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Re: tetrachordal similarity at the '+/- fourth/fifth...'

🔗D. Stearns <stearns@xxxxxxx.xxxx>

3/13/1999 2:27:04 PM

I'm wondering what the general consensus is regarding the
effects of fourth/fifth size on tetrachordal similarity at
the fourth/fifth... For example the 5x8x0* where the fourth
is < 2/5ths of an octave and the fifth is > 3/5ths of an
octave(?)

Dan

*C - - - - - 3 0 5
W | | | | | | | |
2/13 h 3/13 - - - - 8 -
W | | | | | |
5/13 - - - - -
W | | | | |
7/13 h 8/13 - - -
W | | |
10/13 - -
W | |
12/13 h C
W h W W h W h W
h W W h W h W W
W W h W h W W h
W h W h W W h W
h W h W W h W W
W h W W h W W h
h W W h W W h W
W W h W W h W h
W h W W h W h W

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

3/16/1999 12:49:06 PM

Dan Stearns wrote,

>I'm wondering what the general consensus is regarding the
>effects of fourth/fifth size on tetrachordal similarity at
>the fourth/fifth... For example the 5x8x0* where the fourth
>is < 2/5ths of an octave and the fifth is > 3/5ths of an
>octave(?)

>Dan

>*C - - - - - 3 0 5
> W | | | | | | | |
> 2/13 h 3/13 - - - - 8 -
> W | | | | | |
> 5/13 - - - - -
> W | | | | |
> 7/13 h 8/13 - - -
> W | | |
> 10/13 - -
> W | |
> 12/13 h C
>W h W W h W h W
>h W W h W h W W
>W W h W h W W h
>W h W h W W h W
>h W h W W h W W
>W h W W h W W h
>h W W h W W h W
>W W h W W h W h
>W h W W h W h W

I think the 462-cent fourths of 13-tET are borderline as regards melodic
acceptability. They're a little worse than the 533-cent fourths of
9-tET, which work OK melodically to my ear (especially with inharmonic
timbres). Harmonically, of course, handle these intervals with care!