source file: m1470.txt Date: Thu, 9 Jul 1998 12:26:26 -0400 Subject: RE: Helmholtz's and Ellis's tunings 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_01BDAB56.52108656 Content-Type: text/plain >Ellis also constructed a 53 tone irregular tuning, which he called somewhat >oxymoronically "unequally just," from the central 56 tones of the >Duodenarium by ignoring the skhisma and using fifths of 700 and 702 cents >(pp.435 and 465). I thought the duodenarium was a 12-tone scale, Euler's 3^3.5^2 genus. I guess I was wrong. Please straighten me out. ------ =_NextPart_000_01BDAB56.52108656 Content-Type: application/ms-tnef Content-Transfer-Encoding: base64 eJ8+IhwQAQaQCAAEAAAAAAABAAEAAQeQBgAIAAAA5AQAAAAAAADoAAEIgAcAGAAAAElQTS5NaWNy b3NvZnQgTWFpbC5Ob3RlADEIAQWAAwAOAAAAzgcHAAkADAAaABoABAApAQEggAMADgAAAM4HBwAJ AAwAGgAaAAQAKQEBCYABACEAAAA0QUNCOTBGOUY2MTVEMjExQUNEMzAwODA1RkJFM0MwNQA8BwEE gAEAJAAAAFJFOiBIZWxtaG9sdHoncyBhbmQgRWxsaXMncyB0dW5pbmdzAHAMAQ2ABAACAAAAAgAC AAEDkAYA3AYAAC4AAAADADYAAAAAAAMABIAIIAYAAAAAAMAAAAAAAABGAAAAAFKFAAC3DQAAHgAF gAggBgAAAAAAwAAAAAAAAEYAAAAAVIUAAAEAAAAEAAAAOC4wAAMABoAIIAYAAAAAAMAAAAAAAABG AAAAAAGFAAAAAAAACwAAgAggBgAAAAAAwAAAAAAAAEYAAAAAA4UAAAAAAAALAA+ACCAGAAAAAADA AAAAAAAARgAAAAAOhQAAAAAAAAMAEIAIIAYAAAAAAMAAAAAAAABGAAAAABCFAAAAAAAAAwARgAgg BgAAAAAAwAAAAAAAAEYAAAAAEYUAAAAAAAADABSACCAGAAAAAADAAAAAAAAARgAAAAAYhQAAAAAA AB4AJIAIIAYAAAAAAMAAAAAAAABGAAAAADaFAAABAAAAAQAAAAAAAAAeACWACCAGAAAAAADAAAAA AAAARgAAAAA3hQAAAQAAAAEAAAAAAAAAHgAmgAggBgAAAAAAwAAAAAAAAEYAAAAAOIUAAAEAAAAB AAAAAAAAAAIBCRABAAAAxAEAAMABAAA4AgAATFpGdUG0M1ADAAoAcmNwZzEyNdIyAPszNgHoIAKk A+SfBxMCgwBQA9QCAGNoCsDQc2V0MBC2fQqACMg0IDsJbzACgAqBdWNbAFALA2MAQQtgbg4QMAQz MwumID5FbGzFBAAgB0BzbyAFoACANHRyFWB0CYAXoCA1CDMgdAIgZSBpcpkUAGd1C2AFwHR1AwAh FlAsIHdoDeBoIOpoGUBjB0BsGJEX0AeAGRqAYXQKogqAPm94HwbABbACIA3gGyF5ICKRGhBlcXUd E2p1GDD4LCIgA1IZABriCfAYQJsHQBjQNhkDBCBvZh7CKRwFRHUEcW4KwGl1xR6wYh1AaWduBbAa MWkew3NrGpBzAMAXoG53GKAeICIyZgaQHtAgAzfuMBJwIzIkcDIfAxHQHBMDCvMXMChwcC40M4I1 IyM0NjUpLiWIzQqASR7BCGBnaAVAHtJSZCEJd2EXkSAOIC3XGRME8AdAZRpgRRmwBJACJwQgM14z LjVezSUQZwnwHiAuICggGaCvB5AEICggKcJ3HMFnLGD+UBtAKdAikR9BIeAokAnw5iAHgCAQdXQn UBXwAtEXFYMKgBMBADBwAwAmAAAAAAADAC4AAAAAAAsAAgABAAAAHgBwAAEAAAATAAAAVFVOSU5H IGRpZ2VzdCAxNDY5AAACAXEAAQAAABsAAAABvatEUjD5kMeAFfYR0qzTAIBfvjwFAARxd4AAQAA5 AAB+8VFWq70BAwDxPwkEAAAeADFAAQAAAAYAAABQQVVMRQAAAAMAGkAAAAAAHgAwQAEAAAAGAAAA UEFVTEUAAAADABlAAAAAAAMA/T/kBAAAAwCAEP////8CAUcAAQAAADIAAABjPVVTO2E9IDtwPUFj YWRpYW4tQXNzZXQ7bD1NQVJTLTk4MDcwOTE2MjYyNlotNzg5AAAAAgH5PwEAAABLAAAAAAAAANyn QMjAQhAatLkIACsv4YIBAAAAAAAAAC9PPUFDQURJQU4tQVNTRVQvT1U9QUFNL0NOPVJFQ0lQSUVO VFMvQ049UEFVTEUAAB4A+D8BAAAADwAAAFBhdWwgSC4gRXJsaWNoAAAeADhAAQAAAAYAAABQQVVM RQAAAAIB+z8BAAAASwAAAAAAAADcp0DIwEIQGrS5CAArL+GCAQAAAAAAAAAvTz1BQ0FESUFOLUFT U0VUL09VPUFBTS9DTj1SRUNJUElFTlRTL0NOPVBBVUxFAAAeAPo/AQAAAA8AAABQYXVsIEguIEVy bGljaAAAHgA5QAEAAAAGAAAAUEFVTEUAAABAAAcwxIfxUVarvQFAAAgwVoYQUlarvQEeAD0AAQAA AAUAAABSRTogAAAAAB4AHQ4BAAAAIAAAAEhlbG1ob2x0eidzIGFuZCBFbGxpcydzIHR1bmluZ3MA HgA1EAEAAAAuAAAAPEJFMUJGRDA3MzlEOEQxMTFBQ0M4MDA4MDVGQkUzQzA1MTQ5NjFFQE1BUlM+ AAAACwApAAAAAAALACMAAAAAAAMABhAnHDtjAwAHEBwBAAADABAQAQAAAAMAERABAAAAHgAIEAEA AABlAAAARUxMSVNBTFNPQ09OU1RSVUNURURBNTNUT05FSVJSRUdVTEFSVFVOSU5HLFdISUNISEVD QUxMRURTT01FV0hBVE9YWU1PUk9OSUNBTExZIlVORVFVQUxMWUpVU1QsIkZST01USAAAAAACAX8A AQAAAC4AAAA8QkUxQkZEMDczOUQ4RDExMUFDQzgwMDgwNUZCRTNDMDUxNDk2MUVATUFSUz4AAADD WA== ------ =_NextPart_000_01BDAB56.52108656--