The Kiss

Here's another term I came up with.

A "kiss" is 256/255 or 1.00392157 or 6.7758758 cents and could be described as a "tempering limit" or a "maximum deviation from just".

If any melodic or harmonic interval is within +/-6.7758758 cents (a kiss) of a good just interval then the interval should be good.

For me all the notes in a scale should go with the tonic (see my post on crows) according to a sweet melodic interval (i.e. 2/x + 2/y >= 0.25) within 6.776 cents accuracy. Say the scale contains a 9/8 and a 7/5. The distance between them is 56/45 (378.60219 cents) which is not a good harmony interval. 56/45 is 7.71152 cents away from a 5/4 (386.31371 cents) interval. 7.71152 cents is greater than the "maximum deviation from just" (6.7758758 cents) so 56/45 is not a good harmony interval and is not close enough to a 5/4 interval to be good.

We could temper the 7/5 and raise it by, say, 3 cents so now the distance between 9/8 and the tempered 7/5 is 381.60219 cents which is within 6.776 cents of a 5/4 (386.31371 cents) interval. So now the 9/8 and tempered 7/5 "meet" (or "kiss") forming a good harmony interval (an approximate 5/4).

When tempering a just scale where all the notes paired with the tonic form sweet (2/x + 2/y >= 0.25) melodic intervals, each note should be tempered by not more than +/-6.7758758 cents (a kiss).

The origin of the kiss is based on an educated guess backed up with listening tests. The educated guess has to do with the fact that powers of 2 occur a lot in my research and seem significant. 256 is 2 to the power of 8.

John.

http://www.johnsmusic7.com