Talk:Werckmeister temperament

Werckmeister - sources...

Hi - Where did you get the numerical values for the Werckmeister tunings? Unfortunately they are falsely reported in many 20th century sources which were written by people who did not respect the original text or could not interpret it. Particularly the 'IV' or 'septenarius' tunings which have, in fact, nothing at all to do with 1/7 fractions of a comma. What Werckmeister actually said was that the septenarius could be tuned without thinking about divisions of a comma, instead he used exact integer ratios! So any values based on fractions of a comma are total misrepresentations.

I would recommend to obtain a copy of the original text of 1691 and check carefully to see how historically accurate your sources are. Otherwise you run the risk of passing on a false text.

Also, what is the point of giving the cent values to 3 decimal places? No instrument, let alone an organ, could ever be tuned to such precision!!

Best, --Tdent 21:48, 17 November 2006 (UTC)

My main source is [1], which appears to be a scanned copy of "Wilhelm Dupont: Geschichte der musikalischen Temperatur". If you find errors, feel free to correct them! You are right about the cent values. I will remove the decimals. Apus 09:26, 23 November 2006 (UTC)

The post from 21:48, 17 November 2006 doesn't make much sense. Since the Pythagorean comma and the syntonic comma are each ratios of integers, any 1/7 fractions of either comma will also be exact-integer-ratios (UNLESS the 1/7 divisions require taking the 7th root of some fraction (the faction to the 1/7 power), which I don't think you can do with a monochord). All results obtained by using exact-integer-fractions in the four basic operations of arithmetic (addition, subtraction, multiplication, division) will always be, themselves, exact-integer-fractions. Please use numbers (rather than smokescreen nomenclature such as "septenarius" or "comma" to spell out what you mean. I refer to the syntonic comma as "81/80", a notation that doesn't require anyone to go to a dictionary. Everyone already knows what "81/80" means. And this 81/80 is easily input into other mathematical operations to derive other intervals. You can do MATH on "81/80" but not on arcane phraseology such as "syntonic comma", a phrase my spreadsheets don't understand. There's no reason to call 81/80 by anything other than what it is, except in a discussion of how arcane phraseology from ancient sources obscures genuine understanding of tunings to the present day, while in all other disciplines humanity has learned to distrust sources pre-dating the Enlightenment or even the Industrial Revolution, during which epochs we learned how to describe the universe using numbers instead of words. We don't believe that Earth, Air, Fire, and Water are four elements, and we don't believe that there must be a Fifth element just because someone discovered a fifth convex regular polyhedron, nor that every Planet in our Solar System must be associated with a gemstone. My doctor doesn't believe that the blood of a salamander bathed in mercury will cure me. But when it comes to music, everyone writing from ancient times to the Middle Ages is read as The Word Of God Revealed.2600:1700:6759:B000:E894:BFCC:705D:880 (talk) 09:29, 3 August 2024 (UTC)Christopher Lawrence Simpson

Numbering system

Most (all?) sources appear to call the first temperament discussed Werckmeister III rather than Werckmeister I. Referring to the third system Werckmeister wrote about as "Werckmeister I" is at worst original research and at best confusing and unsupported by convention. --Atemperman (talk) 01:14, 13 January 2010 (UTC)

Right now the page uses two numbering systems for the Werckmeister temperaments: the standard one and a new one apparently made up by some author of this page. I think this is confusing. E.g. right now Werckmeister III is called "Werckmeister I (III)". I fail to see how this helps readers. Let's get rid of this and use the standard numbering only. John Baez (talk) 06:10, 5 February 2024 (UTC)

Typo?

The E value for the W I which is |${\frac {256}{243}}{\sqrt[{4}]{2}}$ ||392 | seems to be at least inaccurate since the cent formula would suggest 390. One could argue that 2 cents are not audible, but all the other numbers in the W I and W II tables are correct to 1 cent. — Preceding unsigned comment added by 67.176.93.180 (talk) 22:04, 20 November 2016 (UTC)

I agree 390 is consistent with the ratio given. The value was unexplainedly changed twice [2][3]. I have changed it back to 390. Burninthruthesky (talk) 09:58, 14 February 2017 (UTC)

Confusing first paragraph

I have to paste a copy of some of the first paragraph because my comment is so complicated I need to see what I'm writing about:

QUOTE

The tuning systems are numbered in two different ways: the first refers to the order in which they were presented as "good temperaments" in Werckmeister's 1691 treatise, the second to their labelling on his monochord. The monochord labels start from III since just intonation is labelled I and quarter-comma meantone is labelled II. The temperament commonly known as "Werckmeister III" is referred to in this article as "Werckmeister I (III)".

UNQUOTE

I know some are complaining about the numbering in two ways. I am NOT complaining about that. I hope a source CAN be found that uses this article's two ways of numbering, because, just as the Laws Of Thermodynamics are not always numbered in order in which they were formulated, I think both orders are important. However, the quoted text reads as if coming from some kind of on-line translator-tool. Please be more specific as to what "label[l]ing on his monochord" actually means. What is a "monochord label"? But the worst lapse here is that while it's stated that this article will refer to a tuning using both of the two numbers, it doesn't say which is which. In the text "Werckmeister III", does the "III" refer to the order in which they are listed in the 1691 treatise, or does the "III" refer to "monochord labels"? If it refers to the 1691 list-position, then in the text "Werckmeister I (III)" the "I" refers to mono-chord labeling. Alternatively, if this "III" refers to "monochord labels", then in the text "Werckmeister I (III)" the "I" refers to the 1691 listing. But we don't know which. It's not made clear.2600:1700:6759:B000:E894:BFCC:705D:880 (talk) 08:59, 3 August 2024 (UTC)Christopher Lawrence Simpson