Chapter VI: What is Concert Pitch?
In the last chapter we discussed several different tuning systems, and how they came into being. A tuning system fixes the relative proportions of all the intervals in a music scale, but it leaves the choice of absolute pitch free. This absolute pitch, conventionally assigned to the nota A1 (the A above middle C) and given in Hertz is what we refer to as Concert Pitch. In this chapter we will learn what choices for an absolute pitch have been used historically, and what other proponents or alternatives exist today.
You probably have heard the term A = 440 Hz. This is the concert pitch used today, and it means that the note A1 will be tuned to exactly 440 cycles per second, while the frequency of all other notes will be derived by applying equal temperament to this anchor note to either side, higher and lower tones. It is called concert pitch, because setting absolute pitches to all notes to be played makes it possible for many musicians to play the same piece at the same time and in tune.
The difficulty to derive an appropriate concert pitch, however, is that there is no readily available example in nature to use as guidance, as was the case with the relative intervals, which were derived from the naturally occurring harmonics of a tone. There is no hearable, repeatable natural tone that we can reference to. This is why most cultures have been using arbitrary values to use as concert pitch, with some obvious practical problems. And I say most, because some traditions have used the same pitch intuitively for thousands of years. We will deal with this later in the chapter.
Originally, arbitrary choices of pitch posed no major inconvenience, because most musicians made their own instruments and performed them solo. When more than one musician got together and played, stringed instruments could always be retuned on site to match an accompanying fixed tuning instrument, such as a flute or horn. The problems began to become obvious, when music orchestras began to grow in number and more instruments of fixed tuning were being invented and becoming popular. The nuisance became aggravated as musicians began to travel to other cities, where a different local pitch standard prevailed.
In 1711 the tuning fork was invented by John Shore, a British Court musician. This device constructed out of steel produced a reliable pitch every time it was stricken, and it allowed people to “share” a desired concert pitch by producing many identical tuning forks and giving out replicas. But even so, the people that produced or used the forks did not know what exact pitch they were using, they could only tell empirically, that is by auditory comparison, if two forks were tuned to the same note or not. In other words, the fork’s chosen tuning was arbitrary itself, and not inspired by some higher guidance.
Since tuning forks and other sources of pitch reference, such as church organs keep their tuning over extensive periods of time, we can tell today with precision what kinds of frequencies were being used in the West throughout the centuries. The concert pitch for A in pre-20th century Europe varied from place to place and also within the same place with time as much as 2 semitones, roughly between 400 and 450 Hz. Some well known European and American entities and their pitch of choice are listed below.
1699 Paris Opera House 404 1711 423.5 1720 480 1740 Pitch fork belonging to Handel 422.5 1780 Pitch fork belonging to Handel 1780 Mozart's preferred pitch 1815 Dresden Opera House 1820 Westminster Abbey organ 1826 Dresden Opera House 1834 Vienna Opera House 1834 Stuttgart Conference 1859 French Government regulation 1896 British Philharmonic Pitch 1925 American Music Industry 440 1936 American Standards Association 440 1955 International Organization for Standardization 440
Object or Entity
Pitch of A1 in Hz
Original John Shore tuning fork
Organs played by Bach in Germany
409 421 423.2 422.5 435 436.5
440 435 439
Paris Opera House
Pitch fork belonging to Handel
Pitch fork belonging to Handel
Mozart's preferred pitch
Dresden Opera House
Westminster Abbey organ
Dresden Opera House
Vienna Opera House
French Government regulation
British Philharmonic Pitch
American Music Industry
American Standards Association
International Organization for Standardization
As we can imply from the table above, the usage of concert pitch in Europe prior to international standardization was quite arbitrary. Yet if one compares how music sounds with different concert pitches one can sense a clear qualitative difference. Something subtle changes: some tonalities sound pleasing and others sound, as if they were “fake”. While a certain music using one pitch sounds clear and light, using another pitch makes it sound warmer and more centered. Is this a purely subjective impression? Below you can find some examples to make your own conclusions.
Alternate to the seemingly arbitrary development of absolute pitch in the West, a few other proposals of how to anchor the musical scale have called my attention in a rather significant way. A genuine interest started growing in me, to find the optimal tuning pitch to use in music. Quickly I came across the so-called Ancient Solfeggio Frequencies, a set of tones proposed by Leonard Horowitz. Horowitz’ impressive story about how these long-lost frequencies were finally rediscovered was intriguing, but unfortunately I had to scrap its validity fairly quickly, as I confirmed that these frequencies didn’t from a musically harmonious scale of any kind, whether analytically nor empirically, but rather were limited to forming pretty geometrical relationships to one another.
