Talk:Kite's color notation: Difference between revisions
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: But I don't consider y1 a valid name. I would call 80/81 a descending g1, not a y1. Same for z1, zg1 and sgg1. Considering all the possible 7-note segments of all the possible colors, half of them have no unisons, because the 8ves are less than 1200¢. Some don't even have 2nds, e.g. the central bizogu segment. An 8ve minus the 50/49 comma is a zzgg9 of 1165¢, and a zzgg2 would be a descending rryy-2. My reasoning is that intervals can be either ascending or descending, and also either positive or negative. | : But I don't consider y1 a valid name. I would call 80/81 a descending g1, not a y1. Same for z1, zg1 and sgg1. Considering all the possible 7-note segments of all the possible colors, half of them have no unisons, because the 8ves are less than 1200¢. Some don't even have 2nds, e.g. the central bizogu segment. An 8ve minus the 50/49 comma is a zzgg9 of 1165¢, and a zzgg2 would be a descending rryy-2. My reasoning is that intervals can be either ascending or descending, and also either positive or negative. | ||
:: To this paragraph specifically: to me a "y1" ought to be the interval such that "y1 * w2 = y2", i.e. the interval which "makes things yo". In that sense, 80/81 is y1, to me. The fact that the interval is descending doesn't change the fact that it functions like a y1, in the same way that the fact that 64/63 is ascending doesn't change the fact that functions like a ru1 (i.e. "makes things ru", "ru1 * w2 = ru2"). The fact y1 | :: To this paragraph specifically: to me a "y1" ought to be the interval such that "y1 * w2 = y2", i.e. the interval which "makes things yo". In that sense, 80/81 is y1, to me. The fact that the interval is descending doesn't change the fact that it functions like a y1, in the same way that the fact that 64/63 is ascending doesn't change the fact that functions like a ru1 (i.e. "makes things ru", "ru1 * w2 = ru2"). The fact that y1 is descending is an important fact though, e.g. it can help you remember that y2 is smaller than w2. --[[User:M-yac|M-yac]] ([[User talk:M-yac|talk]]) 03:47, 2 August 2021 (UTC) | ||
:: I just realized this may not work how I thought in color notation. In the FJS (which is what I'm most familiar with) "P1^5" is always the interval which "makes things up-five", e.g. "P1^5 * M2 = M2^5", "P1^5 * M3 = M3^5", "P1^5 * d12 = d12^5", etc. But in color notation "y1 * w3 = sy3", not "y3". So y1 is not the interval which "makes things yo"? Hmm. I think there's still some argument to be made about the "function" of y1 in color notation, but it gets more complicated with the large and small prefixes. (And unfortunately, I still don't have a great intuition for large and small prefixes.) --[[User:M-yac|M-yac]] ([[User talk:M-yac|talk]]) 04:01, 2 August 2021 (UTC) | :: I just realized this may not work how I thought in color notation. In the FJS (which is what I'm most familiar with) "P1^5" is always the interval which "makes things up-five", e.g. "P1^5 * M2 = M2^5", "P1^5 * M3 = M3^5", "P1^5 * d12 = d12^5", etc. But in color notation "y1 * w3 = sy3", not "y3". So y1 is not the interval which "makes things yo"? Hmm. I think there's still some argument to be made about the "function" of y1 in color notation, but it gets more complicated with the large and small prefixes. (And unfortunately, I still don't have a great intuition for large and small prefixes.) --[[User:M-yac|M-yac]] ([[User talk:M-yac|talk]]) 04:01, 2 August 2021 (UTC) | ||
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: Your broader use of the term negative to include descending is mathematically sound. 49/50 is a (positive) zzgg2. It also reduces (eliminates?) invalid color names, which is nice. But negative intervals are different than descending ones, and IMO it's nice to distinguish between them. They feel different. Descending intervals are commonplace and straightforward, but negative intervals only apply to certain JI commas. My narrower usage of negative functions as a warning that interval arithmetic works counter-intuitively. And the concept of descending intervals is well understood and doesn't require a new term like negative. So I think the narrower use of negative is better for pedagogical purposes. | : Your broader use of the term negative to include descending is mathematically sound. 49/50 is a (positive) zzgg2. It also reduces (eliminates?) invalid color names, which is nice. But negative intervals are different than descending ones, and IMO it's nice to distinguish between them. They feel different. Descending intervals are commonplace and straightforward, but negative intervals only apply to certain JI commas. My narrower usage of negative functions as a warning that interval arithmetic works counter-intuitively. And the concept of descending intervals is well understood and doesn't require a new term like negative. So I think the narrower use of negative is better for pedagogical purposes. | ||
:: I very much agree with your assessment that just including the word "negative" and not mentioning whether or not the interval is descending could be very misleading. (You writing out those four cases was very helpful!) I've since added an extra line to the output of xen-calc when the interval is descending, e.g. https://www.yacavone.net/xen-calc/?q=49/50. I am still going to keep the old output though, both because of my "how the interval functions" argument above and because of the fact that the "descending" qualifier has no canonical place in the syntax of color notation. Perhaps you could add it? e.g. "dg1" or "degu1" what I currently call "y1"? --[[User:M-yac|M-yac]] ([[User talk:M-yac|talk]]) 03:47, 2 August 2021 (UTC) | :: I very much agree with your assessment that just including the word "negative" and not mentioning whether or not the interval is descending could be very misleading. (You writing out those four cases was very helpful!) I've since added an extra line to the output of xen-calc when the interval is descending, e.g. https://www.yacavone.net/xen-calc/?q=49/50. I am still going to keep the old output though, both because of my "how the interval functions" argument above and because of the fact that the "descending" qualifier has no canonical place in the syntax of color notation (e.g. the only name I can give 4/5 that satisfies all the descriptions on this page is "gu-3"). Perhaps you could add it, though? e.g. "dg1" or "degu1" what I currently call "y1"? --[[User:M-yac|M-yac]] ([[User talk:M-yac|talk]]) 03:47, 2 August 2021 (UTC) | ||
: Another objection: I see that xen-calc calls 4/5 a gu negative 3rd. Playing a note and adding a note 5/4 below it makes a yo harmony with a distinctly 5-over sound. If we call that interval a gu negative 3rd, that implies a 5-under sound. Sure, you can deduce from the term negative that the color is inverted, but that's extra mental work. I'd rather say the added note is a yo 3rd below the 1st note than a negative gu 3rd above it. | : Another objection: I see that xen-calc calls 4/5 a gu negative 3rd. Playing a note and adding a note 5/4 below it makes a yo harmony with a distinctly 5-over sound. If we call that interval a gu negative 3rd, that implies a 5-under sound. Sure, you can deduce from the term negative that the color is inverted, but that's extra mental work. I'd rather say the added note is a yo 3rd below the 1st note than a negative gu 3rd above it. | ||