RE: Microtonal phones

> -----Original Message-----
>
> From: monz@juno.com (Joseph L Monzo)
> Subject: Microtonal phones
>
> Just thought I'd mention this, since it
> seems we're trying to document all the
> places where we're hearing microtones:
>
> The tones which sound when you press
> numbers on the keypad of a touch-tone
> phone are in ratios. I had figured them
> out once, because their arrangement into
> dyads follows a geometrical pattern
> across the keys, but they were never
> written down.
>
[Loffink, John]

The phone frequencies, known as DTMF, are combinations of two tones as
follows:

freq1, freq2, ratio
'1' 697 Hz, 1209 Hz, 1.73
'2' 697 Hz, 1336 Hz, 1.91
'3' 697 Hz, 1477 Hz, 2.12
'4' 770 Hz, 1209 Hz, 1.57
'5' 770 Hz, 1336 Hz, 1.73
'6' 770 Hz, 1477 Hz, 1.92
'7' 852 Hz, 1209 Hz, 1.42
'8' 852 Hz, 1336 Hz, 1.57
'9' 852 Hz, 1477 Hz, 1.73
'*' 941 Hz, 1209 Hz, 1.28
'0' 941 Hz, 1336 Hz, 1.42
'#' 941 Hz, 1477 Hz, 1.57

The intervals are:
phone closest 12TET
1.28 1.26
1.42 1.41
1.57 1.58
1.73 1.68/1.78
1.91 1.88
2.12 2.12

I don't have a table of intervals handy, but from the above info the only
improvement I see over 12TET are closer approximations to 5/4 and 7/4,
though still not exact.

John Loffink
john.loffink@compaq.com