source file: m1451.txt Date: Thu, 18 Jun 1998 14:48:42 -0400 Subject: RE: Commas and Consistency 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_01BD9AE9.BB275DFE Content-Type: text/plain Paul H., Commas typically arise not within individual chords but over some span in a piece of music, where various harmonies are constructed from a given pitch-class set. The septimal comma in barbershop harmony -- the typical progression is several dominant sevenths, each the dominant of the next. If the roots are tuned Pythagorean, and the chords 4:5:6:7, then the septimal comma arises between the seventh of one chord and the root of the chord two chords later, which notes are the same pitch class. In an even more typical IV-V7-I progression, the septimal comma arises between the root of the first chord and the seventh of the second chord. In such an instance, "hiding" the comma is particularly important for maintaining the coherence of the pitch-class set, in this case the major scale. ------ =_NextPart_000_01BD9AE9.BB275DFE Content-Type: application/ms-tnef Content-Transfer-Encoding: base64 eJ8+IjMSAQaQCAAEAAAAAAABAAEAAQeQBgAIAAAA5AQAAAAAAADoAAEIgAcAGAAAAElQTS5NaWNy b3NvZnQgTWFpbC5Ob3RlADEIAQWAAwAOAAAAzgcGABIADgAwACoABABZAQEggAMADgAAAM4HBgAS AA4AMAAxAAQAYAEBCYABACEAAAA5MzREQ0Q5MEJDMDZEMjExQUNEMjAwODA1RkJFM0MwNQA2BwEE gAEAGwAAAFJFOiBDb21tYXMgYW5kIENvbnNpc3RlbmN5AFYJAQ2ABAACAAAAAgACAAEDkAYApAcA AC4AAAADADYAAAAAAAMABIAIIAYAAAAAAMAAAAAAAABGAAAAAFKFAAC3DQAAHgAFgAggBgAAAAAA wAAAAAAAAEYAAAAAVIUAAAEAAAAEAAAAOC4wAAMABoAIIAYAAAAAAMAAAAAAAABGAAAAAAGFAAAA AAAACwAAgAggBgAAAAAAwAAAAAAAAEYAAAAAA4UAAAAAAAALAA+ACCAGAAAAAADAAAAAAAAARgAA AAAOhQAAAAAAAAMAEIAIIAYAAAAAAMAAAAAAAABGAAAAABCFAAAAAAAAAwARgAggBgAAAAAAwAAA AAAAAEYAAAAAEYUAAAAAAAADABSACCAGAAAAAADAAAAAAAAARgAAAAAYhQAAAAAAAB4AJIAIIAYA AAAAAMAAAAAAAABGAAAAADaFAAABAAAAAQAAAAAAAAAeACWACCAGAAAAAADAAAAAAAAARgAAAAA3 hQAAAQAAAAEAAAAAAAAAHgAmgAggBgAAAAAAwAAAAAAAAEYAAAAAOIUAAAEAAAABAAAAAAAAAAIB CRABAAAAkQIAAI0CAADMAwAATFpGdVvUlXoDAAoAcmNwZzEyNdIyAPszNgHoIAKkA+MJAgBjaArA