tag:blogger.com,1999:blog-264226589944705290.post2381730548119216431..comments2023-11-05T03:45:25.001-08:00Comments on God Plays Dice: Rosh Hashanah, and somehow the circle of fifths.Michael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-264226589944705290.post-46345226764216896872007-09-13T18:15:00.000-07:002007-09-13T18:15:00.000-07:00Whoa! I never knew about that drift in the Hebrew ...Whoa! I never knew about that drift in the Hebrew calendar. And on the time scale of Jewish history, it really adds up---if Rosh Hashanah existed 5768 years ago, they would've celebrated it nearly a month earlier compared to the seasons! Of course, little human-error glitches in the calendar have probably shifted it by more than a month over the last few millenia...<BR/><BR/><I>Islam forbids leap months</I><BR/><BR/>Seriously?! I mean, I can understand forbidding adultery, or theft, or intoxication... but did anyone really want leap months bad enough to warrent a scriptural injunction against them?<BR/><BR/>p.s. By the way, I think you've got a typo. Shouldn't "no later than September 6" read "no earlier"?Aaronhttps://www.blogger.com/profile/18281785407407667986noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-8917355288258212332007-09-13T07:12:00.000-07:002007-09-13T07:12:00.000-07:00Actually, the circle of fifths is related to anoth...Actually, the circle of fifths is related to another "almost" equality. To describe a fifth in terms of diatonic tones gets the picture precisely backwards.<BR/><BR/>When we move a tone (say on a stretched string) up an octave -- a harmony we can instantly recognize -- we multiply its frequency by two. Similarly, when we move it up a fifth we multiply its frequency by 3/2. So let's start with a frequency T (for "tonic") and start moving up by fifths, dropping down by an octave (marked with a *) when convenient:<BR/><BR/>T<BR/>1.5 T<BR/>1.125 T*<BR/>1.6875 T<BR/>1.265625 T*<BR/>1.8987375 T<BR/>1.423828125 T*<BR/>1.06787109375 T*<BR/>1.601806640625 T<BR/>1.20135498046875 T*<BR/>1.802032470703125 T<BR/>1.35152435302734375 T*<BR/>1.0136432647705078125 T*<BR/><BR/>So we've gone up by 12 fifths and dropped down by seven octaves and are almost within one "cent" of the tonic, which is barely as much as people can distinguish.<BR/><BR/>So we throw these tones into order to get the chromatic scale and pretend that the twelve fifths and the seven octaves match up. And then we pick out whichever cluster of them our culture thinks sound good together and use them most of the time.Anonymousnoreply@blogger.com