Talk:Equal division of the octave

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Okay, let's say for the moment that "equal temperament" and "equal division of the octave" are totally different things, even though most people in the world, even most music theorists, couldn't really say how. Why can't we say how different they are in the same article? Pretty please? —Keenan Pepper 00:23, 16 June 2006 (UTC)

I have problems with the structure of the article on equal temperament, which I've spelled out on its discussion page. I also think it's too long and confusing for people who just want to understand the basic idea of equal temperament. So I'd rather see more numerous, and shorter, articles, each clarifying or defining one aspect of that complex notion.yoyo 15:01, 16 June 2006 (UTC)

If that article is in bad shape, why not improve it instead of abandoning it and creating redundant new articles? —Keenan Pepper 01:26, 17 June 2006 (UTC)

• The article on equal temperament is a confusing mish-mash. Mostly when the term is used, it means 12 equal temperament, so the article concentrates mostly on that. Sometimes, it means n-equal temperament for any n, and it tries to discuss that also.

• Meanwhile, edo means, and has always meant, any equal division of the octave, and can accomodate a discussion of the general rank one tuning, which is where you take any step size (a geometric series.) It would be difficult to expand the material in equal temperament to cover more about this, given its purpose. Moving it to "12 equal temperament" has its own problems. Creating this article seems like the best choice. Gene Ward Smith 19:05, 16 June 2006 (UTC)

What problems are those? There ought to be a separate article about the equal division of the octave into 12 parts, because as we all know, that's not the only way to do it. —Keenan Pepper 01:26, 17 June 2006 (UTC)

Logically, there ought to be articles called 12 equal temperament and equal temperament, with the article on equal temperament being about n-et. But that's not what the phrase normally means. Gene Ward Smith 03:13, 17 June 2006 (UTC)

Well, if we're going to go by what things "normally" mean, equal temperament and equal division of the octave normally mean exactly the same thing. I think the distinction between the general concept and the specific instance of 12 is way more important to make than the distinction between "temperament" and "division". —Keenan Pepper 18:53, 17 June 2006 (UTC)

I can see these as being two different things. For one thing, some people don't like the word 'temperament' when applied to most EDOs. 13 and 11 for example - what is being tempered here? Now 19, that's a temperament, sure, no controversy. The EDO set is a specific thing that Ivor pioneered. However, separating EDO and tET over this issue leaves us to wonder about nonoctaves. Many of them I think qualify as temperaments, like 88cET for sure is a temperament. But what about 57cET, is that a temperament? Maybe not, and it's not an EDO, so then where are we? Well, we are maybe left staying with the historical/traditional usage of temperament to mean an equal-step tuning. But nobody uses the term EST. Xj 04:16, 31 August 2006 (UTC)

I tried rephrasing the lead, but maybe it makes the article into more of a stub.

In music, an equal division of the octave, or EDO, is a system of musical tuning which divides the octave into equal parts, but unlike the more common term Equal temperament, EDO does not imply any systematic approximation, or tempering of other rational intervals, although both may indicate identical tunings. EDOs often are employed in unfamiliar sounding xenharmonic music.

Mireut 15:43, 6 November 2006 (UTC)

Responding to Xj and Mireut: I think "temperament" applies to any system of tuning which produces irrational intervals, which every EDO does, as well as every Equal Temperament. The relationship between an irrational tuning and rational intervals is imposed by the physical properties of tonal sounds and the human ear, and it is this that implies temperament and not the other way around. You can't really make an EDO that is not a "temperament". If you would reserve "temperament" for only those irrational tunings which have "good" approximations of some chosen set of rational intervals, the line is going to become very difficult to draw (which intervals, how close?).

I think I said earlier on the equal temperament discussion page that I think this article should be merged into the ET article. It really is a subset of equal temperament, and the subtleties of the implications of this term verses TET are too nebulous to be worthwhile of inclusion in Wikipedia. All we should do is mention it, and explain clearly what it means. The vague contextual differences I don't think can be properly described, and should be learned by experience elsewhere. - Rainwarrior 17:00, 6 November 2006 (UTC)