Overtone music in 432Hz

Since 1975 the ISO standard 16-1975 is valid (here you can buy it for 40 CHF). It sets the concert pitch a1 at a frequency of 440Hz. As early as 1939, this tuning was agreed upon at a conference in London and endorsed as a recommendation by the ISO in 1955. With its adoption as a standard, unification was sealed, promoting musical exchange, trade of musical instruments and audio equipment.

Already in the 1980s some people rejected the standard and propagated the alternative tuning a1=432Hz. Sometimes there was also talk about “scientific tuning” c1=256Hz – under Pythagorean tuning the two are identical (between c and a there are three pure fifths); under equal temperament a1=432Hz corresponds to a 5.9Cts higher c1=256.86Hz [siehe Anhang unten für mathematische Herleitungen]). These groups are still present today on various websites (e.g. here), Telegram and Youtube channels. There are even apps that let you listen to your own music library tuned down to 432Hz. On the alphorn, the idea has arrived in the form of 432Hz adapters. Question: What to make of this? Here is an overview of the lines of argumentation for 432Hz:

1. Bel canto and historical practice: The first exponents of the 432Hz movement were opera singers. At a well-received Schiller Institute conference in 1988, a baritone and a soprano explained how high pitch posed problems for bel canto. For example, Verdi wrote his music for about 430Hz; register changes and the associated timbre were in harmony with the musical phrases. Unnatural register changes and high pitches over time went to the health of the artists. Over 2’000 well-known artists signed a petition for a lower concert pitch to protect singers and instruments. However, this can best be interpreted as a plea for “historical practice”: historical works should be performed in the tuning and instruments of their time.
2. Scientific oscillations. Accordingly, c1=256Hz reflects frequencies observable in nature. The Schumann Resonance is prominently mentioned. Otto Schumann proved in 1956 that the earth’s surface and the ionosphere form a cavity resonator for electromagnetic waves whose fundamental natural frequency is 7.83Hz. If you octave this frequency five times, you end up with 250.5Hz; this value corresponds approximately to a c1=256Hz. However, the mixing of electromagnetic waves and sound is problematic and the deviation of 37Cts does not fit the idea of pure harmony. The same applies to the observation that DNA emits electromagnetic waves 42 octaves above 256.54Hz.
3. Cosmology: Rudolf Steiner considered music in the context of the non-audible cosmic order. He sees the basic of harmonic tuning in the daily solar cycle. If you increase the basic frequency (1 “oscillation” per day) by 22 octaves, 3 fifths and 2 thirds, you end up with c1=256Hz. Following this logic, the earth hums in a “g” – but not in the ascending pure fifth but in a combination of three fifths and two thirds. This results in a very complicated frequency ratio of 675/512 that can hardly be identified as harmonic(listen here). Similar cosmological arguments can be spun even further. The crucial question remains whether we actually perceive the motion of celestial bodies as oscillations.
4. Numerology: Occasionally a1=432Hz is propagated, because 432 is a “special” number – 4×108! Similar arguments exist for 256. Sometimes a connection to the Fibonacci series is made (neither 256 nor 432 are part of the Fibonacci numbers). All these arguments have a problem in the denominator, though: Hz are based on seconds, and the division of time into seconds is – musically speaking – completely arbitrary.
5. Effect on matter: The oscillation behavior of matter at different frequencies is often visualized(kymatics). The images published by believers of scientific tuning look nicer at 432Hz than at 440Hz. For example, the sun in the cover image of this post is taken from a popular photo, which is supposed to show the water surface at 432Hz. Other visualizations work with sand. However, kymatic images are always the result of the resonant cavity, i.e. depending on the size and mass of the shell/resonant surface, a different frequency will fit.
6. Conspiracy theories: For completeness it should be mentioned here that some exponents reject a1=440Hz because the standard was installed by the Nazis and the Rockefellers for the oppression of mankind. Such conspiracy theories have no historical basis. A brief summary of the history of the adoption of ISO 16 can be found here.
7. Perception and health: The question remains how 432Hz affects people. As early as the 1980s, a study by an anthroposophical researcher showed that most people, in a direct comparison, perceive the same piece in 432Hz versus 440Hz as warmer. The study is still cited today despite numerous methodological problems. Empirically it can be shown that a change in tuning (possibly also a slowing down) is first perceived as positive – 432Hz seems warmer than 440Hz in the first impression, but then 415Hz also seems warmer than 432Hz (note: a change of the concert pitch from 440Hz to 415Hz is identical to a transposition by a semitone downwards – a F horn instead of F#). Furthermore, recent studies show that we have a more accurate pitch memory than previously thought(Levitin effect) and that the preference for any kind of lower pitch therefore also plays outside of a direct comparison. Studies on the processing of music in the brain clearly conclude that intervals dominate in music perception – not a stable effect of temperament. This is also coherent with three millennia of music theory from India and East Asia via Pythagoras to differently tuned alphorns – how could one have determined the frequency before the 20th century? Opinions are also divided on unconscious effects on health. A few (small) studies try to show a positive influence of music in 432Hz on the heart, physiological reactions at the dentist or the subjective satisfaction; however, there are also studies that cannot confirm such a connection. Thus, the only thing that remains undisputed is that the followers of 432Hz subjectively experience more positive sensations when listening to down-tuned music – those who want to believe in this create their own reality.

