Talk:Savart

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I have added an audio example to the article. Hyacinth (talk) 08:45, 9 August 2008 (UTC)

What is a savart?

This article says things that I don't understand. As a matter of fact, I don't know what a savart is and I begin to wonder whether anyone knows. The article begins saying that

One savart is equal to one thousandth of a decade (10/1: 3,986.313714 cents): 3.9863 cents.

Now, one thousandth of 10, unless I am mistaken, is 0.01. What this phrase apparently says is that the savart is equal to 1/1000 of the value of 10 in cents, but that is not the same as 1/1000 of 10! A few lines later, the article defines the savart as follows:

$s=1000\log _{10}{\frac {f_{1}}{f_{2}}}$

But if ${\frac {f_{1}}{f_{2}}}$ is equal to 10/1, as said above, of which log₁₀ is 1, then one must conclude that s of 10/1 = 1000. Is that the same as 1/1000 of 10???

The article later says:

The savart is named after the French physicist and doctor Félix Savart (1791–1841) who advocated the earlier similar interval of the French acoustician Joseph Sauveur (1653–1716).

I have been unable to find where Savart ever advocated that. So far as I have been able to verify, Savart never mentions Sauveur, nor the eptaméride. As a matter of fact, there is no evidence that Savart ever mentioned the savart, which apparently was not known before the early 20th century. That it was named in reference to Savart does not suffice to indicate that Savart advocated it. The article says that "The unit was given the name savart sometime in the 20th century," which appears to contradict the idea of "Savart's definition" mentioned earlier.

As a matter of fact, the main source for the savart and its first definition is in a note by A. Guillemin presented in 1902 to the Académie des Sciences in Paris (https://gallica.bnf.fr/ark:/12148/bpt6k30902/f980#). Guillemin writes (my translation):

In acoustics, one mainly uses two units: the octave for large intervals, the comma for the little ones. Both are quite inconvenient [...]. I suggest to replace the octave and the comma by the savart Σ and the millisavart σ. I call savart the interval 10/1 of which the log = 1. [Etc.]

There would be a lot more to discuss about this text, but the above will suffice for now. Several consequences must be drawn:

• What we call savart today is Guillemin's millisavart.
• If I understand Guillemin correctly, the savart is not a logarithmic unit: it is the interval 10/1, and not its log.
• There is something confusing, though, namely that the millisavart hardly could be 1/1000 of the savart if they weren't both logarithmic units.

Today, the savart can be defined by a logarithmic measure of the octave (2/1). Depending on the number of decimals considered, the octave $=1000\log _{10}{\frac {2}{1}}$ = 301,03 (the frequent definition of the savart), or 301 (the eptameride), or 300 (Wood's rounding). But how one came to this starting from Guillemin's description (or from a supposed definition by Savart himself) remains quite unknown.

Any advice will be welcome. — Hucbald.SaintAmand (talk) 13:13, 11 May 2023 (UTC)

See

• Young 1939
• Pikler 1966
• Segal 2015

Dondervogel 2 (talk) 21:32, 11 May 2023 (UTC)

Thanks a lot. I'll carefully read that. Note that Segal (you link was incorrect, but I had it already) says that savarts were proposed by Savart while, so far as I can tell, nothing indicates that savarts were named before 1902.

A first glance also made me realize (from reading Young –I'll have to go back to Fletcher) why some say that savarts are logarithms of frequencies, instead of logarithms of ratios. Among others Pierre Schaeffer, À la recherche d'une musique concrète, writes "The ear is not sensitive directly to [frequency and amplitude] but, following a fundamental law of pshycho-physics, it is sensitive to their logarithm: one will call height of the sound the logarithm of its frequency and one will measure it in octaves – or in their submultiples the savarts." It goes without saying that the pitch (the "height of the sound") is not measured in octaves, nor in savarts, and that the ear of course is sensitive to frequencies! The modern height of A4 is 440 Hz, not four octaves and a major sixth, unless I am mistaken.

It remains that our article says nothing of all this and that what a savart really is (or how it has been described) is rather confused. The problem is that there exists no secondary source about all this (I mean, no secondary source about this confused situation), so that in WP it would count as original research. Thanks once again — Hucbald.SaintAmand (talk) 08:42, 13 May 2023 (UTC)

Thank you for pointing out my error with the Segal link (now corrected). I've no doubt the article can be improved. Suggestions are welcome! Dondervogel 2 (talk) 10:09, 13 May 2023 (UTC)

Paret & Sibony (2017) is also relevant. See p70-71. Dondervogel 2 (talk) 10:32, 13 May 2023 (UTC)

Thanks once again. There are plenty of books like Paret and Sibony, who define the savart as the 301th or 300th part of the octave (Paret and Sibony themselves appear hesitant between the two), but remain unable to give a reference for that definition, nor to say when the savart came in existence.

The fact that Savart himself lived before Ellis made people think that the savart is older than the cent. There also is the obvious similitude between the savart and Sauveur's heptameride, which made people think that the first was another name for the second. This is true, at least in one of the modern definitions of the savart (1/301 of the octave), but it does not follow that the savart was conceived with the heptameride in mind.

I still did not find any 19th-century reference to the savart, and I believe there is none. The savart seems more or less to stabilize with Alexander Wood's Physics of Music of 1944 and what I'd like to find are earlier references. Harvey Fletcher, as Young mentions in the article of 1939 to which you refered, suggests to represent pitch by a logarithmic curve starting from C (16.35 Hz, corresponding to A4=440 Hz). The ASA, in its Acoustical Terminology (1960 edition) mentions cents, but not savarts.

