Frequency Systems in Sound Work

When I work on a Sound Journey, I make decisions about frequencies that cannot be seen in the piece: which fundamental, which beating, which tuning. These decisions come from different sources: acoustics, brain research, musical tradition and models of thought that formed in the 20th century. I keep these sources separate here because they have different degrees of reliability. What is physics, I call physics. What is a model, I call a model. And where there is no evidence, I write that down.

A word first about weighting. That something has not been measured does not mean that it is not true. It only means that it has not been measured. Science is one source, tradition is a second, and the experience of many listeners is a third. I let all three have their say here and say each time which one is speaking at that point. What you make of it is up to you.

Brainwave Entrainment

In EEG, frequency components are often roughly divided into delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (around 13–30 Hz) and gamma (over 30 Hz). The boundaries differ depending on the specialist convention. Certain states can be associated with individual bands – for example pronounced slow activity in deep non-REM sleep or alpha during calm wakefulness with closed eyes. No band by itself denotes a particular state of consciousness. The Brainwave Entrainment hypothesis assumes that rhythmic external stimuli can influence neural activity towards their repetition frequency.

Three methods are used for this. Binaural beats arise as an auditory impression when each ear receives a slightly different tone as separately as possible, in practice usually through headphones. At 530 Hz on the left and 520 Hz on the right, a pulsing at 10 Hz can be perceived. Heinrich Wilhelm Dove described the phenomenon in 1839; Gerald Oster summarised it and the state of research at the time in “Auditory Beats in the Brain” in 1973. Robert Monroe was among the early commercial users; his US patent 3,884,218 was filed in 1970 and granted in 1975. Monaural beats are already mixed before they reach the ear and work through loudspeakers. Isochronic tones are tone pulses that are regularly and distinctly switched on and off, or amplitude-modulated. A reliable source for the widespread claim that this term goes back to Arturo Manns in 1981 cannot be found.

Research on the effect is inconsistent. A systematic review by Ingendoh and colleagues (PLOS ONE, 2023) included fourteen EEG studies on binaural beats: five reported findings in line with the entrainment hypothesis, eight contradictory findings and one mixed finding. Because of considerable methodological differences, the question could not be decided. For me, binaural beats are a describable auditory phenomenon and a compositional means. That they reliably pull the brain into a desired band is not established.

Solfeggio frequencies

Horowitz and Puleo published six numerical values in 1999: 396, 417, 528, 639, 741 and 852 Hz. In present-day meditation music, a series of nine with 174, 285 and 963 Hz often appears; when and by whom these values were added is not documented in reliable sources. Within this modern teaching, spiritual meanings are attributed to the numbers; 528 Hz, for example, is associated with transformation.

The earliest reliable evidence found in this research for the series is the book jointly published in 1999 by Leonard G. Horowitz and Joseph Puleo. In it, Puleo reports retrospectively that he had obtained the six numbers in the 1970s through a numerological evaluation of Numbers 7:12–83. Numerology interprets numbers symbolically; it is not a scientific method of measurement. The passage documents the authors’ self-description, not an independent historical tradition.

What medieval solfeggio really is

The solmisation attributed to Guido of Arezzo uses the syllables ut, re, mi, fa, sol and la from the half-lines of the hymn Ut queant laxis. They name positions in a hexachord, not absolute pitches in hertz. The earliest reliable evidence found in this research for the specific modern series of 396 to 852 Hz dates from 1999; it does not belong to Guido’s system. There is no robust clinical evidence for healing effects attributed to the individual numbers. In particular, no corresponding DNA study establishes that audible sound at 528 Hz repairs human DNA. On Weltenklänge I use the numbers as fundamentals, drones or compositional points of reference – not as evidence of effect.

There is no historical evidence for an ecclesiastical prohibition of the numbers 396, 417, 528, 639, 741 and 852 Hz; the earliest reliable evidence found in this research for this series dates from 1999. The hymn to St John the Baptist Ut queant laxis is documented by around 800 at the latest and is therefore older than Guido’s use. In the reform of the missal carried out after the Council of Trent, tropes were removed and the numerous medieval sequences in the Missale Romanum of 1570 were reduced to four. Another reform under Urban VIII had Latin hymn texts and their metre revised; several religious orders did not adopt the versions completely. These were interventions in repertoire and texts, not prohibitions of fixed hertz values.

I work with them nonetheless. In Healing Joy it is 528 Hz, in Lumin Spheres 639 Hz, in A New Dawn 852 Hz. For me, the origin of a number is one question and what I hear with it when composing is another. The series gives me a starting point from which I work my way along when building a piece, and the feedback on these pieces is good. Nothing can be proven by this, and I do not claim that either.

432 Hz and the concert pitch of 440 Hz

A = 440 Hz is not a natural constant, but a historically negotiated technical convention. Before standardisation, pitch standards varied, sometimes considerably, by time, place, institution and instrument. France set A = 435 Hz in 1859; British piano manufacturers agreed on a reference of 439 Hz in 1899. Historical pitch standards were sometimes below and sometimes also above 440 Hz.

An international conference at the BBC headquarters in London recommended A = 440 Hz in 1939. The reasons were a uniform reference independent of temperature and practical advantages in electronic generation compared with 439 Hz. The choice is therefore a convention, but not without reason or arbitrary.