c2V0MDYgBxMCgH0KgAjIIDubCW8OMDUCgAqBdWMAUC0LA2MAQQtgbg4QMDNCMwumIFBhdQMgSLwu LAqiCoQKgAhQbQDAMQQgdHlwDeAHQGx5hiAKwAQAZSBubwVAKQPwdGgLgCALgGRp0HZpZHUHQCAQ 0AWwkmQEIGJ1BUBvdgSQ7CBzA3AYwHMKsBlyGHAOIBgABZAYwG9mIG1qdQ3RLBkQaASQGMB2/xiB CGAEIBDhBGADAAeRCsCnGMAFoACAdHIUUHQJgHYgA1IcAWcZwAnwHCF0ORDQLWMLYAQREREuIP5U HUAhMQUwB3AaEheCG9KqYgrAYgSQcxpQcB4F+RhgLS0X0CGhF+UcIANgfwnBBBAdwBlxISIbARoR ZD8DcAuAAHAFQCYCAjBoc/UdEGUA0GgkQyaHHJEkUuhuZXghYUko5ANgGPCZHpR0dSlAH5BQeRlA 7GFnBbAnsG4dEABwH5ADJFIaRTQ6NTo2Ov43HRAkUQOgJFIh3RiDGpH9ESB3CeEtpSczHIICICxF 3yvXKhIoxjEEL3BvGjYLYP0fcHIdEg3gJ+AY4R6FLbP+YRthIIMaMCDyKYEb8QOgDyciHLArcSSH SVYtVvg3LUklCi1DLe8u/zHb/GZpEQAFQDEMMBk5VB7x9x+QGkM2Y3MUUCfgG7MfIHcAcBxgHRAi GVAZsBVAIt8sFCJ0BCAKsSIAYxZQCsD7GFEHcHAJESbSAhAFwADA/wuAAZALgEERQVUdQkCBKMb/ II0dEBlhGUEEIBggGLEkUp0AwGoFsQTwB0BlLhTRFwFAFsMR0QBJsAAAAAMAJgAAAAAAAwAuAAAA AAALAAIAAQAAAB4AcAABAAAAEwAAAFRVTklORyBkaWdlc3QgMTQ1MAAAAgFxAAEAAAAbAAAAAb2a yJ3FbrIwFQYBEdKs0gCAX748BQAHoMOgAEAAOQCQ2km36Zq9AQMA8T8JBAAAHgAxQAEAAAAGAAAA UEFVTEUAAAADABpAAAAAAB4AMEABAAAABgAAAFBBVUxFAAAAAwAZQAAAAAADAP0/5AQAAAMAgBD/ ////AgFHAAEAAAAzAAAAYz1VUzthPSA7cD1BY2FkaWFuLUFzc2V0O2w9TUFSUy05ODA2MTgxODQ4 NDJaLTgwOTMAAAIB+T8BAAAASwAAAAAAAADcp0DIwEIQGrS5CAArL+GCAQAAAAAAAAAvTz1BQ0FE SUFOLUFTU0VUL09VPUFBTS9DTj1SRUNJUElFTlRTL0NOPVBBVUxFAAAeAPg/AQAAAA8AAABQYXVs IEguIEVybGljaAAAHgA4QAEAAAAGAAAAUEFVTEUAAAACAfs/AQAAAEsAAAAAAAAA3KdAyMBCEBq0 uQgAKy/hggEAAAAAAAAAL089QUNBRElBTi1BU1NFVC9PVT1BQU0vQ049UkVDSVBJRU5UUy9DTj1Q QVVMRQAAHgD6PwEAAAAPAAAAUGF1bCBILiBFcmxpY2gAAB4AOUABAAAABgAAAFBBVUxFAAAAQAAH MHJa2Nznmr0BQAAIMP5dJ7vpmr0BHgA9AAEAAAAFAAAAUkU6IAAAAAAeAB0OAQAAABcAAABDb21t YXMgYW5kIENvbnNpc3RlbmN5AAAeADUQAQAAAC4AAAA8QkUxQkZEMDczOUQ4RDExMUFDQzgwMDgw NUZCRTNDMDUxNDk1RTBATUFSUz4AAAALACkAAAAAAAsAIwAAAAAAAwAGENj1eE4DAAcQlAIAAAMA EBAAAAAAAwAREAEAAAAeAAgQAQAAAGUAAABQQVVMSCxDT01NQVNUWVBJQ0FMTFlBUklTRU5PVFdJ VEhJTklORElWSURVQUxDSE9SRFNCVVRPVkVSU09NRVNQQU5JTkFQSUVDRU9GTVVTSUMsV0hFUkVW QVJJT1VTSEFSTU9OAAAAAAIBfwABAAAALgAAADxCRTFCRkQwNzM5RDhEMTExQUNDODAwODA1RkJF M0MwNTE0OTVFMEBNQVJTPgAAACKf ------ =_NextPart_000_01BD9AE9.BB275DFE--