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Message: 6931 Date: Sun, 22 Jun 2003 12:59:35 Subject: Re: 12 equal to meantone conversion algorithm From: Carl Lumma Pretty simple, compared to this: http://lumma.org/stuff/adaptive.txt * -Carl
Message: 6937 Date: Mon, 23 Jun 2003 10:27:09 Subject: Re: 12 equal to meantone conversion algorithm From: Graham Breed Gene Ward Smith wrote: > I should point out that this is only true if the chromatic scale is > not harmonized. My algorithm, while very simple, does not work on the > crude level of note-for-note, but is based on note-sets. If the > chromatic passage was harmonized in a way which leads back to C, for > instance by C-A-D-cm-C-F-D-G-fm-F-C7-G7-C, back to C we would come. I also have some code for 12-equal to meantone conversions, and I managed to write it without using complex numbers! It's at http://www.microtonal.co.uk/gesualdo.zip - Ok * I don't know how out of date that is, but I do have a more recent version on my Revo. One difference is that I have found passages in Gesualdo that it doesn't convert correctly. There's a total of 3 wrong chords. From what I remember, these can be resolved by using a different gamut depending on whether he used a Bb in the key signature. The gamut restrictions could possible be removed by using a flexible key center. Take everything relative to the average number of steps on the spiral of fifths, calculated recursively as total(n) = k*total(n-1) + note number(n) = k*number(n-1) + 1 center(n) = total(n)/number(n) Then, k=0 means it calculates each new chord looking at only the previous chord, and k=1 makes it remember all previous chords equally, which will give very conservative results. I didn't implement this for the Gesualdo program, because it isn't a rule he was likely to follow, but it might work for an automated tuning program. Graham
Message: 6939 Date: Mon, 23 Jun 2003 13:49:59 Subject: Re: 12 equal to meantone conversion algorithm From: Manuel Op de Coul Have a look at this too: ÖFAI technical reports * Manuel
Message: 6941 Date: Tue, 24 Jun 2003 06:07:59 Subject: Re: Interval Database Experiences From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Porres" <decuritiba@y...> wrote: > I just checked an explanation about continued fractions and it's > amazing, I see you're using convergents and semi-convergents on your > Excell table, it seemed at first kinda complicated, but I guess I'll > dig it... > > but hey, what does it have to do with that pdf file ( Self Similar > Pitch Structures - Clampitt ) ??? I downloaded that once and couldn't > figure it out to, let me dig the traditional harmony first, I'm still > studying Bach's counterpoint technique. Sorry to take so long to reply. It is the same mathematics put to a different purpose. In Clampitt's paper it is applied in the logarithmic pitch domain, whereas you're using it in the linear frequency domain. Clampitt is finding ratios representing fractions of an octave (or other interval of periodicity) (i.e. degrees of equal temperaments) where you are finding ratios representing frequency ratios (i.e. justly intoned intervals when the numbers are small). It's nice that the same mathematical tool has these two different applications to tuning. You might say Clampitt is applying it to melodic properties while you are applying it to harmonic ones. > ha ha ha, good job on your notation research, specially by keeping up > the good humor, since you're involved in Scala, would you know of a > complete table of name intervals? I guess that would be useful... I'm not really "involved in Scala", but the file 'intnam.par' (and its equivalents in other languages) that comes with Scala, is very useful. With a little work it can be imported into a spreadsheet and sorted by interval size or whatever. -- Dave Keenan
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