For Jacky -- ranges of allowable mistuning

Hi Jacky,

I think you asked this before, but it just popped into my mind again, so I thought I'd take another look. Monz, John de Laubenfels, Joseph, Margo and others might be interested too.

According to the corrected van Eck's model, for generalized musical conditions (s=1.5%), the various simple ratios (shown in the center of each line) are the most likely interpretations for the following ranges of interval sizes (the most likely just outside that range are shown in parentheses):

....(22/23)...> -66�<....1/1....> 66�<....(23/22)...
....(25/13)...>1141�<....2/1....>1259�<....(25/12)...
....(26/9)....>1847�<....3/1....>1957�<....(28/9)....
....(27/7)....>2348�<....4/1....>2452�<....(29/9)....
....(13/9)....> 654�<....3/2....> 750�<....(14/9)....
....(17/7)....>1745�<....5/2....>1628�<....(18/7)....
....(13/10)...> 458�<....4/3....> 537�<....(11/8)....
....(17/5)....>2132�<....7/2....>2206�<....(18/5)....
....(13/8)....> 848�<....5/3....> 921�<....(12/7)....
....(11/9)....> 353�<....5/4....> 419�<.....(9/7)....

However, the more "pastelized" the timbre, the more Terhardt's stretching effects come into play, and the more these cents values should be increased by a small percentage of themselves, say 1-2% . . . this latter effect may explain the predilection for stretched intervals among the more "timbrally creative" composers.

Joseph, note that Blackjack can sometimes squeeze more than one different interval between these bounds; so, for example, we have a "just" 4/3 as well as a "sloppy" 4/3 in Blackjack . . .