Hi folks. Been fooling around a lot with Tunelab 97 recently, and have posted a little here and there about it and have the following suggestion / request for anyone who has Tunelab 97 or any other program machine that allows one to do this. Instead of tempering an octave.... I suggest to temper an octave 5th and in the following manner. Tune A4 (1) to 440, and D3 (3) to 440. ie a perfect 3:1 ninteenth. Then sample A4 (3) to get the frequency of its 3rd partial and divide that by 440 and take the 19th root of the quotient. Multiply 440 times this number, gives you the frequency (Hz) of D#3 (3). Repeating this multiplication for each new frequency 19 times will give you frequencies for the third partial for every note from D3 to A4. And I suggest along with this temperament, tuning the rest of the piano so that the perfect 19th is constant over the whole range of the piano. Tunelab 97 allows you to do the temperament automatically by using the Numerical editor. You simply enter the values for 3rd partials of D3 and A4 via the "Add Current Setting to Reference" item under the "Edit" drop menu and then "Set" the tuning with the numerical editor for this range using those two notes. This gives you a perfectly even spaced set of 3rd partials for the range D3 - A4. Since the 3rd partial is one of the two partials we listen too when we establish the beat rates of 3rds, it is really nice to have them evenly spaced. The 4th partial ends up also very evenly spaced in this area of the piano in all but the poorest of quality instruments. The rest of the tuning then is perfectly set up for keeping the 3:1 19ths perfect. This can be easily accomplished by a combination of direct referencing, and using the existing 3rd partials already stored for the "temperament 19th". From A#3 and upwards to E6 simply tune the fundemental to the frequencies stored in tunelab for D#3 (3) - A4 (3). After that simply direct reference the 3rd partial of A#4 upwards to get corresponding fundementals for the remaining treble notes . For the bass, direct reference the fundemental of A4 downwards to get corresponding frequencies of 3rd partials for notes C#3 downwards. You get very fast at doing this with a little practice. The results are astounding, and oddly enough seem to fit extremely well with Virgil Smiths declaration that the "natural beat tuned" octave results in a slightly extended 6:3 octave type, which suggests to me that Virgil relies heavily on establishing perfect 19ths. There is at least one standard ear test for octaves that corresponds to this. That would be comparing the beat rate of a major sixth with the beat rate of double octave major third (common lower note). In anycase... looking at the resulting octaves themselves... they end seem to up with slightly and evenly stretched 2:1's and 4:1's and 8:1s everywhere. I havent looked in detail or plotted this out accurately yet... just watched what tunelab is telling me when I play these relations against any coincident frequency I am working with at any given time. This summer I want to take a day or two and plot out all the relevant frequencies for this tuning and graph whats happening to the 2:1, 4:1, 8:1, 4:2, 8:2, 8:4, 6:3 , 12:6, and the 3:1, 6:2. Any of you who have the time should try this tuning approach. I think you will be very suprised at the clarity of the tuning, and especially of the effect on sustain in the higher treble this particular matching of partials produces. As for general stretch guidlines.. this results in stretch values that are well within reasonable values. C8 (1) typically is around 32 cents sharp... which is what you see in Cyber Ears tunings, and is in each case exactly the sampled result of F6 (3). Give it a try ! Cheers RicB Richard Brekne RPT NPTF Griegakadamiet UiB
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