I continued to search for naturally occurring constant frequencies, such as those described by the motion of the planets. The first observation I made, based on the notion of up-scaling the frequencies of rotation of the Earth, originally proposed by Hans Cousto, was that the equivalent frequencies in the hearable range between the rotation of the Earth around the Sun, and its rotation in one day about its axis formed a harmonic interval. The calculation is simple, and is derived as follows:
Frequency of rotation of the Earth in 1 year: Once every year, or fyear = 1 / (365.25*24*60*60 seconds) = 3,17 *10-8 Hz. Applying the 32nd octave to this frequency yields f’year = fyear * 232 = 136.1 Hz.
Similarly the frequency of rotation of one Earth day is calculated by applying the 23rd octave as follows: f’day = (1/(24*60*60)) * 223 = 97.09 Hz. The interval ratio of these two frequencies yields 136.1:97.09 = 1.40, which corresponds to a diminished fifth interval.
Another interesting connection was my discovery that the Tibetan monks always sing their OM mantras in a tone varying little around the up-scaled frequency of the Earth’s year, or 136.1 Hz. I came to this conclusion by listening to all the genuine Tibetan Chants recordings available in the Bavarian State Library (about 10 CDs) and measuring the pitch using a digital equalizer. Not only their voices intonate that frequency, but their monastery bells have also been tuned to this frequency for as old as these well-preserved objects can still be dated and tested today. Furthermore, if you continue to build higher octaves of the OM wave, exactly at the 54th octave you arrive at a wavelength within the visual range of 596 nm. The corresponding color of this octave is a bright orange, which is the color chosen by these very same monks to wear in their robes. Given that the human visual frequency range is very narrow (the complete range of all tones of orange goes only from 585 to 620 nm), that’s a very accurate bull’s-eye hit. That’s when I began to interpret, that perhaps these highly spiritual men had some kind of profound connection to higher design principles that govern the universe; and could somehow intuitively select the right tone to use in chanting, and the right color to wear in clothing, if one wanted to be in total harmony with the planet we all live on. If this wasn’t an accurate intuitive assertion the coincidences would simply be mind-boggling.
Later I came across another popular frequency, also regarded as sacred in some circles, namely the A = 432 Hz tone. I began to take it seriously, when I read that this A was also mentioned by Rudolf Steiner, the father of Anthroposophy. Steiner, who besides being the inventor of Homeopathy was also a philosopher and mystic, proposed the use of C = 256 Hz as concert pitch. This frequency, also referred to during the European classical era as the philosopher's C, is derived mathematically by starting with the number 1 and building the square over and over until it reaches the hearable range. Using Pythagorean tuning, one would arrive at an A located precisely at 432 Hz using Steiner’s proposal.
Much to my satisfaction, I was able to see a further unifying of several alternative pitches into a single musical scale, once I realized that the frequencies of rotation of the Earth, which I had already known to be ‘musical’, fit also astonishingly well in the scale that contain both the C = 256 Hz and the A = 432 Hz. When using Pythagorean tuning, the Earth’s year, which is also the OM of the Tibetan monks, fits as the note C# within only 7.5 cents, and the Earth’s Day fits as the G within 19.6 cents. Keep in mind, that the average person cannot tell that a note is out of pitch below the +/- 25 cent range [source].
Finally, I would like to mention the relevance of the A = 432 pitch from the point of view of Cymantics, which is the study of visible sound through the arranging of a malleable material by means of oscillation. Cymantic analysis of a continuous ascending pitch reveals that when the pitch aligns to any harmonic or sub harmonic of 432 Hz, the geometrical forms display special features of sacred geometry and objective beauty. Dozens of such experiments have been posted informally on the internet’s media sharing platforms, but a formal study performed by the acoustics engineer John Stuart Reid stands out. The following are Reid’s own words about the results:
“ 432 Hertz pops out as a triangle, every time we image it … We concluded that the number 3 was somehow universally connected to 432 Hertz …We captured it on video also and it looks like it's alive, it writhes and pulsates and refuses to take up any other form. We researched the reason why it takes up this geometry and it turns out to be an interesting case: When A is tuned to 432Hz the frequencies of the other A's shift (within a decimal point) to 27 Hz, 54, 108, 216, 864, 1728 in other octaves. D becomes 576 Hz which becomes 9 Hz, 18, 36, 72, 144, 288, 1152 in other octaves. E becomes 324 Hz which becomes 81 Hz, 162, 648, 1296 in other octaves. All of these frequencies are divisible by 3...”
What Reid didn’t mention, was that all those numbers registered during his measurements have a digit sum equal to 9, for example the number 432: 4 + 3 + 2 = 9. Not all numbers, which are divisible by three, have a digit sum of 9; the digit sum of all numbers divisible by three can be 3, 6 or 9. The fact that all octaves of these 432 Hz harmonics add up to just 9 coincides with the sum of the symmetric pure intervals, which also result in the number 9, as discussed in Chapter III.