source file: m1455.txt Date: Mon, 22 Jun 1998 14:21:02 -0400 Subject: RE: Double Equal Temperament 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_01BD9E0A.83CD5358 Content-Type: text/plain >page 274: "The primary selective system, which dominates the music of the >western world, is known as equal temperament and consists of a series of 12 >semitones. It is possible to construct a tuning system which would permit >execution of other systems of intonation, such as mean temperament, just >intonation, and the inflections of special types of intonation. The author has >devised a system of tuning, "double equal temperament," which successfully >unifies these systems of intonation. (See Appendix C.)" Double Equal Temperament, or 144-tET, does not provide for anything resembling traditional "mean temperament" (presumably meaning meantone temperament). The fifths of meantone temperament are typically around 696-698 cents, while 144-tET contains no intervals between 692 and 700 cents. 288-tET would be required to unify meantone with these other systems of tuning. ------ =_NextPart_000_01BD9E0A.83CD5358 Content-Type: application/ms-tnef Content-Transfer-Encoding: base64 eJ8+IgUSAQaQCAAEAAAAAAABAAEAAQeQBgAIAAAA5AQAAAAAAADoAAEIgAcAGAAAAElQTS5NaWNy b3NvZnQgTWFpbC5Ob3RlADEIAQWAAwAOAAAAzgcGABYADgAVAAIAAQAXAQEggAMADgAAAM4HBgAW AA4AFQADAAEAGAEBCYABACEAAAA4MUVBMkNCOEUyMDlEMjExQUNEMjAwODA1RkJFM0MwNQA1BwEE gAEAHQAAAFJFOiBEb3VibGUgRXF1YWwgVGVtcGVyYW1lbnQABgoBDYAEAAIAAAACAAIAAQOQBgAI CAAALgAAAAMANgAAAAAAAwAEgAggBgAAAAAAwAAAAAAAAEYAAAAAUoUAALcNAAAeAAWACCAGAAAA AADAAAAAAAAARgAAAABUhQAAAQAAAAQAAAA4LjAAAwAGgAggBgAAAAAAwAAAAAAAAEYAAAAAAYUA AAAAAAALAACACCAGAAAAAADAAAAAAAAARgAAAAADhQAAAAAAAAsAD4AIIAYAAAAAAMAAAAAAAABG AAAAAA6FAAAAAAAAAwAQgAggBgAAAAAAwAAAAAAAAEYAAAAAEIUAAAAAAAADABGACCAGAAAAAADA AAAAAAAARgAAAAARhQAAAAAAAAMAFIAIIAYAAAAAAMAAAAAAAABGAAAAABiFAAAAAAAAHgAkgAgg BgAAAAAAwAAAAAAAAEYAAAAANoUAAAEAAAABAAAAAAAAAB4AJYAIIAYAAAAAAMAAAAAAAABGAAAA ADeFAAABAAAAAQAAAAAAAAAeACaACCAGAAAAAADAAAAAAAAARgAAAAA4hQAAAQAAAAEAAAAAAAAA AgEJEAEAAADxAgAA7QIAAFsEAABMWkZ1rE693wMACgByY3BnMTI10jIA+zM2AeggAqQD5J8HEwKD AFAD1AIAY2gKwNBzZXQwELZ9CoAIyDQgOwlvMAKACoF1Y38AUAsDDNABwQjQAEELYG6RDhAwMzML