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.
- 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)
- Rainwarrior wrote:
- "I think "temperament" applies to any system of tuning which produces irrational intervals, which every EDO does, as well as every Equal Temperament."
- I disagree, as noted on the ET article's Talk page. A temperament is a tempering, or the result of the action of tempering. It's not for nothing that the words "temper" and "tamper" sound similar. The basic notion of tempering is that some exact or original thing is altered, as for example when we temper steel. But I'm not going to lose my temper over this ...! I would hope to see the present page remain, with something very like Mireut's definition in place, as I think it captures the essential difference. A musician using an EDO may have no desire to approximate any just ratios whatsoever (octaves included). And this article could also supply some history, citing examples of xenharmonic composers like Ivor Darreg. BTW, did Darreg invent the term? If not, who did? yoyo 18:10, 17 December 2006 (UTC)
- Rainwarrior wrote:
- Well, look at the EDO article. The key sentence seems to be "saying "edo" carries no implication that the intervals are being used to approximate rational intervals other than the octave", and then paradoxically the next paragraph says "these divisions are singled out because they have better than average ability to represent rational numbers with small numerators and denominators". I'm not saying that EDO doesn't have the connotation we're talking about, but the thing is, making a distinction between EDOs or TETs based on whether they approximate rational intervals is, well, how do you do it? Which EDOs don't?
- I mean, okay 2,3,4,6 and 12 are already covered by common practice. 5 has a reasonable fifth, 7 does a little better than 5. The uncommon notes in 8 does a dead on impression of a few 11-limit intervals. 9 similarly has a really good 7-limit. 10 isn't much better than five, but now has a reasonable major third. 11 and 13 aren't as good as 12 but they still do a decent job, and things get better as the number gets higher so I'll leave off here. How much deviation from just is too much to be considered a temperament? Or are we going to be classifying scales based on the composers intent?
- Anyhow, regardless of this argument, the article as basically NO material. If we replaced in Equal temperament "To avoid ambiguity, the term Equal Division of the Octave, or EDO is sometimes preferred." with "To avoid connotations of the word temperament, the term Equal Division of the Octave, or EDO is sometimes preferred.", we'd have the full content of this article right there in Equal Temperament (maybe even add on the end ", especially when the goal of the composer is an unfamiliar sound, or Xenharmony."). Even if you think it could be expanded, we could do that expansion in an EDO heading at equal temperament until it becomes large enough to warrant an article. Personally, I don't think much expansion (that is distinct from Equal temperament) can really be done on this. - Rainwarrior 20:28, 17 December 2006 (UTC)
I'm merging this with equal temperament because there's nothing in its text that isn't already there, the article is tiny, and it's been that way for months and months. There's a healthy selection of peculiar links and references here (what's with all of the integer sequences?). I don't know what they're for, really, since this article is tiny, but I'm archiving them here on the talk page in case there's any use for them. (How does an article with so many sources have so little text?) Rainwarrior 05:23, 3 April 2007 (UTC)
Also A117536, A117537, A117539, A117554, A117555, A117556, A117557, A117558, A117559, A117577, A117578, and A054540.
- James Murray Barbour, "Music and Ternary Continued Fractions", American Mathematical Monthly, 55 (1948), 545-555
- James Murray Barbour, Tuning and Temperament: A Historical Survey, Michigan State College Press, East Lansing, 1951; reprint Da Capo Press, New York, 1973, 228 pages; reprint Dover, New York, 2004
- Easley Blackwood, The Structure of Recognizable Diatonic Tunings Princeton University Press, Princeton NJ, 1985
- John H. Chalmers Jr. "Construction and Harmonization of Microtonal Scales in non-twelve-tone Equal Temperaments", Proceedings of the 8th International Computer Music Conference, ICMA, 534-555
- Ramon Fuller, "A Study of Microtonal Equal Temperaments", Journal of Music Theory 35 no. 1-2, (1991), 211-237
- Donald E. Hall, "A Systematic Evaluation of Equal Temperaments Through N=612", Interface 14 no. 1-2, (1985), 61-73
- Kees van Prooijen, "A Theory of Equal-Tempered Scales", Interface 7 no. 1, (1978), 45-56 [1]
- William S. Stoney, "Theoretical Possibilities for Equally Tempered Musical Systems", The Computer and Music, Harry B. Lincoln (ed.), Cornell University Press, Ithaca, 1970, 163-171
Category:Musical scales Category:Musical set theory Category:Equal temperaments
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.
