## 11

If you play the resonant frequency of a cancer cell and that same frequency 11 times higher (eleventh harmonic of that resonant frequency) then the cancer cells break. This means that the eleventh harmonic is a destructive harmonic. Skip to 8:50 in this video if you just want to hear about the 11th harmonic.

528 Hz is the 11th harmonic of 48 Hz (48 x 11 = 528). In this audio you can hear how unpleasant this interval is.

The following image is of Ptolemy's intense diatonic scale, which is what equal temp is based on (tuning equal temp to 432 brings you very close to this, with most notes coming within 1 Hz of these frequencies).

From top to bottom the pic shows the 7 notes in the Ptolemy's major scale, do-re-mi-fa-sol-la-ti.

From left to right shows the same scale with higher octaves of 1, 3, 5, 7, 9, 11, 13, 15, 27 and 45 etc as reference pitches.

The ratios on the far left show how the intervals work. For example the ratio between D = 288 and A = 432 is 3/2 (perfect fifth) You can multiply any frequency by the first number in a ratio and divide it by the second to get the new frequency EG: 288 x 3 and then / by 2 = 432. The intervals in this scale are mostly right out of the harmonic series, so most of the notes are also harmonics of the reference pitch for that key.

The colored blocks show shared notes / harmonics. Because notes that share harmonics sound better together than ones that don't, 1 and 3 or 9 and 5 etc will sound good together, but 1 and 11 or 7 and 13 etc will not. You can also see that 27 / 432 is the perfect 3/2 fifth of 9 / 288, which makes it in good harmony with 1 Hz. 396, 528 and 440 are all harmonics of the 11th harmonic of 1, so they don't sound good with the colored blocks. You don't see 7, 11 or 13 in the ratios on the far left, because ratios with them in obviously sound bad.

From top to bottom the pic shows the 7 notes in the Ptolemy's major scale, do-re-mi-fa-sol-la-ti.

From left to right shows the same scale with higher octaves of 1, 3, 5, 7, 9, 11, 13, 15, 27 and 45 etc as reference pitches.

The ratios on the far left show how the intervals work. For example the ratio between D = 288 and A = 432 is 3/2 (perfect fifth) You can multiply any frequency by the first number in a ratio and divide it by the second to get the new frequency EG: 288 x 3 and then / by 2 = 432. The intervals in this scale are mostly right out of the harmonic series, so most of the notes are also harmonics of the reference pitch for that key.

The colored blocks show shared notes / harmonics. Because notes that share harmonics sound better together than ones that don't, 1 and 3 or 9 and 5 etc will sound good together, but 1 and 11 or 7 and 13 etc will not. You can also see that 27 / 432 is the perfect 3/2 fifth of 9 / 288, which makes it in good harmony with 1 Hz. 396, 528 and 440 are all harmonics of the 11th harmonic of 1, so they don't sound good with the colored blocks. You don't see 7, 11 or 13 in the ratios on the far left, because ratios with them in obviously sound bad.

So out of all of the millions of intervals in the universe, 396, 528 and 440 happen to be offset from 432, 288, 512 etc by this precise 11th harmonic... really odd.