Talk:19 equal temperament

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Music theory

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Magic temperament?

Theres some reference made in this page and on 22 equal temperament to a magic temperament. I would suggest that it's confusing and should be removed, since we don't even have an article on it to follow up on. Any objections? - Rainwarrior 04:37, 7 May 2006 (UTC)[reply]

I totally understand magic temperament and I could write an article on it but the problem is it would mostly be original research (well, not original to me, but thought up by members of the tuning list and not published in any peer-reviewed thing). I fear that's a problem with many articles related to tuning and temperament. —Keenan Pepper 04:53, 7 May 2006 (UTC)[reply]

Hmm. I'd say to go ahead with the article then. It at least wouldn't be out of place around here... but even if it's a scale no one's published, unless you think it's so obscure that it doesn't belong on wikipedia. If the source is the tuning list (...is that on Yahoo?) I guess you won't have much to link to, but you can at least explain its origins. My objection to its reference in this article is that there's no point in defining 19 temperament in terms of other things that aren't themselves worthy of an article on wikipedia. - Rainwarrior 05:03, 7 May 2006 (UTC)[reply]

Done. See if you can understand it and improve it. I'm looking for an example of a piece written in it, which I know exists because I've heard one before, but I can't seem to find any. —Keenan Pepper 05:46, 7 May 2006 (UTC)[reply]

The only thing I don't quite understand is the compatibility thing. Do you just mean that those EDO temperaments that have slightly-flat-from-just major thirds are considered magic-compatible? I might also mention that the term "tempers out" is something that has always bothered me a little. I haven't seen it anywhere except wikipedia, but in most of the uses I've seen it's not stated directly which interval is being tempered (traditionally, of course, it is only fifths that are tempered), and merely providing a comma's ratio doesn't really indicate how that ratio came about from the tuning system. "Tempers out", as I see it used on Wikipedia, is really only properly descriptive when you already know how the tuning system works. (What literature does the term appear in?) - Rainwarrior 18:27, 7 May 2006 (UTC)[reply]

This is what I mean by "compatible": The definining feature of Magic temperament is that five 5/4 "major thirds" exceed an octave by a 3/2 "perfect fifth". In 12-equal, this is not the case, because a major third is 4 steps, and 4*5 - 12 = 8, which is a minor sixth, not a perfect fifth, so 12-equal is not compatible with Magic. In 19 and 22, it is the case, so they are. It's not a strict definition because it depends on which approximations you use, for example 13-equal has two different approximations to 3/2 which are about equally bad, so it's not clear whether it's compatible or not, but it doesn't really matter because 13-equal is so bad anyway. Any "good" equal temperament will have a well-defined approximation to simple just intervals, so you can say whether it's compatible with a given linear temperament.

The practical meaning of all this is that if you have a piece written in Magic temperament, you can perform it in 19-equal or 22-equal, and the two will sound different but in both cases the harmony will work out. You definitely can't perform it in 12-equal, though. That's why I think compatibility is a good word to describe it. Meantone is compatible with 12, 19, and 31, so you can take something by Bach and play it in 19 or 31 and it sounds great, but if you try to play it in 22 you'll fail miserably, because it's incompatible. —Keenan Pepper 21:01, 7 May 2006 (UTC)[reply]

This is a good clarification, and explains that sort of usage of the term throughout the pages on tuning. (What, though, if the magic temperament is extended too far to be accomodated? Being a "linear temperament", isn't it infinitely extendable?). I might take a tour through the temperaments pages one of these days and try to replace or define these terms which seem to have become technical jargon. - Rainwarrior 22:17, 7 May 2006 (UTC)[reply]

For the 19 equal temperament page, under the "Scale Diagram" - all Steps are labeled "63" (cents). I don't know what compelled me to check this, but I've found that there are actually three steps in the sequence with a 64 cent interval. They are: B to B#/Cb (189 to 253), D# to Eb (568 to 632), and Gb to G (947 to 1011). —Preceding unsigned comment added by 98.80.12.132 (talk) 18:40, 16 May 2010 (UTC)[reply]

