is necessary. If, as would be advisable IMO, we instead want 6:1 19ths in the bass, the task of filling in cells is that much simpler. At whatever point you want that to happen, you simply duplicate the pitch and number value of the note an octave higher (eg, 3rd partial of C3 becomes 6th partial of C2).</div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>I'm afraid statements like "Stopper claims to have a new way for a VTD to deal with inharmonicity that is automatic. He says the VTD display readings are based neither on single-partials nor multi-partials, but rather are based upon a new approach" make me very, very skeptical and wary. Personally, I don't believe in magic. ETDs are based largely on quite simple principles and straightforward math, and they work very well to produce acceptable tunings. I guess I would be willing to say that the system I described above is a way to deal with inharmonicity that is automatic. I'd be very surprised if his system is much different. "VTD display readings are based neither on single-partials nor multi-partials, but rather are based upon a new approach" is pure gibberish to me. If it doesn't compare a measured pitch to a standard in the background (or two or more measured pitches to two or more standards in the background in the case of multi-partials), I, for one, can't imagine what else it would be doing that would be useful in tuning. Measuring and comparing, that's the name of the game.</div><div><div apple-content-edited="true"> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>Regards,</div><div>Fred Sturm</div><div>University of New Mexico</div><div><a href="mailto:fssturm@unm.edu">fssturm@unm.edu</a></div><div><br class="webkit-block-placeholder"></div></div></span><br class="Apple-interchange-newline"> </div><br><div><div>On Sep 29, 2008, at 12:18 PM, Kent Swafford wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div dir="ltr">These tunings were done with Bernhard Stopper's PureTuner VTD; it runs on PocketPC.<div><br></div><div>You need to know just a bit about the software before you can understand why the good results are so interesting. Stopper's tunings are based theoretically on a pure twelfth divided into 19 equal half-steps. This VTD takes no measurements from the piano being tuned in order to calculate a tuning; one just boots up the program, determines a pitch level for the tuning, and starts tuning.</div> <div><br></div><div>Stopper claims to have a new way for a VTD to deal with inharmonicity that is automatic. He says the VTD display readings are based neither on single-partials nor multi-partials, but rather are based upon a new approach.</div> <div><br></div><div>Stopper claims that the results are consistent and superior. He claims that that although the tunings are rather wide, there is an overall, synchronous effect that gives a clean, beatless effect to chords. He claims the software will deliver a best fit tuning for any level of inharmonicity.</div> <div><br></div><div>I have been using the software since June and I am finding that the claims all appear to be true. I offer the recordings of Steinway D and a Bosendorfer Imperial tuned together with Stopper's software as evidence.</div> <div><br></div><div>I admit to some discomfort because Stopper has stated his intention to withhold most explanations of how this all works.</div><div><br></div><div>The bottom line, though, is that the tunings sound good. Good enough for my workplace which is a demanding university environment.</div> <div><br></div><div><br></div><div>Kent</div><div><br></div><div><br></div><div><br><div><br><div class="gmail_quote">On Sat, Sep 27, 2008 at 7:37 PM, Mark Schecter <span dir="ltr"><<a href="mailto:mark@schecterpiano.com">mark@schecterpiano.com</a>></span> wrote:<br> <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">Hi, Kent.<br> <br> They do sound well-matched, especially when you play the chromatic scale; apart from that, it's hard to judge.<br> <br>...<br> <br> Thanks.<br><font color="#888888"> <br> -Mark Schecter<br> </font><br> PS OK, I'll bite. How did you go about it? Thanks!<div><div></div><div class="Wj3C7c"><br> <br> Kent Swafford wrote:<br> <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> I wanted to see if I could improve my ability to tune a Steinway D and a Bosendorfer Imperial together. The Steinway has relatively high inharmonicity and the Bosendorfer has very, very low inharmonicity. Some of you will be familiar with the problem.<br> <br> I have uploaded an audio file to:<br> <br> <a href="http://www.kentswafford.com/mp3/d_dorf.mp3" target="_blank">http://www.kentswafford.com/mp3/d_dorf.mp3</a><br> <br> The recording attempts to show that each piano is well-tuned with itself and that the pianos also are tuned together. The Steinway plays first and should be on the right. The pianos are side by side. There are a number of bad unisons in the high treble, especially on the Bosendorfer. You are welcome to come try to tune them yourself.<br> <br> In the recording you hear:<br> <br> Steinway arpeggios<br> Bosendorfer arpeggios<br> Bosendorfer chord of nature progression<br> Steinway chord of nature progression<br> Chromatic scale played both on both pianos together<br> <br> I think the results are good. How I did this may surprise a few...<br> <br> Later.<br> <br> <br> Kent Swafford<br> <br> <br> <br> </blockquote> </div></div></blockquote></div><br></div></div></div></blockquote></div><br></div></body></html>