The note before the note

Every sung note is prepared before it sounds. The breath is taken, the vocal folds come together, the larynx and tongue take a position, and the brain has already formed an expectation of the pitch it is about to hear.

So there is already, in every singer, a note before the note: a predicted pitch. Stage Three asks the singer to make that prediction deliberate, clear and steady, and to start the sound from it.

Inner hearing

These findings do not show that training inner hearing improves singing; the studies are correlational. They do show that the link between hearing a note inwardly and singing it accurately is real enough to be worth training and testing.

The zero point in the sutra’s terms

In the author’s reading, the zero point is “within hearing” before there is anything to hear. The singer has entered the stream of listening (Stage Two) and is not waiting for the sound as an object to be judged. The note exists only as the expectation of a pitch. Then breath and vocal folds are allowed to meet that expectation, rather than the throat being made to produce a result.

The sutra goes on: “the two marks of sound and silence no longer arose”. For the singer, the image is that the silence before the note and the note itself belong to one continuous listening. The note does not break the silence; it appears within it.

The inner fundamental: 432 and 528 Hz

The author teaches singers to keep a fixed inner reference pitch, an “inner fundamental” that they can call up without any instrument, and uses the frequencies 432 Hz and 528 Hz, and the overtones built on them, as images for it. These two numbers carry a great deal of popular belief, so the facts need to be set out plainly.

import math

def cents(f, ref):
    return 1200 * math.log2(f / ref)

A4 = 440.0
def et(n):                      # equal-tempered pitch n semitones from A4
    return A4 * 2 ** (n / 12)

print(f"432 vs A4=440: {cents(432, A4):+.1f} cents")
print(f"528 vs C5={et(3):.2f}: {cents(528, et(3)):+.1f} cents")
print(f"528/432 = {528/432:.4f} = 11/9 -> {cents(528, 432):.1f} cents")
for f in (432, 528):
    print(f, "octaves:", [f / 2**k for k in range(4)],
          "harmonics:", [f * k for k in range(1, 5)])
# 432 vs A4=440: -31.8 cents
# 528 vs C5=523.25: +15.6 cents
# 528/432 = 1.2222 = 11/9 -> 347.4 cents
# 432 octaves: [432.0, 216.0, 108.0, 54.0] harmonics: [432, 864, 1296, 1728]
# 528 octaves: [528.0, 264.0, 132.0, 66.0] harmonics: [528, 1056, 1584, 2112]

The exercises of Stage Three

What the third stage does not claim

It does not claim that any frequency is sacred or healing, nor that inner hearing can replace training the ear with real sound. Inner hearing is built from outer hearing; a singer who has never heard a note clearly cannot imagine it clearly. The claim is that once a note is known, starting it from the inner sound rather than from effort is a better habit, and that this can be measured.

Summary

• Every note is prepared before it sounds: the brain predicts the pitch it is about to hear, and the ear prepares for it.
• Imagining music uses much of the machinery of hearing; vivid auditory imagery goes together with more accurate pitch imitation.
• Stage Three starts each note from a clearly heard inner pitch in the silence before the sound, the “zero point”.
• 432 and 528 Hz are used only as images for a fixed inner reference; there is no reliable evidence that they have special effects, and the experiment in Chapter 8 does not use them.
• That starting from inner hearing improves the accuracy of note onsets is a hypothesis.