Talk:56edo: Difference between revisions

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== Metallic fifths ==

From what I've seen, the golden fifth most likely refers to the fifth of [[golden meantone]] at 696.214{{c}}, and the silver fifth to the fifth of [[argent tuning]] at 702.944{{c}}. By the recurrence I calculated the bronze metallic fifth to be about 707.037{{c}}. The statement is worded quite confusingly, and I can't find anything on this wiki referring to an exact formula, and the page for [[metallic harmonic series]] doesn't contain anything about this. This statement should definitely at least be reworded to be less confusing to beginners, and probably not be in the first sentence.

From what I've seen, the golden fifth most likely refers to the fifth of [[golden meantone]] at 696.214{{c}}, and the silver fifth to the fifth of [[argent tuning]] at 702.944{{c}}. By the recurrence I calculated the bronze metallic fifth to be about 707.037{{c}}. The statement is worded quite confusingly, and I can't find anything on this wiki referring to an exact formula, and the page for [[metallic harmonic series]] doesn't contain anything about this. This statement should definitely at least be reworded to be less confusing to beginners, and probably not be in the first sentence.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 19:45, 18 January 2026 (UTC)

:Yup, that's the right math. The metallic fifths follow a pretty simple formula where you multiply the current one by x and then add the previous one in the series, so edos that approximate the bronze fifth increasingly closely are 5, 17, 56, 185, (non patent vals from here on) 611, 2018, etc. Outside those first three, they're not that useful as the number of patent vals drops off rapidly, but they do produce mathematically pleasing scales which also closely approximate quite a few good ratios so they're definitely worth mentioning. [[User:Yourmusic Productions|Yourmusic Productions]] ([[User talk:Yourmusic Productions|talk]]) 23:38, 18 January 2026 (UTC)

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 == Metallic fifths ==
-From what I've seen, the golden fifth most likely refers to the fifth of [[golden meantone]] at 696.214{{c}}, and the silver fifth to the fifth of [[argent tuning]] at 702.944{{c}}. By the recurrence I calculated the bronze metallic fifth to be about 707.037{{c}}. The statement is worded quite confusingly, and I can't find anything on this wiki referring to an exact formula, and the page for [[metallic harmonic series]] doesn't contain anything about this. This statement should definitely at least be reworded to be less confusing to beginners, and probably not be in the first sentence.
+From what I've seen, the golden fifth most likely refers to the fifth of [[golden meantone]] at 696.214{{c}}, and the silver fifth to the fifth of [[argent tuning]] at 702.944{{c}}. By the recurrence I calculated the bronze metallic fifth to be about 707.037{{c}}. The statement is worded quite confusingly, and I can't find anything on this wiki referring to an exact formula, and the page for [[metallic harmonic series]] doesn't contain anything about this. This statement should definitely at least be reworded to be less confusing to beginners, and probably not be in the first sentence.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 19:45, 18 January 2026 (UTC)
+:Yup, that's the right math. The metallic fifths follow a pretty simple formula where you multiply the current one by x and then add the previous one in the series, so edos that approximate the bronze fifth increasingly closely are 5, 17, 56, 185, (non patent vals from here on) 611, 2018, etc. Outside those first three, they're not that useful as the number of patent vals drops off rapidly, but they do produce mathematically pleasing scales which also closely approximate quite a few good ratios so they're definitely worth mentioning. [[User:Yourmusic Productions|Yourmusic Productions]] ([[User talk:Yourmusic Productions|talk]]) 23:38, 18 January 2026 (UTC)