source file: m1457.txt Date: Wed, 24 Jun 1998 16:01:37 -0400 Subject: Schillinger, Double Equal Temperament, and McLaren 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_01BD9FAA.E516B32E Content-Type: text/plain >Schillinger only claims that "the micro-units are the best >averages for >all differences between units of the 12th root of 2 and just intonation >(natural scale)". No, Schillinger also claims that his system can represent "mean temperament," which must mean meantone temperament. This was both in your original quote and in Brian McLaren's Xenharmonikon 17 article, "A Short History of Microtonality in the 20th Century." But Schillinger is incorrect. Meantone tuning, the tuning of choice for music from 1500-1700 and much music thereafter, is built upon consecutive perfect fifths of 694.8 to 698.4 cents. 144tET ("double equal temperament") contains no intervals between 691.7 and 700 cents, so cannot represent meantone tuning. 288tET does have a 695.8-cent interval, so it can be used to represent meantone tuning. Although I'm probably one of very few people to have already read McLaren's XH17 article, it does contain other factual inaccuracies, some McLaren's own. For example, a positive tuning is one with perfect fifths larger than 700 cents, not necessarily one with perfect fifths larger than the just 3/2 (702 cents). However, the article is amazingly comprehensive and I wish I had had access to all that information earlier. Apparantly, Bosanquet studied 22-tET extensively, and Ogolevets proclaimed it the future of music (along with 17-tET). The section of my paper entitled "History of 22" now seems really underinformed. But my chances of ever being able to get a hold of those writings seems very small -- anyone know if McLaren actually had the primary sources on hand? ------ =_NextPart_000_01BD9FAA.E516B32E Content-Type: application/ms-tnef Content-Transfer-Encoding: base64 eJ8+IicUAQaQCAAEAAAAAAABAAEAAQeQBgAIAAAA5AQAAAAAAADoAAEIgAcAGAAAAElQTS5NaWNy b3NvZnQgTWFpbC5Ob3RlADEIAQWAAwAOAAAAzgcGABgAEAABACUAAwAsAQEggAMADgAAAM4HBgAY ABAAAQAlAAMALAEBCYABACEAAAA0OURGMjEyRDc1MEJEMjExQUNEMjAwODA1RkJFM0MwNQAlBwEE gAEAMwAAAFNjaGlsbGluZ2VyLCBEb3VibGUgRXF1YWwgVGVtcGVyYW1lbnQsIGFuZCBNY0xhcmVu ABYSAQ2ABAACAAAAAgACAAEDkAYANAoAAC4AAAADADYAAAAAAAMABIAIIAYAAAAAAMAAAAAAAABG AAAAAFKFAAC3DQAAHgAFgAggBgAAAAAAwAAAAAAAAEYAAAAAVIUAAAEAAAAEAAAAOC4wAAMABoAI IAYAAAAAAMAAAAAAAABGAAAAAAGFAAAAAAAACwAAgAggBgAAAAAAwAAAAAAAAEYAAAAAA4UAAAAA AAALAA+ACCAGAAAAAADAAAAAAAAARgAAAAAOhQAAAAAAAAMAEIAIIAYAAAAAAMAAAAAAAABGAAAA ABCFAAAAAAAAAwARgAggBgAAAAAAwAAAAAAAAEYAAAAAEYUAAAAAAAADABSACCAGAAAAAADAAAAA AAAARgAAAAAYhQAAAAAAAB4AJIAIIAYAAAAAAMAAAAAAAABGAAAAADaFAAABAAAAAQAAAAAAAAAe ACWACCAGAAAAAADAAAAAAAAARgAAAAA3hQAAAQAAAAEAAAAAAAAAHgAmgAggBgAAAAAAwAAAAAAA AEYAAAAAOIUAAAEAAAABAAAAAAAAAAIBCRABAAAADAUAAAgFAAAbBwAATFpGdXY17uIDAAoAcmNw ZzEyNdIyAPszNgHoIAKkA+SfBxMCgwBQA9QCAGNoCsDQc2V0MBC2fQqACMg0IDsJbzACgAqBdWNb