piA+CrAAZ2UgMjc0OiBoIlRoF+BwBRAAwHIUeSASQGwFkHRpdgEX4HN5c3RlbSyIIHdoDeBoIGQD cC0LgGEZ8AQgdBhxbXVxDdEgb2YbMgqiCoA+LncHkBnwBKF3BbBsZIMaIAQAIGtub3cDoOJhBCBl cXUHQBswGgA6cASQYQeAAjAeIG5kviAFoACBGeAEIBvhYRkRvwiBIDMOIBxFEkAawHQCIDEHkC4g SQVAHaFwbz0EEGkCYBfgIhAfs3Ry9xVgH2EbMHUDABawGbUaNX0dMHUdYBiQBJAh8RxFZbp4BZB1 GXACIBvSbxtB/wXAGcQgMwuAIhEa8CcxGiD+cxVgGoAeMQeAA5EeyRogfmobkCZWKLofghtCC4Bm 1xlDH9Eb0nMe8GMHMRswXnke8ChtImAYYmEnEGjfBbESEBHQHFQBAHYEAAmAXyByJOQb4iRzGiAi GqB1syMyHm8sIho1KXFjB5Dkc2YlwGx5HEQK8xeQfSRxZiDSG0ESQCf/L1UoMwZgF+BBcB7wH5Bp eGAgQy4pIjW4CoBENTL0RR5zVCpaBbExNOA0LXRFVBogGqAHkbcd4AVAGKBvMTABACACEPsFwABw eRtAJJIUACHRAmC7JJIj4GE5cCciHpEiKf7tNHAoGKAHkHUAwAJgGQDfKfIkkinyIhIeuikvpDaw /QGAaCAzQt8fQxQALmIN4B8HQEIhCsAIYB+RNjk22i1HwDgfsB9BcxojI0F/PIUfsgGQC4A9Qiii BJB2ewdABCBiElAcsAnwR7EyOR9zNzAScEhDImAyOL44SUMlpErwPuEecGkUAf8jYjaCQjRDEwPw G0A29SevfSRkLhZBAtEVgwqAEwEAAVKgAAAAAwAmAAAAAAADAC4AAAAAAAsAAgABAAAAHgBwAAEA AAATAAAAVFVOSU5HIGRpZ2VzdCAxNDU0AAACAXEAAQAAABsAAAABvZ31Hui4LOeQCeIR0qzSAIBf vjwFAAUiEmAAQAA5AOBrZIMKnr0BAwDxPwkEAAAeADFAAQAAAAYAAABQQVVMRQAAAAMAGkAAAAAA HgAwQAEAAAAGAAAAUEFVTEUAAAADABlAAAAAAAMA/T/kBAAAAwCAEP////8CAUcAAQAAADMAAABj PVVTO2E9IDtwPUFjYWRpYW4tQXNzZXQ7bD1NQVJTLTk4MDYyMjE4MjEwMlotOTAzNgAAAgH5PwEA AABLAAAAAAAAANynQMjAQhAatLkIACsv4YIBAAAAAAAAAC9PPUFDQURJQU4tQVNTRVQvT1U9QUFN L0NOPVJFQ0lQSUVOVFMvQ049UEFVTEUAAB4A+D8BAAAADwAAAFBhdWwgSC4gRXJsaWNoAAAeADhA AQAAAAYAAABQQVVMRQAAAAIB+z8BAAAASwAAAAAAAADcp0DIwEIQGrS5CAArL+GCAQAAAAAAAAAv Tz1BQ0FESUFOLUFTU0VUL09VPUFBTS9DTj1SRUNJUElFTlRTL0NOPVBBVUxFAAAeAPo/AQAAAA8A AABQYXVsIEguIEVybGljaAAAHgA5QAEAAAAGAAAAUEFVTEUAAABAAAcw4GtkgwqevQFAAAgwWFPN gwqevQEeAD0AAQAAAAUAAABSRTogAAAAAB4AHQ4BAAAAGQAAAERvdWJsZSBFcXVhbCBUZW1wZXJh bWVudAAAAAAeADUQAQAAAC4AAAA8QkUxQkZEMDczOUQ4RDExMUFDQzgwMDgwNUZCRTNDMDUxNDk1 RTdATUFSUz4AAAALACkAAAAAAAsAIwAAAAAAAwAGEMBPB7cDAAcQ4QIAAAMAEBABAAAAAwAREAEA AAAeAAgQAQAAAGUAAABQQUdFMjc0OiJUSEVQUklNQVJZU0VMRUNUSVZFU1lTVEVNLFdISUNIRE9N SU5BVEVTVEhFTVVTSUNPRlRIRVdFU1RFUk5XT1JMRCxJU0tOT1dOQVNFUVVBTFRFTVBFUkFNRU5U AAAAAAIBfwABAAAALgAAADxCRTFCRkQwNzM5RDhEMTExQUNDODAwODA1RkJFM0MwNTE0OTVFN0BN QVJTPgAAAJu/ ------ =_NextPart_000_01BD9E0A.83CD5358--