TUNING TEMPERAMENTS (A4=440/435/430.5/415HZ) by Roel Hollander

HOW DID A4=440HZ BECOME A STANDARD?
Before concert pitch A4=440Hz became the tuning and manufacturing standard for instruments, there was no (International) Standard Pitch. But, we can find the following historical references concerning 440Hz as Concert Pitch, predating the standardization if this Concert Pitch:

1834 — The Stuttgart Conference (a Congress of Physicists — “Deutsche Naturforscherversammlung”) adopts Scheibler’s recommendation for A4=440Hz as the standard pitch (the Stuttgard or “Scheibler pitch”), based on Johann Scheibler’s studies with his Tonometer. It consisted of 52 forks tuned from A 219 2/3 to A 439 1/2 at 69 degrees Fahrenheit. The device and his amazingly accurate method of measuring beats were described in Scheibler’s book “The Physical and Musical Tonometer”. It is not unlikely that the “Streicher Piano Company” adopted Scheibler’s recommendation for A=440 shortly after the Stuttgart Congress.

1836–1839: A= 441, Paris. Opera pianos. Tuning fork owned by M. Leibner who tuned the pianos of the opera at the pitch of the orchestra. In 1849 it agreed precisely with the oboe of M. Vorroust.

Date unknown. A=440.5, Paris. Opera. Fork said to have been adjusted by Pleyel.

1845 A=439.9, Turin Italy. Tuning fork.
1859 A=441, Dresden. Opera. Tuning fork sent to the French Commission by Kapellmeister Reissiger, who wrote: The great elevation of the diapason destroys and effaces the effect and character of ancient music, of the masterpieces of Mozart, Gluck and Beethoven.

In 1862 German physician and physicist Hermann Ludwig Ferdinand von Helmholtz, publisched his work “the Sensations of Tone as a Physiological Basis for the Theory of Music”. In this work Hermann Helmholtz refers to A at 440Hz several times.

In 1880 Alexander Ellis wrote an important essay “The History of Musical Pitch” for the Society of Arts in London. Ellis cites early research on the measurement and history of musical pitch in the work of the German physicist Johann Heinrich Scheibler (1777–1837). Ellis’ research suggests that there was a connection between Scheibler in Stuttgart and the piano maker Johann Baptist Streicher in Vienna. A tuning fork with the name “Streicher” written in ink on one of the prongs and measuring A=443.2 was found in Scheibler’s collection of forks after his death.

1896 — Britain’s Royal Philharmonic starts using A4=439Hz.
In 1926 the American music industry reached an informal standard of 440 Hz, many did use it already before, now pretty much all were using it in instrument manufacturing. (No supporting documentation found).

1939 — The majority of attending members at an international conference in London supports A4=440Hz. (Note: no supporting documentation found).

1955 — International Organization for Standardization adopts A4=440Hz. (Note: no supporting documentation found).

1975 — The International Organization for Standardization affirms the International Concert Pitch A4=440Hz under ISO 16:1975.

“DIAPASON NORMAL” (A4=435Hz)
The only official (law binding) National concert pitch close to 432Hz, was a concert pitch called “diapason normal” at 435Hz. In 1859 (February 16), the French government passed a law to set the National Standard to A4=435Hz.

Some of the first references* to 435Hz are:

Around 1825–1830, A=435Hz. Dresden. Tuning fork owned by Kapellmeister Reissiger.

1859 A=435Hz, Karlsruhe, Germany. Pitch at the German opera. Kapellmeister Jos. Strauss felt that this pitch fatigued his singers the least and was the best pitch for the performance of operas from all periods. Strauss’ fork became the pitch standard for the French Commission’s Diapason Normal.

1859 A=435.3Hz, Paris. Fork representing the French Commission’s Diapason Normal Pitch. Presented by the Commission to John Broadwood & Sons Piano Co. in London.

