Hi Fred Fred writes: ...... 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. I'd say you are absolutely correct. I think you will find that octave types and 12th types have an un-noticed relationship relative to their <<wideness>>. We all know that in general the higher order of octave type you use, the wider the interval... but 12th types fit right inbetween as you go. 2:1, 3:2, 4:2, 6:3, 6:2, 8:4, 10:5, 9:3. Seems to follow that the larger the spread between the to numbers in the ratio of the interval type... the greater the spread. I haven't got this 100% confirmed... but its something I've been noticing more and more. Pocket Tune Labs partial switching button along with my P-12ths template curve makes it real handy to cross check all interval these types on the fly. Its particularly useful in getting a beautiful big base sound to cross check interval types... particularly 4:2 6:3, 6:2 and 9:3. No matter what instrument you have (para-inharmonicity aside) the lower order intervals will tend to converge at a point slightly wide (between a half and one bps) where some higher order will come nearly pure. That tends to be the cleanest bass spread for any piano. On some pianos it will be the 6:3 that is clean... others the 6:2... on big grands down in the lowest bass the 9:3 is my choice quite often. 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. ......... In the US... yeah.. most folks end up stretching the high area way more then this. F6 has its 3rd partial typically around 35 cents offset... which puts C8's fundamental there. For the bass.. Jim Coleman and I exchanged several emails about the narrowness of the 12th in the base when I first put my Tune Lab P 12ths tuning public. Eventually thats what got me onto 12th types instead of octave types. Now I cross check to see that several key interval types are all acceptable. It makes Tune Lab a functional multi-partial ETD really... tho it is set up as a single partial apparatus. A word on our German friend Stopper. He has done some deeper maths to justify the use of the 12th interval quite a ways back... along the kinds of lines of older maths done for different temperaments through time. That said... the basic idea of tuning P-12ths clearly out dates his work. The aural test is the major 6th and the double octave major 3rd. Been around for a long time. I generally run a 5:4,5:3,5:2,5:1 test aurally. With the 5 being the reference note. All 4 should have a similar beat rate with the 5:4 and 5:1 being just a tad faster then the other two, and the 5:2 being even less so faster then the 5:4. This yeilds a very slightly wide 4:2 for the lower pair of the double octave and a consistantly wide 4:1 2:1 for the double octave itself and the higher octave. You can keep an eye on the 4:3 and 3:2 inbetween the lower pair as well as you go if you like. All both easy and quick to do both aurally and using TL's partial switching button. Cheers RicB
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