- 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)
- Rainwarrior wrote:
- "I think "temperament" applies to any system of tuning which produces irrational intervals, which every EDO does, as well as every Equal Temperament."
- I disagree, as noted on the ET article's Talk page. A temperament is a tempering, or the result of the action of tempering. It's not for nothing that the words "temper" and "tamper" sound similar. The basic notion of tempering is that some exact or original thing is altered, as for example when we temper steel. But I'm not going to lose my temper over this ...! I would hope to see the present page remain, with something very like Mireut's definition in place, as I think it captures the essential difference. A musician using an EDO may have no desire to approximate any just ratios whatsoever (octaves included). And this article could also supply some history, citing examples of xenharmonic composers like Ivor Darreg. BTW, did Darreg invent the term? If not, who did? yoyo 18:10, 17 December 2006 (UTC)
- Rainwarrior wrote:
- Well, look at the EDO article. The key sentence seems to be "saying "edo" carries no implication that the intervals are being used to approximate rational intervals other than the octave", and then paradoxically the next paragraph says "these divisions are singled out because they have better than average ability to represent rational numbers with small numerators and denominators". I'm not saying that EDO doesn't have the connotation we're talking about, but the thing is, making a distinction between EDOs or TETs based on whether they approximate rational intervals is, well, how do you do it? Which EDOs don't?
- I mean, okay 2,3,4,6 and 12 are already covered by common practice. 5 has a reasonable fifth, 7 does a little better than 5. The uncommon notes in 8 does a dead on impression of a few 11-limit intervals. 9 similarly has a really good 7-limit. 10 isn't much better than five, but now has a reasonable major third. 11 and 13 aren't as good as 12 but they still do a decent job, and things get better as the number gets higher so I'll leave off here. How much deviation from just is too much to be considered a temperament? Or are we going to be classifying scales based on the composers intent?
- Anyhow, regardless of this argument, the article as basically NO material. If we replaced in Equal temperament "To avoid ambiguity, the term Equal Division of the Octave, or EDO is sometimes preferred." with "To avoid connotations of the word temperament, the term Equal Division of the Octave, or EDO is sometimes preferred.", we'd have the full content of this article right there in Equal Temperament (maybe even add on the end ", especially when the goal of the composer is an unfamiliar sound, or Xenharmony."). Even if you think it could be expanded, we could do that expansion in an EDO heading at equal temperament until it becomes large enough to warrant an article. Personally, I don't think much expansion (that is distinct from Equal temperament) can really be done on this. - Rainwarrior 20:28, 17 December 2006 (UTC)
I'm merging this with equal temperament because there's nothing in its text that isn't already there, the article is tiny, and it's been that way for months and months. There's a healthy selection of peculiar links and references here (what's with all of the integer sequences?). I don't know what they're for, really, since this article is tiny, but I'm archiving them here on the talk page in case there's any use for them. (How does an article with so many sources have so little text?) Rainwarrior 05:23, 3 April 2007 (UTC)
Also A117536, A117537, A117539, A117554, A117555, A117556, A117557, A117558, A117559, A117577, A117578, and A054540.
- James Murray Barbour, "Music and Ternary Continued Fractions", American Mathematical Monthly, 55 (1948), 545-555
- James Murray Barbour, Tuning and Temperament: A Historical Survey, Michigan State College Press, East Lansing, 1951; reprint Da Capo Press, New York, 1973, 228 pages; reprint Dover, New York, 2004
- Easley Blackwood, The Structure of Recognizable Diatonic Tunings Princeton University Press, Princeton NJ, 1985
- John H. Chalmers Jr. "Construction and Harmonization of Microtonal Scales in non-twelve-tone Equal Temperaments", Proceedings of the 8th International Computer Music Conference, ICMA, 534-555
- Ramon Fuller, "A Study of Microtonal Equal Temperaments", Journal of Music Theory 35 no. 1-2, (1991), 211-237
- Donald E. Hall, "A Systematic Evaluation of Equal Temperaments Through N=612", Interface 14 no. 1-2, (1985), 61-73
- Kees van Prooijen, "A Theory of Equal-Tempered Scales", Interface 7 no. 1, (1978), 45-56 [1]
- William S. Stoney, "Theoretical Possibilities for Equally Tempered Musical Systems", The Computer and Music, Harry B. Lincoln (ed.), Cornell University Press, Ithaca, 1970, 163-171
Category:Musical scales Category:Musical set theory Category:Equal temperaments