1859 A=435.4Hz, Paris. The French Commission Diapason Normal as actually constructed by Secretan and preserved at the Paris conservatory.
In the United States this pitch was sometimes called “International pitch.” It was recommended by Chickering in Boston as the ideal pitch for tuning Chickering pianos.

1859 A=435.34Hz Paris. Secretan made a dozen tuning fork copies of the French Diapason Normal. Excluding one of these forks which is clearly too flat, A=435.34 is the general average pitch of the other eleven forks.

Close to 435Hz (+1Hz / -1Hz) are:

1829 A=434Hz, Paris. Tuning fork used by the piano maker M. Montal.
Around 1834 A=434Hz, Paris. Pitch of the Paris opera.
Around 1834 A=433.9Hz, Vienna. Orchestra fork measured by Scheibler and referred to as “Vienna minimum.”

1878 A=436Hz, London. Standard pitch of church organs taken from Metzler’s tuning fork.

415HZ — BAROQUE PITCH “STANDARD”
Baroque music is a style of Western art music composed from approximately 1600 to 1750.

The most popular Temperament of that era was Equal Temperament, but various composers did experiment with other Temperaments as well, J. S. Bach for example wrote The Well-Tempered Clavier to demonstrate the musical possibilities of well temperament.

Only since the invention of the Tuning Fork in 1711 (late Baroque period) by trumpeter John Shore there was an easy reference tool for setting the pitch.

Old historical pitch forks provide now physical references to the various pitches used in the past globally. Edward E. Swenson made a list with old historical tuning forks that have been preserved.

According to various sources (including Wikipedia, www.baroque.org, Philharmonia Baroque Orchestra, et cetera) A4=415Hz was the pitch “standard” used for Baroque music during it’s era, roughly a semitone lower than the modern standard concert pitch of A4=440Hz (440Hz — 100 cents = 415.3046975799438Hz).

An accepted exception is for French baroque repertoire, which is often performed with A4=392Hz, approximately a semitone lower again.

A high Concert Pitch would require high tension on strings of chordophone (string) instruments (the main instrument group for Baroque music).

High-pitched strings vibrate faster, generating brighter but “thinner” sound. The low 415Hz pitch generated a warmer, fuller tone relative to other (higher) pitches used around that time.

Another reason mentioned for using a low pitch was related to the design of a characteristic Baroque instrument used: the Harpsichord. This instrument was entirely made from wood. If the tension on the strings would be set too high, the pressure on the wood-work could “deform” the instrument.

One of the reasons why 415Hz as Concert Pitch was used during the Baroque era was related to the desired timbre and the design of the instruments used.

But, not only classical composers and musicians were aware of the change of timbre. In the more resent history some great artists have tuned their instruments a semitone down to change the timbre of their instrument while still being compatible with the 440Hz standard.

One of these artists that used the “Baroque Pitch” was Jimi Hendrix. Another famous band that applies that does pitch their instruments a semitone down, is U2. Some guitarists and bassists refer to it as “E♭ (E‐flat) tuning or D♯ (D‐sharp) tuning”.

SHOULD YOU USE CONCERT PITCH A4=415HZ?
It is important to keep in mind that the change of tonality AND timbre by lowering the pitch with a semitone, does work with acoustic and electric (amplified) instruments best.

Strings for example oscillate with a lower pitch at a lower rate and the body of the instrument would thus vibrate and resonate with this lower rate as well.

If you want to perform the work of for examle Jimi Hendrix or U2, or perform the work of the great classical composer from the Baroque era, then it would be a logical decision to use this Concert Pitch.

With electronic instruments or sampled / recorded material ONLY the tonality would change (A4=415Hz would now simply sound pretty much the same as the Ab would sound if A4=440Hz would have been used).

Yes, the whole piece of music would sound a semitone lower (and that could slightly effect the overall room sound a bit different due to the response of the acoustic of the surrounding space), but the timbre would not really change and that is what the changing of pitch is mostly about.

THE “SCIENTIFIC PITCH” (C4=256Hz)
WHAT IS THE “SCIENTIFIC PITCH”?