Somehow this discussion is unsatisfying. The numerous arguments for 432Hz and 256Hz are not watertight. Nevertheless, the idea of a universal fundamental frequency is decidedly intriguing. I would very much like to blow tones on the alphorn in a meditative state, to which the universe and matter resonate in perfect harmony. So let’s put the doubts aside for a moment and assume that there really is a universal harmonic frequency at 432Hz or 256Hz. What would this mean for the alphorn?

432Hz are 32Cts below 440Hz. For this tuning, you have to lengthen the alphorn 1.85% by pulling it apart or using an adapter – an F# horn by 6.5cm, an F horn by 6.8cm. Horns tuned to 442Hz – which is widespread today – have to be tuned down by 40Cts and therefore need a longer adapter (2.3%, i.e. 8cm or 8.5cm). Aiming at c1=256Hz adds another 6Cts (approx. 1.2cm). This results in at least 8 different adapter models! Moreover, to always be in perfect harmony, the alphorn would have to be retuned depending on air temperature and pressure – and then intonated perfectly by the player.

However, this way one has only tuned the concert pitch. Alphorn music consists of the overtones, the frequency of which depends on the fundamental of the alphorn. F is 7 semitones below C. To make it a pure fifth, you could extend the adapter by another 4mm. This would achieve pure intervals for the (notated) C, G and D, but not for the other playable harmonics. The case becomes more complicated with F# horns. The sounding c and a do not occur at all in the overtone series in F#. Thus, on an F# horn with adapter, neither the fundamental nor any other playable overtone has a harmonic relationship to c1=256Hz or a1=432Hz! Even worse: in the cosmological line of argumentation, cosmic register changes are also spoken of; instead of being transposed into harmony with the solar system, the F# horn in a1=432Hz is transposed directly into the meteorite belt according to this anthroposophical logic. Here I see a consistency problem: the 432Hz scene is fixated on the tuning of the concert pitch, but then leaves the questions about pure tuning and keys completely aside. Why should an overtone instrument like the alphorn be tuned to a non-playable concert pitch via equal temperament?!

The alternative to adapters would be specifically built instruments. An obvious solution would be an alphorn in A with tuning a1=432Hz (length about 3m and thus close to many historical alphorns…) or a buechel in C with slightly lower tuning c1=256Hz (a “Sun-Buechel”) or c1=250.5Hz (a “Schumann-Resonance-Buechel”). It would be very interesting to test the effect of such instruments.

Appendix – Mathematical derivations

• In equal temperament, one semitone step corresponds to a factor of 2^(1/12). Therefore from a1=432Hz we arrive at c1=432Hz*2^(-9/12)=256.86Hz.
• One day has 24*60*60=86’400 seconds. If c1=256Hz oscillates 256 times per second, this c1 oscillates 256*86’400=22’118’400 times per day. The conversion into intervals is done by factorization. 22’118’400=2^15*3^3*5^2=2^22*[3/2]^3*[5/4]^2, so 22 octaves, 3 fifths and 2 thirds.
• If c1=256Hz, then you end up 5 equal semitones below at g=191.78Hz. The corresponding g of the earth is 24 octaves above 1 revolution / day, so 2^24/86’400 = 194.18Hz. Deviations in Cts are calculated using ln(F1/F2)/ln(2^(1/1200)). Thus the difference between 194.18 and 191.78Hz is: ln(194.18/191.78)/ln(2^(1/1200)=21.5Cts.
• To calculate the adapters, L_2 =L_1*f_1/f_2. If f_1=440Hz and f_2=432Hz, L_2=L_1*440/432=L_1*1.0185 (i.e. +1.85%).