How this came about, step by step

Johann Heinrich Scheibler proposed 440 Hz in 1834. France set A = 435 Hz in 1859, British piano manufacturers agreed on A = 439 Hz in 1899, and the American musicians’ union officially adopted 440 Hz in 1917. The London conference recommended the same value in 1939; ISO R 16 followed in 1955 and ISO 16 in 1975. The standard is a reference and does not compel individual ensembles to use exactly this value. Modern orchestras tune sometimes higher, ensembles of historically informed performance often differently and often lower, depending on the repertoire.

What can actually be calculated with 432 and 440

Joseph Sauveur chose 256 vibrations per second in 1713 for a fixed reference tone in the middle octave, because the octaves can then be represented as powers of two. This choice was later called philosophical or scientific pitch.

With the Pythagorean ratio 27:16, C = 256 Hz gives A = 432 Hz mathematically. In twelve-tone equal temperament, the same C would instead give A ≈ 430.54 Hz. Conversely, A = 440 Hz in equal temperament gives C ≈ 261.63 Hz, with the Pythagorean ratio C ≈ 260.74 Hz. Which number results therefore also depends on the tuning system.

The numerical match at 136.10 Hz

Cousto’s model gives about 136.10 Hz for the Earth year. In twelve-tone equal temperament, C sharp at A = 432 Hz is calculated at around 136.07 Hz and at A = 440 Hz at around 138.59 Hz. The first value is therefore coincidentally very close to Cousto’s calculated value.

This proximity is a mathematical correspondence between Cousto’s octave-doubling model and a Western equal temperament with A = 432 Hz. It establishes neither a fixed frequency of the syllable OM nor a historical connection to Indian music. In Indian art music, the fundamental Sa is chosen to suit the voice or instrument; the other pitches are relative to it.

The numerical match proves neither a health effect nor a traditional OM tuning. For me, it can nonetheless be a compositional point of reference; that is my musical decision, not historical or scientific proof.

Verdi, and what is wrongly attributed to him

432 Hz is often called Verdi tuning. In the 19th century, Verdi supported limiting the rising pitch standard and expressed a preference in 1884 for 432 vibrations per second, above all with a view to uniformity and singing voices. Cosmological and naturopathic interpretations come from later campaigns, especially from the circles around the Schiller Institute since 1988.

What research says, and what listeners say

Two sources, and I take both seriously.

Subjective judgements can be systematically collected in studies. Unstructured feedback from everyday life is, however, more susceptible to selection, expectation and memory effects than blinded, pre-planned comparisons. I nevertheless take the feedback seriously for my musical decision.

That is why I tune many pieces to 432 Hz: I like the sound, the numerical connection is compositionally interesting to me, and the feedback fits my experience. No promise of healing is associated with this.

Planetary tones

Hans Cousto states that he developed the concept of the “Cosmic Octave” in 1978; he published it in detail in 1984. The procedure transfers very slow astronomical periods into an audible range through repeated frequency doubling. An octave corresponds to a doubling of frequency.

The calculation step by step

If a mean solar day is set at 86,400 seconds, 2²⁴ ÷ 86,400 gives around 194.18 Hz. A mean tropical year of about 365.2422 days corresponds to around 31,556,926 seconds; 2³² divided by this value gives around 136.10 Hz. In Cousto’s sound practice, such calculated values are used as tuning-fork, drone or compositional frequencies. Cousto called 136.10 Hz the Earth-year tone or OM tone. This name comes from his modern model and is not a fixed pitch of the Indian OM tradition.

The calculation procedure itself is undisputed; it is only a multiplication by powers of two. What it is not: physical evidence that these tones resonate with celestial bodies or produce a particular effect on people. There is no such evidence. The appeal lies elsewhere: the method gives a composition a point of reference outside one’s own arbitrary choice.

I use the planetary tones nonetheless, and often. In A New Dawn, even the tempo follows the solar frequency of this calculation, and in Visions, Creativity and Deep Relax, the tones are part of the sound image. What this gives me is an order that does not depend on my taste on that day. A piece thereby receives a reference that lies outside me. Whether this reference does anything beyond the calculation, I do not know, and I do not present it that way here.

Further frequencies, briefly

Three further frequency topics at a glance

Schumann resonance around 7.8 Hz. Winfried Otto Schumann described natural electromagnetic modes of the Earth–ionosphere cavity in 1952; corresponding signatures were observed in 1960. The lowest mode is typically around 7.8 Hz and varies with the ionosphere. The electromagnetic signal is not itself audible as sound. If the numerical value is used as an acoustic pulse rate, this is a compositional analogy, not a physical conversion.

Gamma around 40 Hz. Laboratory and early clinical research investigates rhythmic visual and acoustic stimuli around 40 Hz. An EEG response during stimulation is measurable; no confirmed cognitive or therapeutic benefit follows from this yet. For me, the research can be a compositional point of reference, but does not make a recording a treatment.

Tuning systems beyond equal temperament. Just intonation uses selected simple numerical ratios, such as a fifth 3:2, a fourth 4:3 or a major third 5:4. Pythagorean tuning is built above all on pure fifths; its major third 81:64 differs from 5:4. With harmonic sounds, appropriately tuned partials can produce less beating. Which tuning is useful depends on key, harmony and timbre.

How I deal with this

I use these systems because they give me an order when composing and because in working with them I hear something I value. What I do not do is claim that they have been proven. My Sound Journeys are music for meditation and personal development. They are not medical treatment, do not replace a doctor, naturopath or psychotherapy, and I make no promise of healing.