Duaine: I remember reading of a set of tuning forks made a century or more ago to use to tune Equal Temperament. Each note was tuned so that there were four beats per second heard between the fork and the note. This got me to thinking and I tried something with a pitch source instead of forks and posted the results on PianoWorld. Hope you enjoy it: (Copied from a PianoWorld post) I worked out the theory for using a guitar tuner to tune the temperament quite a while ago, but only recently have I actually tried it to see if it is feasible. Whether it is practical or not depends on the situation. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ GUITAR TUNER TEMPERAMENT THEORY: The theoretical musical pitches (using the twelfth root of two) when raised a “certain amount” above the pitches necessary for a piano’s iH (inharmonicity) and chosen octave type, or stretch, will produce a beat rate between the raised theoretical pitches and the piano’s stretched pitches that is the same for every note. The “certain amount” that the pitches are raised must result in the difference in cents between the raised theoretical pitches and the piano’s stretch pitches doubling for every octave going down the scale. This will hold true for that portion of the piano that has a linear iH slope and the octave type does not change. By using a theoretical pitch source (a guitar tuner) where the base pitch can be adjusted, this “certain amount” can be found for two already tuned notes, such as an octave, so that they have the same beat speed with the pitch source. All other notes will then be in tune when they also have the same beat rate. These notes need not be fundamental pitches; they can be partials, which is more practical. SEQUENCE: When I tried this I used a Peterson VS-II thru a small amplifier. The base pitch was adjustable to within 0.1 cent. A typical guitar tuner does not have this amount of control or accuracy, but I will address that later. Also, I tuned the temperament octave F3-F4 and judged the beat rate by ear rather than with metronome. (I didn’t expect it to work as well as it did.) The results were fairly progressive M3s. For those that were not progressive, the error was easily determined by listening to the beat rate with the pitch source which on my Walter Console was about 3 bps. Tune A4 to a pitch source (A-440). Tune A3 to A4 for the desired octave stretch. Adjust the pitch source’s base pitch so that it’s A5 to the piano’s A3 produces a beatless 4:1 double octave. Next, compare the pitch source’s A6 to the piano’s A4. Since we are dealing with the 4th partial of A4, every 1 cent difference in pitch will equal 1 bps. The number of bps (and cents) that this 4:1 double octave is narrow is the number of bps (and cents) that this 4:1 double octave will need to be tuned wide. Let’s say it beats 4 bps, which is also 4 cents. By raising the pitch source’s base pitch 8 cents, by either using the controls, or by listening to the beat rate (perhaps with a metronome) an A4-A6 4 cent wide 4:1 double octave beating 4 bps will result. Also, an A3-A5 8 cent wide 4:1 double octave beating 4 bps will result. (It would be best to compare these beat rates to make sure they are equal.) Now all the piano’s notes that are tuned as a 4 bps wide 4:1 double octave to the pitch source will result in the pitches being adjusted for the piano’s iH and the chosen octave type, or stretch. ACCURACY: In order to have progressively beating M3s, each M3 must be no larger nor smaller than about 7/8 cents of the intervals chromatically above and below it. So in order to guarantee progressively beating M3s, each note must be tuned to within about 0.2 cents of ideal. If the pitch source does not have an accuracy of better than 0.2 cents, progressive M3s cannot be expected without later refinement. If the base pitch of the pitch source cannot be adjusted to less than 0.2 cents, then if all notes are tuned to the same beat rate, the M3s at the end of the octave cannot be expected to beat progressively. However, by using a beat rate that is interpolated between the beat rates for A3-A5 and A4-A6, there can be less inaccuracy. This would be appropriate for a common guitar tuner that has an adjustment of 1 Hz at A440 (about 4 cents). Since we are dealing with the fourth partial A3 thru A4, ½ bps thru 1 bps will equal 1 cent error. So, 1/10 bps thru 1/5 bps (or 1 beat in 10 thru 1 beat in 5) accuracy is needed to guarantee progressive M3s. A metronome might be useful. There is also the possibility of errors at wire gauge changes. PRACTICALLITY: This may be just trivia to some, a mere curiosity or even nonsense to others. But I do have a limited use for this technique because I do not use an ETD. I would probably try this if I needed to tune a non-ET temperament. The VS-II has a number of pre-programmed UTs and any others could be tuned by using offsets. Those that want to set a temperament electronically but do not want to look at an ETD (or are visually impaired and can’t) may want to try this technique. Also, this technique is not restricted to starting with an octave, since all notes beat the same with the pitch source. If a perfect fifth or twelfth or whatever tuning is desired, this can be accommodated by using the twelfth root of two times the number of half-steps in the interval to determine how high the “certain amount” that the pitch source’s base pitch must be raised. Or it can be determined thru trial and error by comparing the beat rates of the two notes of the interval with the notes of the pitch source, which should be checked anyway. There is one reservation I have about this technique. It may be allowable and effective in the PTG mid-range exam. Even if it meets the letter of the exam, I don’t think it would be in the spirit of the exam. On Fri, Feb 27, 2009 at 10:18 PM, Duaine & Laura Hechler <dahechler at att.net> wrote: > I think I can probably do the rest. But what about setting the > temperament with tuning forks ? > > -- > Duaine Hechler > Piano, Player Piano, Pump Organ > Tuning, Servicing & Rebuilding > Reed Organ Society Member > Florissant, MO 63034 > (314) 838-5587 > dahechler at att.net > www.hechlerpianoandorgan.com > -- > Home & Business user of Linux - 10 years > > > -- Regards, Jeff Deutschle Please address replies to the List. Do not E-mail me privately. Thank You.
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