That's because 1200 / 19 ≈ 63.1579 cents, not precisely 63 cents. The numbers are all rounded to the nearest cent, hence three (19 * 0.1579 = 3.0001) of the differences appear to be 64 but in reality they're all the same (≈ 63.1579). -- Glenn L 03:20, 17 May 2010 (UTC)

External links to music

Please see Wikipedia talk:WikiProject Tunings, Temperaments, and Scales#External links to music. —Keenan Pepper 19:45, 3 September 2006 (UTC)[reply]

The following examples need to be replaced with links to HTML files describing them, or migrated to the wikipedia Commons. - Rainwarrior 04:53, 4 September 2006 (UTC)[reply]

Foum by Jacob Barton short mp3 file

Prelude 1 for 19ET Piano by Jeff Harrington mp3 file

Prelude 2 for 19ET Piano by Jeff Harrington mp3 file

Prelude 3 for 19ET Piano by Jeff Harrington midi file

Juggler by Aaron Krister Johnson ogg file

Dead link

During several automated bot runs the following external link was found to be unavailable. Please check if the link is in fact down and fix or remove it in that case!

http://gewi.uni-graz.at/~cim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf
- In 19 equal temperament on 2011-05-25 06:47:22, Socket Error: 'A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond'
- In 19 equal temperament on 2011-06-21 05:27:50, Socket Error: 'A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond'

--JeffGBot (talk) 05:28, 21 June 2011 (UTC)[reply]

"Scale Diagram"

I get that this is not an easy topic even for smart people. I certaintly don't have it down yet, myself, and I'm not particularly stupid regarding music. I would urge those who do understand this 19 equal temperament thingy to continue seeking to make this article clearer. I'm not saying it's bad. But the "Scale Diagram" section is a good example, with this:

The 19-tone system can be represented with the traditional letter names and system of sharps and flats by treating flats and sharps as distinct notes, but identifying B♯ as enharmonic with C♭ and E♯ with F♭.

See, when one (such as myself) does not yet understand this topic, one wonders if this is actually an error. He thinks, "In normal temperament, or whatever it's called, B♯ is enharmonic with C♮, or just plain 'C', and E♯ is enharmonic with F♮. Is that maybe what they really meant to say?" One doesn't know, because one is in a bit over his head!

Maybe (assuming the statement is not in error) some sort of comparison to, uh, ordinary temperament is appropriate at this point in the article, that section, near that statement, just to help drag some of us out of the deep waters of confusion.

--Ben Culture (talk) 15:14, 1 September 2012 (UTC)[reply]

Circulating

This article contains the sentence "Costeley understood and desired the circulating aspect of this tuning," but does not explain what "circulating" means in this context. Why not add a few words explaining this? 173.88.246.138 (talk) 04:14, 27 June 2021 (UTC)[reply]

JI Interval Approximation Diagram Error

the interval 7/6 is incorrectly placed on the diagram, at 266.87cents it should be between the 4th and 5th steps of 19edo 2600:4040:90D1:9600:6583:1518:4DAA:828F (talk) 04:07, 3 May 2023 (UTC)[reply]

"The fact that traditional western music maps unambiguously onto this scale"

Here is the reason. In $n$ -EDO the perfect fifth is set to $n':=\operatorname {round} (n\log _{2}{\frac {3}{2}})$ -steps wide, so the chromatic semitone is $7n'-4n$ -steps wide. The width of the chromatic semitone is, roughly speaking, the number of "different" sharp or flat symbols needed (for example, for $n=17,24,31$ this value is 2, so we need two kind of sharps: the ordinary sharp and the half-sharp; for $n=53$ this value is 5 so we need a lot more different accidentals). To map unambiguously our traditional music, we need

$7n'-4n=7\operatorname {round} (n\log _{2}{\frac {3}{2}})-4n=1,$

and the solutions to which are $n=5,12,19,26,33,40,47$ . 129.104.241.115 (talk) 18:48, 9 December 2024 (UTC)[reply]