I'll have to search further, but your help is welcome – and others should feel free to participate. — Hucbald.SaintAmand (talk) 14:14, 13 May 2023 (UTC)

You could be right. For what it's worth, I am not aware of any use of the unit "savart" prior to Young 1939. (BTW, I also checked the 1942 edition of ASA's Acoustical Terminology and found a definition of 'cent', but not 'savart') Dondervogel 2 (talk) 14:50, 13 May 2023 (UTC)

But even Young (1939) does not mention the savart. He writes "Various subdivisions of the octave are considered in light of their ease of calculation and significance, and the semitone, including its hundredth part, the cent, is shown to be suitable." He refers to Fletcher (1934) who doesn't even mention cents. So, for the time being, the only pre-1950 sources appear to be Guillemin (1902) and Wood (1944).

Wood does not refer to Guillemin and writes p. 53 (of the 6th edition, 1962): "Such a unit is the 'savart', which we shall define in such a way that there are 25 savarts to the tempered semitone, 50 to the tempered tone, and 300 to the true octave." And pp. 54: "A unit which is arithmetically very simple is obtained by putting [the pitch interval] K = 1000. This was the unit suggested by Savart. For the octave it gives us

Octave = 1000 log 2 = 301-03 savarts.

This is a convenient size of unit, but it is very inconvenient to have a fraction for the octave and fractions for the tempered tones and semitones as well as for the true intervals. In this book we shall use a slightly modified savart by taking

K = 300/log 2

This makes K approximately 1000, and for quick calculations this value can be used."

Wood also mentions cents, but only in passing, as "used by the translator of Helmholtz' work." Neither Savart, nor Ellis are in his bibliography (Helmholtz is, but without the name of the translator), and there is no indication of where Savart would have suggested the unit. — Hucbald.SaintAmand (talk) 17:10, 13 May 2023 (UTC)

Young 1939 (p135) does mention the savart. He writes:

• "1 octave = 301.03 savarts = 1000 millioctaves
• ...
• A savart is easily computed, since the number of savarts representing the interval between f2 and f1 is merely 1000Xlog10(f2/f1) ... There is the alternative definition (Bouthillon, 1935) of 300 savarts to the octave, but in this case the convenient computation requires binary logarithms."

Dondervogel 2 (talk) 17:19, 13 May 2023 (UTC)

This is not the Young 1939 of which you provided the link above. I'd be much interested to have it. — Hucbald.SaintAmand (talk) 19:02, 13 May 2023 (UTC)

Another link error? I'm sorry. I'll try to work out where I went wrong and fix it. Dondervogel 2 (talk) 19:17, 13 May 2023 (UTC)

I found it. Your link above was but to a summary, the correct link is this one. Thanks again. — Hucbald.SaintAmand (talk) 20:21, 13 May 2023 (UTC)

Aha, well done. That is indeed the correct article. I am relieved to see some mitigating circumstances on my part (same year, same title and same author). Dondervogel 2 (talk) 21:48, 13 May 2023 (UTC)

Since you were so helpful with these sources, would you by chance have access the the Revue d'Acoustique and to L. Bouthillon's article "Définitions de grandeurs acoustiques" quoted by Young 1939b (note 5, p. 135)? I didn't find it on Internet, even although I usually find all what can be found. I sent messages in several bottles around here... Thanks in advance. — Hucbald.SaintAmand (talk) 14:50, 14 May 2023 (UTC)

A colleague sent me a copy of Bouthillon's article in the Revue d'Acoustique. The savart is defined there as usually is the case, as 1/301,03 or 1/300 of an octave, but the article says nothing about how this relates to Guillemin's description (which is not mentioned). Bouthillon does refer to earlier descriptions, including in the Revue d'Acoustique which, I am informed, may be made accessible online in a few weeks from now. The earlier description in the Revue d'Acoustique, vol. I, apparently was 1/300 of an octave, in 1932.

With this, I may be cutting hairs in four, but I find it striking nevertheless that we still don't know when the savart began to be defined in terms of log(2) – also, none of the early sources that I was able to read up to now makes the link with Sauveur and the heptameride. — Hucbald.SaintAmand (talk) 20:10, 15 May 2023 (UTC)

Excellent progress. Thank you for the feedback. It's probably time to consolidate by updating the article with your main findings. Dondervogel 2 (talk) 21:27, 15 May 2023 (UTC)

I now have copy of the relevant numbers of the Revue d'Acoustique. The first volume (1932, p. 90) defines the savart as an "interval equal to 1/300 of the octave. The logarithm of a savart equals log(2)/300 = 0,001."

This is a strange way of expressing things, because the first part (the savart as 1/300 octave) implies that the savart is a logarithm, but the second part defines its logarithm as 1/300 of the log of the octave. It would seem that, for them, 1/300 of the octave and 1/30 of the log of the octave – and in a way, the savart and its logarithm – are one and the same thing.

I don't know whether such a confusion is common among acousticians, but it obviously is at the origin of some confusion in later definitions.

Vol. 1 of the Revue d'Acoustique spends several pages to the project of a vocabulaire acoustique which, it says, is similar to the work done and published in the Journal of the Acoustical Society of America, vol. II n. 3. Unfortunately, the pages of this Journal available on its website ([1]) do not seem to include this terminological material.

I am informed that the Revue d'Acoustique may become available on Internet later this year. We may perhaps wait until then before modifying the article, as it will allow us to better refer to that publication. — Hucbald.SaintAmand (talk) 10:58, 16 May 2023 (UTC)