source file: m1380.txt Date: Thu, 9 Apr 1998 09:34:34 -0700 (PDT) Subject: Touch-Tone Pitches and Intervals From: John Chalmers 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