Scientific pitch, also known as philosophical pitch, Sauveur pitch or Verdi tuning, is an absolute pitch standard that sets middle C (or C4) to 256 Hz.

All the octaves of C are an exact round number in the binary system. For example, this frequency for middle C, 256 Hz, can be represented by (100000000)two.

More usefully, the octaves of C remain a whole number all the way down to 1 Hz (in either counting system).

C4=256Hz was first proposed in 1713 by French physicist Joseph Sauveur, promoted briefly by Italian composer Giuseppe Verdi in the 19th century, then advocated by the Schiller Institute beginning in the 1980s.

“HISTORICAL FACTS ABOUT THE SCIENTIFIC PITCH C4=256Hz?”

In the list below, I have listed references about A4 = 340Hz / 341Hz. As noted above, A4=430.5Hz (aprox.) if C4=256Hz.

Between 1690’s and the early 1700’s, French acoustic physicist Joseph Sauveur first researched then proposed the “philosophical pitch” or “scientific pitch” (C4=256Hz) standard.

Ernst Chladni (1756–1827), the leading acoustician in his time, defined defined C=256hZ as the scientific tuning in his textbook on the theory of music.

c.1810 A=430.0, Paris. Tuning fork belonging to M. Lemoine, a “celebrated amateur.”

In 1885 Giuseppe Verdi proposes the use of the Scientific Pitch (C4=256Hz) as new standard at an conference in Vienna without success.

In 1988 the Schiller Institute initiated a campaign to make the “scientific pitch” (C4=256Hz) the new Standard Concert Pitch.

SO, WHY LOWER THE CONCERT PITCH? (CONCLUSION)

From all I have read and checked I think that there are two things we have to look at: “What changes at the source?” and “How does these changes at the source effect the surrounding space?”.

CHANGES AT THE SOURCE
For some instrumentalists a lower pitch could make a performance easier.

A lower pitch would mean less tension on the strings of an instrument (and vocal chords as well), there for less “energy” is required to set the source “in motion”.

Lower tension on a string would also mean that you could pull a string further up, with other words you have more flexibility to pitch-up a tone.

A lower pitch would also mean a possible difference in natural frequency response, generating difference in resonance of the instrument itself.

Due to the change of resonance of the instrument the “timbre” could change as well (also depending on the material the instrument is made of and the vibratory nature of that material).

Low frequencies do not displace as much energy as high frequencies do, but they contain the energy better.

By lowering the pitch the vibration and resonance within the instrument and the air in resonators could lasts longer.

THE EFFECTS ON THE SURROUNDING SPACE
As mentioned earlier in this article we know that high frequencies tend to “bounce of” anything in their path, while lower frequencies tend to “bend around” those objects.

Even though the difference between using Concert Pitch 440Hz or 432Hz is relatively small, the “reflection” of sound from the objects it is surrounded by and the room (where the the source is in) is a little less.

This is most clear with the hi-end frequencies like for example hi-hats and cymbal splashes.

In particular in places with a lot of hard surfaces (concrete, glass, et cetera) a (small) difference in reflection, absorption and resonance can be heard.

In the open air the difference in reflection and resonance between using Concert Pitch 440Hz and 432Hz is not really detectable though.

When using powerful sound systems or loud acoustic instruments, a part of the vibrations generated with that sound system or instruments might find resonance in the room where the sound is generated.

The natural frequencies of the matter of this this room might resonate differently.

After all, lower frequencies generate less energy displacement then high frequencies do, thus a little less response in resonance from the natural frequencies of the room.

HOW LOW SHOULD YOU GO?
Well, you might like to try 435Hz (Diapason Normal) or 432Hz … or lower?

I suggest you start exploring the options yourself, at the end music is about you expression yourself the way that suits you best, right?

