File talk:Music intervals frequency ratio equal tempered pythagorean comparison.svg

Why does this extend up to 3:1? It contains no intervals in that range. &mdash; Gwalla | Talk 22:03, 10 August 2008 (UTC)
 * Indeed, it would give more room to show the subtleties of difference if it spanned only from 1:1 to 2:1 but kept the same image height. — Preceding unsigned comment added by 96.42.124.32 (talk) 15:35, 26 May 2011 (UTC)

I certainly appreciate what this chart tries to do, though I believe it is horribly inaccurate. Firstly, the Perfect Fourth (ratio 4:3), as the inversion of the Perfect Fifth (ratio 3:2), should be almost identical (less than 2 cents different) between both equal and Pythagorean. The P5 is right, so why is the P4 so wildly off? It would seem likely that point actually represents the ratio 27:20, a 5-limit alternative to the Pythagorean 4:3, which is about 19.6 cents sharp from equal -- but that is certainly not Pythagorean, and so has nothing to do with what this chart is alleged to depict (and even standard 5-limit tuning uses the Pythagorean 4:3 as it is purer than 27:20 anyway). Additionally, the Minor Second suffers the same sort of condition: the Pythagorean ratio is 256:243, which is -9.8 cents from equal, but on this chart it appears that the 5-limit 16:15 is used instead, which is +11.7 cents from equal. Yet again, the Minor Third should be -5.9 cents (Pythagorean 32:27) while it is shown at what appears to be +15.6 cents (5-limit 6:5). Still more, the Minor Sixth should be -7.8 cents (Pythagorean 128:81) but is shown at +13.7 cents (5-limit 8:5), and the Minor Seventh should be -3.9 cents (Pythagorean 16:9) but is shown at +17.6 cents (5-limit 9:5). Also, while not technically incorrect, it is only a half-truth to depict the tritone as +11.7 cents (Pythagorean 729:512); this is called the Pythagorean Augmented Fourth, and as a stack of three whole tones a tri-tone is indeed an Augmented Fourth, though this interval is also called the High Pythagorean Tritone in relation to its inverse, the Low Pythagorean Tritone, otherwise called the Pythagorean Diminished Fifth (1024:729), which is -11.7 cents from equal; if either of these intervals is depicted in such a chart, the other should be as well, as they are both approximated as enharmonic equivalents in standard equal tuning. Ultimately, with all the minor intervals depicting 5-limit ratios and all the major intervals depicting Pythagorean ratios, this chart doesn't even represent basic just intonation, much less the Pythagorean tuning it claims. It is desperately in need of revision or replacement; I would do it myself if I had the appropriate software and skills. — Preceding unsigned comment added by 96.42.124.32 (talk) 15:18, 26 May 2011 (UTC)
 * I got the ratios off of Wikipedia, so they would need to be fixed there as well. 76.252.46.136 (talk) 18:31, 9 June 2011 (UTC)
 * The intervals as presented in Wikipedia's list are currently correct; they may not have been when the graphic was made. — Preceding unsigned comment added by 96.42.124.32 (talk) 03:47, 20 June 2011 (UTC)

The perfect fourth should only be 2 cents away from equal tempered. I didn't check out the rest of the intervals, but that is a glaring error and people should treat this diagram with caution. I like idea of it. Check out Barbour's Tuning and Temperaments. — Preceding unsigned comment added by 207.237.75.3 (talk) 20:17, 21 September 2011 (UTC)