Touch-Tone Pitches and Intervals

Joseph Monzo: According to the specs of the Intersil GE CMOS=20
handbook (Ivor Darreg, personal communication, 1989) the=20
pitches of the Touch-Tone pads were chosen not to make any=20
harmonic relations. The nominal frequencies are 697, 770, 852,=20
941, 1209, 1336, 1477, and 1633 hz, but the actual ones=20
implemented in chips are 699.13, 766.17, 847.43, 947.97,=20
1215.88, 1331.68, 1471.851, and 1645.01 hz. and these are=20
derived by down-division of an oscillator at 3579644 hz.=20
(The tolerances are all within 1%, but this is about=20
a comma, of course.) Other chips may have different values,
but I imagine all will be +-1% or less of the specs.

Two-Tone Combinations (9 and 16 button boards).

Char's=09Lower Higher=09Cents =09=09Actual

1=09697=091209=09953.50=09=09958.04
2=09697=091336=091126.43=09=091115.54
3=09697=091477=091300.13=09=091288.80
4=09770=091209=09781.06=09=09799.52=09=09=09
5=09770=091336=09953.99=09=09957.01
6=09770=091477=091127.69=09=091130.27
7=09852=091209=09605.87=09=09625.00
8=09852=091336=09778.79=09=09782.50
9=09852=091477=09952.49=09=09955.76
*=09941=091209=09433.87=09=09430.91
0=09941=091336=09606.78=09=09588.40
#=09941=091477=09780.48=09=09761.66

16 button boards:
A=09697=091633=091473.95=09=091481.36
B=09770=091633=091301.51=09=091322.83
C=09852=091633=091126.32=09=091148.32
D=09941=091633=09954.31=09=09954.22


Ivor Darreg presented these as an example of the ubiquity of=20
non-12-tet intervals in our environment and thought=20
that they would aid "detwelvuating" all of us.


To his table of nominal values, I've added a column of cents=20
computed from the actual values on the GE CMOS chip. While=20
some of these intervals are reasonable close to JI values,=20
many are not.=20

Ivor's point was that they weren't very close to 12-tet values either.
I noticed an interesting pattern in the nominal pitches --they fall
rather close to a mildly stretched 14-tet (two sets of 7-tet offset
by 1/14 octave).

Nominal Cents From =09Nominal Cents From
In Hz.=09697 Hz=09=09In Hz=091209 Hz & 697=20
697=090=09=091209=090=09953.50 =09
770=09172.44=09=091336=09172.93=091126.43
852=09347.63=09=091477=09346.63=091300.13
941=09519.64=09=091633=09520.45=091473.95


Fourteen-Tone Equal Temperament on 697 Hz=20
and the TOUCH-TONE Pitches =20
=09
No.=09Cents=09=09Hertz =09=09T-T =09=09Cents =20

0=090 =09=09697 =09=09697=09=090
1=0985.71 =09=09732.38
2=09171.43 =09=09769.55 =09=09770=09=09-1.0
3=09257.14 =09=09808.61=20
4=09342.86 =09849.65=09=09852=09=09-4.8
5=09428.57 =09892.78
6=09514.29 =09938.09=09=09941=09=09-5.4
7=09600 =09=09985.71
8=09685.71=09=091035.74 =20
9=09771.43 =091088.31
10=09857.14=09=091143.55 =20
11=09942.86 =09=091201.59 =091209=09=09-10.6
12=091028.57=09=091262.58 =20
13=091114.29=09=091326.66 =091336=09=09-12.1
14=091200=09=091394
15=091285.71=09=091464.76=09=091477=09=09-14.4
16=091371.43=09=091539.10
17=091457.14=09=091617.22=09=091633=09=09-16.8

Just for fun, I computed a least-squares minimized=20
stretched 14-TT tuning.

Least-Squares Stretched 14-Tone Equal Temperament=20
on 697 Hz Compared to the TOUCH-TON=A8 Pitches =20

No.=09Cents=09=09Hertz =09=09T-T Cents Error =20

0=090 =09=09697 =09=09697=09=090.0
1=0986.68 =09=09732.79
2=09173.36 =09=09770.41 =09=09770=09=09+0.9
3=09260.04=09=09809.96=20
4=09346.72 =09851.55=09=09852=09=09-0.9
5=09433.40 =09895.27
6=09520.08 =09941.24=09=09941=09=09+0.4
7=09606.76=09=09989.56
8=09693.44=09=091040.37=20
9=09780.12 =091093.78
10=09866.80=09=091149.94 =20
11=09953.48 =09=091208.98 =091209=09=09-0.0=09
12=091040.16=09=091271.05
13=091126.83=09=091336.31 =091336=09=09+0.4
14=091213.51=09=091404.92
15=091300.19=09=091477.06=09=091477=09=09+0.1
16=091386.87=09=091552.89
17=091473.55=09=091632.62=09=091633=09=09-0.4


See my article in Xenharmonikon 15 and also Ivor's Xenharmonic=20
Bulletin 12.=20

Given the closeness of 14-tet and the Touch-Tone pitches, for a
conceptual piece, one might play a page from a phone book .


--John