I will though sum-up a few low pitches used in music history, you can start your own “research” from there …

THE HISTORICALLY LOWEST MENTIONED PITCH USED FOR A4 (AT 360HZ)
If we take a look at the last couple of centuries we notice pitches as low as A4=360Hz (English pitchpipe organs) have been used.

To put that in perspective: 370Hz is exactly to 3 semitions (300 cents) below 440Hz.

THE “BAROQUE PITCH” (A4=415HZ)
This pitch was commonly used during the “Baroque period” (1600–1760). 415Hz is 101 cents or 1.01 semitone below the present 440Hz standard.

With other words, Concert Pitch 440Hz is 415Hz transposed a semitone up. A4=415Hz as Concert Pitch might be an option when using acoustic instruments (due to differences in resonance and timbre).

When using electronic instruments this pitch-shift is useless (see information earlier in this article).

THE “SCIENTIFIC PITCH” C4=256HZ (A4=430.5–432HZ)
Also known as also known as philosophical pitch, Sauveur pitch or Verdi tuning, was first proposed in 1713 by French physicist Joseph Sauveur, promoted briefly by Italian composer Giuseppe Verdi in the 19th century, then advocated by the Schiller Institute beginning in the 1980s.

All the octaves of C are an exact round number in the binary system. The exact pitch of A4 depends on the Temperament you use.

If you use Equal Tone Temperament we find A4 at 430.5Hz, but if you use the Pythagorean Temperament you will find A4 at 432Hz.

Other Temperaments could generate different results for the exact pitch of A4 when using C4=256Hz as Concert Pitch.

THE “DIAPASON NORMAL” (A4=435HZ)
In 1859 (February 16), the French government passed a law to set the National Standard to A4=435Hz, the only official (law binding) National concert pitch in recorded history.

ARE THERE ANY DISADVANTAGES USING A LOWER PITCH?

Unfortunately YES, there are …

The biggest disadvantage of using a lower (or higher) pitch then the present standard A4=440Hz is the tuning difficulties/issues that occur when using particular instruments.

Not all instruments can change Concert Pitch!!! It is important to be aware of this when composing and producing music.

If you intend to perform live using a different Concert Pitch, then make sure the instruments of the the musicians you invite for the gig can handle a pitch change.

If you only compose and produce in order to release music, then it is possible to change the pitch (and temperament) in post production for those instruments that do not handle the pitch change well, if all instruments were recorded on separate tracks.

Another disadvantage about using a different Concert Pitch is one for DJ’s. Mixing tracks that use different Concert Pitches does sound horrible, the dissonance can be mood-killing.

Naturally DJ’s could re-pitch their whole repertoire (time consuming), or play only tracks produced using the same Concert Pitch (limits repertoire).

Fixing the difference in Concert Pitch real-time is at present time (2014) no proper solution, not even with modern DJ gear such as “Traktor” or “Serato”.

AFTERWORD
Now, I do like to make clear that the difference between the present A4=440Hz pitch standard and the A4=435Hz (“Diapason Normal”) or A4=432Hz & C4=256Hz as Concert Pitch will not be a difference of “night and day”.

Using another (lower) Concert Pitch such as A4=432Hz is not like some “magic trick” that will make a piece of music suddenly sound great that if played and recorded the same way but 8Hz higher (at 440Hz) would not sound very well.

The “intention” (passion, energy, et cetera) of the performers and “mastery” of both musicians and sound engineers still play the biggest role when it comes to something sounding great.

A different pitch might create a different “perspective” …

A lower pitch (then A4=440Hz) might enlarge the sensation of an extended “dimensionality” at best, but only if that dimensionality was there to begin with.

432-Tuning nor any other Concert Pitch or temperament can “create” what isn’t there to begin with … and that does start with the composition itself, the story that is going to be told, and stands or falls with the accomplishments of the total of artists involved.

Concert Pitch 432Hz is perhaps more something you could call “fingerspitzengefühl” … that is, for those who have “ear” for it.

What really changes the way a piece of music sounds like is the change of Temperament …


Originally published at klapatas.livejournal.com.