Question for Monz

Monz-

Is there a generally accepted term for the small intervals (analogous to
commas) formed by the difference between, for example:

(6/5)^6 and 3 (six JI minor thirds and a 3rd harmonic)?

or

(6/5)^5 and 2.5 (five JI minor thirds and a 5th harmonic transposed an octave
down)?

or

(5/4)^8 and 6 (eight JI major thirds and the 6th harmonic)?

or

(5/4)^4 and 1.2 (four JI majot thirds and 6/5)?

Just curious, and didn't see them any known place (e.g. 'comma') in your
dictionary....

Best,
Aaron.

--
OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'

hi Aaron,

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:

> Monz-
>
> Is there a generally accepted term for the small
> intervals (analogous to commas) formed by the difference
> between, for example:
>
> (6/5)^6 and 3 (six JI minor thirds and a 3rd harmonic)?
>
> or
>
> (6/5)^5 and 2.5 (five JI minor thirds and a 5th harmonic
> transposed an octave down)?
>
> or
>
> (5/4)^8 and 6 (eight JI major thirds and the 6th harmonic)?
>
> or
>
> (5/4)^4 and 1.2 (four JI majot thirds and 6/5)?
>
> Just curious, and didn't see them any known place
> (e.g. 'comma') in your dictionary....

the first two are examples of the "kleisma":

http://tonalsoft.com/enc/kleisma.htm

<2, 3 5>-monzo

< 0, 1 0> = 3
< 6, 6 -6> = (6/5)^6
----------
<-6, -5 6> = kleisma

<-1, 0 1> = 5/2
< 5, 5 -5> = (6/5)^5
----------
<-6, -5 6> = kleisma

in the third example, you really meant to increase
the 6/5 by an 8ve:

<-8, 0 4> = (5/4)*4
< 2, 1 -1> = (6/5)*2
----------
-10, -1 5> = magic comma

that third one is an example of the "magic comma" or
"small diesis":

http://tonalsoft.com/enc/diesis.htm

(definition #4. "magic comma" really deserves its own entry.)