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Well temperaments


There are plenty of well temperaments based on twelve notes per octave, such as Young and Werckmeister, which may have inspired 12-EDO in the western world.  But has anyone worked this spirit in reverse to develop microtonal tunings that have well tempered characteristics?  For example, taking 19-EDO and sweetening certain intervals in some keys at the expense of others in order to obtain a more colourful sound when modulating.

If none of these exist to our knowlege, perhaps we can develop something like that here - theoretically, of course.

Yes this has been the subject of discussion for about 15 years now on the Tuning list on Yahoo. MOS scales, or rank 2 temperaments which we credit Ervin Wilson with are the "new" temperaments involving 2 step sizes for the scale.  Paul Erlich and others expanded Wilson's ideas in a paper "P. Erlich, A middle path between just intonation and the equal temperaments, Xenharmonikon 18 (2006), pp. 159 199." which details a large list of temperaments which have been made scale charts in my microtonal guitar books. For example in 19-EDO there is Magic, Liese, Negri, Flattone (meantone), Sensi, and many more.
Gene Ward Smith is also toiling away at the Xenharmonic wiki. This will tell you all you need to know...

Pretty much all the 2-step MOS scales have been named already... up to like 200+tet ...Where we're at now, is rank 3- with 3 interval sizes. In order to get these you need to change the dimensionality of the 5 limit lattice.. the rank refers to the number of generators basically--  if you can figure out how to create rank 3 scales that actually happen to have only 3 notes, you're smarter than pretty much everyone right now. ahaha ...

Thanks, Ron.

I would much like to hear such tuning in action.


--- Quote from: bostjan on July 25, 2011, 10:10:23 AM ---Thanks, Ron.

I would much like to hear such tuning in action.

--- End quote ---

yo yo

There are some sick musical examples - all you ahve to look for is the new temperament you wanna hear... so say you want to hear what "Hanson" temperament sounds like - which is another term for kleismic temperament. - the tuning-list chose Hanson to honor the late Larry Hanson I believe... There is more to it than that, but thats basically it.... so you search Hanson temperament, or perhaps Hanson comma pumps... then you will find the new progressions, buried in there, the scale itself is fun, but the comma pumps really use the scale to make "new" progressions which sound tonal and natural.

so here you go -

"In this system, rather than 4 minor thirds landing you at the octave, 6 minor thirds lands you at an octave + a fifth. The minor thirds in this system are even closer to the harmonic series than the familiar ones in 12-equal, which contributes to the "bright" feel of this tuning. Don't think too much about the name "Hanson.""   

notice how the new interval sizes / generators lead to different harmonics and map them in different ways

here are more, as well as another hanson example to feast your ears upon.

I actually tried this with scala once.
I made a 19-tone meantone tuning, with a fifth of 696.5c as a generator, with 12 or 13 up from the starting note and 12 or 13 down, and tempered the overlaps to a unison. The nice thing about it was although it sounded different in each key, the 'detuned' distant fifths weren't that far off from the 'generator' ones so it was still very consonant and 'nice' sounding.


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