AFALA2MAQQtgbg4QMMQzMwumID5TEgADECpsC4BnBJAgAiBsedQgYwthbQQgdBIQBUBiIhjQZSBt DeADYC16dQMAdAQgCsAZUBkyYo0HkHQKogqAPmF2BJBuYRfQBCACEHIa9heQINpkBpBmBJAJ8GMH kRqwlHR3CeEgGdRvZhpjaw4gGNAgA2BvBUAecTJBGiBuZCBqdRrQIO0LgHQCIBjwaQIgGvQK890X MCggoQhwB0AgBPAHQDBlKSIuIQgKgE5vziwGABdpB0BzbxhbF3DJBCBzeRrQZW0YUAOR/RQAcBQA EkACMBkQB4ADkR0mIXAbgQeAAjAsIiD+dxdwEgAZYCAiJ1MnUiCBIxpRJ7guIFQlsndhzx1xH1Af EAuAIHkIYRgAzQUQZwuAIjFxdR9QGVAbH9IrwUIHIQOgTWNM6RoxbicEIFgJ8BIRBGDtAwBrAiAe 0DcaISDAGGBSZSPAIkEGAGgJESC2SAQAIIByGEAecU0ZgvsgghegdBhAK8EZMgHQHwEmQycBCHB5 LihgQnW/BUAXWiXBC4AFoRQAYyqx/k0plxnRFlAjwBkyNjQeYv0SAG8N4BlQG/Eo0g3gG+DDA2Ee 0DUwMC0vgDkQvx/DKOAotDhxGTEUAGEBgGcEkCPAJcFidQMQBUB1vnAvUQWgAIAFkDPQaRtw/iAn 0R0ANWAb4AaQGNAeU+A2OTQuOBjAJNA+AFg4LjQYUCcBcyrAMQA0NHRFVCAoIu5kCGACYBlQZSzQ IjEnqbwiKTwSAZALgAQgbiTQOyBhBJB2JKEdhz4AMS7/L5Ef4TlSPvMjwCTCAHBCMB8FQCaoKYg2 QyrAMjg4Xz+SP/AHkRIQPLFhPfE1/T4wLT7yQldEsxnwJlMasH8eABJAH/A+YUV/Roci6kGTO6Aw gHVnHxBJJyZA+SbAb2IBoBgxKdIecRtx7xhAHQAH4CfQbwtQGlEk0HVH5Gw6sWQYQFDCLfpI/y+K SdFHk0GlGAA6ghvgANC3IgAiMSyBYzxwG5BjCJBHRKMHgC35b3duKsBG+QWxZXgoAE/hI8BIMDvg /wCQPJM29SXBKdID8B8BPO39C2ByF9IY0QOgRClFMing/R1RcwrAAxBOlFlfWm0ZMukgEzMvH7Ao OVAfsD7z6ikqwEhWoGUbcTaUL7XzNLIoAGF6F7EYMgNwJsGvGUAAgUgCH+FJXTFzTcH/R9Ef8GSy VPFccT5SHJIY0/8LgBvxAMAgwkBQCsAXoASQeSrAQXAKsSmhGDAjwEL/V/AAcCzQElAiUCIAHNBK kfgyMi0/klcwJiBjg2gy+R/ST2cG8GERGgFOIRhj90qRSdEZMmYz0AhwTtM4RP4oB0ACIDdAXUMv gGmyYLH/KuAZUDxRZtNtQhhACrAn0d9AUAIwGfAikB/wIjDZaZD/KGBCMAfgEkAmMAQgOrEXkP8Y QBnQBIFmZAmAKsAzwnAR/xIBHUMecWESGqE3Ik5hUAPvF9AFQEgwMIBsH/Aec1fwf10hBRAgwBZQ JdFyg08jc3MAwByhLS0fwSvwKeFr/3IyBpAt9mUhVIIYMWSyGTL/JsAHcArAeOEIYXTjA6BbEXxk PxXhAtEVgwqAEwEAAX6gAwAmAAAAAAADAC4AAAAAAAsAAgABAAAAHgBwAAEAAAATAAAAVFVOSU5H IGRpZ2VzdCAxNDU2AAACAXEAAQAAABsAAAABvZ+Hta4tIdjYC3UR0qzSAIBfvjwFAAgKSCAAQAA5 AGBN9eSqn70BAwDxPwkEAAAeADFAAQAAAAYAAABQQVVMRQAAAAMAGkAAAAAAHgAwQAEAAAAGAAAA UEFVTEUAAAADABlAAAAAAAMA/T/kBAAAAwCAEP////8CAUcAAQAAADQAAABjPVVTO2E9IDtwPUFj YWRpYW4tQXNzZXQ7bD1NQVJTLTk4MDYyNDIwMDEzN1otMTAwOTQAAgH5PwEAAABLAAAAAAAAANyn QMjAQhAatLkIACsv4YIBAAAAAAAAAC9PPUFDQURJQU4tQVNTRVQvT1U9QUFNL0NOPVJFQ0lQSUVO VFMvQ049UEFVTEUAAB4A+D8BAAAADwAAAFBhdWwgSC4gRXJsaWNoAAAeADhAAQAAAAYAAABQQVVM RQAAAAIB+z8BAAAASwAAAAAAAADcp0DIwEIQGrS5CAArL+GCAQAAAAAAAAAvTz1BQ0FESUFOLUFT U0VUL09VPUFBTS9DTj1SRUNJUElFTlRTL0NOPVBBVUxFAAAeAPo/AQAAAA8AAABQYXVsIEguIEVy bGljaAAAHgA5QAEAAAAGAAAAUEFVTEUAAABAAAcwQlL15KqfvQFAAAgwLrMW5aqfvQEeAD0AAQAA AAEAAAAAAAAAHgAdDgEAAAAzAAAAU2NoaWxsaW5nZXIsIERvdWJsZSBFcXVhbCBUZW1wZXJhbWVu dCwgYW5kIE1jTGFyZW4AAB4ANRABAAAALgAAADxCRTFCRkQwNzM5RDhEMTExQUNDODAwODA1RkJF M0MwNTE0OTVGNUBNQVJTPgAAAAsAKQAAAAAACwAjAAAAAAADAAYQjl3mqgMABxAmBQAAAwAQEAEA AAADABEQAAAAAB4ACBABAAAAZQAAAFNDSElMTElOR0VST05MWUNMQUlNU1RIQVQiVEhFTUlDUk8t VU5JVFNBUkVUSEVCRVNUQVZFUkFHRVNGT1JBTExESUZGRVJFTkNFU0JFVFdFRU5VTklUU09GVEhF MTJUSFJPT1QAAAAAAgF/AAEAAAAuAAAAPEJFMUJGRDA3MzlEOEQxMTFBQ0M4MDA4MDVGQkUzQzA1 MTQ5NUY1QE1BUlM+AAAAxIo= ------ =_NextPart_000_01BD9FAA.E516B32E--