source file: m1470.txt Date: Thu, 9 Jul 1998 12:23:36 -0400 Subject: RE: Sauveur and (hepta)merides From: "Paul H. Erlich" This message is in MIME format. Since your mail reader does not understand this format, some or all of this message may not be legible. ------ =_NextPart_000_01BDAB55.ECC61EBE Content-Type: text/plain >Reading this, I wondered where Sauveur came up with 301, and Ellis tells >me it is a 7-way subdivision of his cycle of 43 merides (hence, >heptamerides, duh). However, what is his reasoning for choosing 43? I >quite figure out much that's very noteworthy about 43 except that it's >very close to 1/5-comma meantone. That was a very important consideration at the time. However, at least as important was the fact that the base-10 log of 2 is .3010, and since in Sauveur's day everyone was working with tables of logs rather than computers or calculators, heptamerides turned out to be very convenient. Just look up a ratio on a table of logs, multiply by 1000, and that's how many heptamerides it is! ------ =_NextPart_000_01BDAB55.ECC61EBE Content-Type: application/ms-tnef Content-Transfer-Encoding: base64 eJ8+IiYQAQaQCAAEAAAAAAABAAEAAQeQBgAIAAAA5AQAAAAAAADoAAEIgAcAGAAAAElQTS5NaWNy b3NvZnQgTWFpbC5Ob3RlADEIAQWAAwAOAAAAzgcHAAkADAAXACQABAAwAQEggAMADgAAAM4HBwAJ AAwAFwAkAAQAMAEBCYABACEAAABFOENBOTBGOUY2MTVEMjExQUNEMzAwODA1RkJFM0MwNQBDBwEE gAEAHwAAAFJFOiBTYXV2ZXVyIGFuZCAoaGVwdGEpbWVyaWRlcwCbCgENgAQAAgAAAAIAAgABA5AG ANAHAAAuAAAAAwA2AAAAAAADAASACCAGAAAAAADAAAAAAAAARgAAAABShQAAtw0AAB4ABYAIIAYA AAAAAMAAAAAAAABGAAAAAFSFAAABAAAABAAAADguMAADAAaACCAGAAAAAADAAAAAAAAARgAAAAAB hQAAAAAAAAsAAIAIIAYAAAAAAMAAAAAAAABGAAAAAAOFAAAAAAAACwAPgAggBgAAAAAAwAAAAAAA AEYAAAAADoUAAAAAAAADABCACCAGAAAAAADAAAAAAAAARgAAAAAQhQAAAAAAAAMAEYAIIAYAAAAA AMAAAAAAAABGAAAAABGFAAAAAAAAAwAUgAggBgAAAAAAwAAAAAAAAEYAAAAAGIUAAAAAAAAeACSA CCAGAAAAAADAAAAAAAAARgAAAAA2hQAAAQAAAAEAAAAAAAAAHgAlgAggBgAAAAAAwAAAAAAAAEYA AAAAN4UAAAEAAAABAAAAAAAAAB4AJoAIIAYAAAAAAMAAAAAAAABGAAAAADiFAAABAAAAAQAAAAAA AAACAQkQAQAAALkCAAC1AgAAmgMAAExaRnX828sqAwAKAHJjcGcxMjXSMgD7MzYB6CACpAPknwcT AoMAUAPUAgBjaArA0HNldDAQtn0KgAjINCA7CW8wAoAKgXVjWwBQCwNjAEELYG4OEDAEMzMLpiA+ UmVhQmQLgGcgdGgEACzwIEkgdwIgBIEJgBhARmgYkQYBdXZlCHAgRGNhB4AgdXAYQGnhF9AgMzAx GBAAcBjA2EVsbAQAF8BlGzAR0HsKsQqAPhnhGlAcYAQgYQAgNy13YXkgc1R1YheAdgQAaQIgIBhv ZiAX4RmweWNs4xkgHhE0MyAHgAUQAQCFBCAoGPBuY2UsG9UfGPAFMBnRH2MYEGR1aAApLiAgSG93 Ze0ZcHIYEBjgYRyDHkIUADxhcwIgF5ICEBmhaG+ubwCQF6EfED8h0Ekb1YxxdRpQGSBmaWcIcPUe wXUFQG0VYBpwF9AioM4nBCAiMR0wbm8bgBhQPQAgaB0wAaAmUh8RZXj/IAAFMSbiHGEnIBvUCvMX MA8nUx6gJFAZIHRvIDHoLzUtBaBtAMAfMQBwsStgbmUuKegKgFQiku8dEByyJ1MHcHAJESxRGbD/ AiAAkASBIqAd0iKhF9ArQf8HcSHAIfcioR6wI2AFQC3hdy6ILdIwMmYA0Ck1MDJi2SNgZS0WcDGA bxewHhHqMhySLhqRMBrEJGEgAG8cYAOgGUUnIWQdISIiefcsgS3DJ+FrF5IaQwGRHrD/BCAeETSh IyEioBjxJtIDoD0r0XAmYASQOXEZomxj/nULYCtgEjAYECCqF8AIcO8skBjAJlIrYWIZICq0AiCX GXADAAnwdCHASnUxwfkJAG9rGgIc0C+THgAv4e85FDmGGBAmkGwvsAtQHTD+Yh0wFnBCwBrEJuUk MAfg7wOBHTA8exxzIRXhAtEVgwsKgBMBAEaQAAAAAwAmAAAAAAADAC4AAAAAAAsAAgABAAAAHgBw AAEAAAATAAAAVFVOSU5HIGRpZ2VzdCAxNDY5AAACAXEAAQAAABsAAAABvatEUjD5kMeAFfYR0qzT AIBfvjwFAAPnLCAAQAA5AEC/hexVq70BAwDxPwkEAAAeADFAAQAAAAYAAABQQVVMRQAAAAMAGkAA AAAAHgAwQAEAAAAGAAAAUEFVTEUAAAADABlAAAAAAAMA/T/kBAAAAwCAEP////8CAUcAAQAAADIA AABjPVVTO2E9IDtwPUFjYWRpYW4tQXNzZXQ7bD1NQVJTLTk4MDcwOTE2MjMzNlotNzg2AAAAAgH5 PwEAAABLAAAAAAAAANynQMjAQhAatLkIACsv4YIBAAAAAAAAAC9PPUFDQURJQU4tQVNTRVQvT1U9 QUFNL0NOPVJFQ0lQSUVOVFMvQ049UEFVTEUAAB4A+D8BAAAADwAAAFBhdWwgSC4gRXJsaWNoAAAe ADhAAQAAAAYAAABQQVVMRQAAAAIB+z8BAAAASwAAAAAAAADcp0DIwEIQGrS5CAArL+GCAQAAAAAA AAAvTz1BQ0FESUFOLUFTU0VUL09VPUFBTS9DTj1SRUNJUElFTlRTL0NOPVBBVUxFAAAeAPo/AQAA AA8AAABQYXVsIEguIEVybGljaAAAHgA5QAEAAAAGAAAAUEFVTEUAAABAAAcw9gvk+lSrvQFAAAgw vh7G7FWrvQEeAD0AAQAAAAUAAABSRTogAAAAAB4AHQ4BAAAAGwAAAFNhdXZldXIgYW5kIChoZXB0 YSltZXJpZGVzAAAeADUQAQAAAC4AAAA8QkUxQkZEMDczOUQ4RDExMUFDQzgwMDgwNUZCRTNDMDUx NDk2MURATUFSUz4AAAALACkAAAAAAAsAIwAAAAAAAwAGEBHediADAAcQNAIAAAMAEBABAAAAAwAR EAEAAAAeAAgQAQAAAGUAAABSRUFESU5HVEhJUyxJV09OREVSRURXSEVSRVNBVVZFVVJDQU1FVVBX SVRIMzAxLEFOREVMTElTVEVMTFNNRUlUSVNBNy1XQVlTVUJESVZJU0lPTk9GSElTQ1lDTEVPRjQz TUVSAAAAAAIBfwABAAAALgAAADxCRTFCRkQwNzM5RDhEMTExQUNDODAwODA1RkJFM0MwNTE0OTYx REBNQVJTPgAAAIOs ------ =_NextPart_000_01BDAB55.ECC61EBE--