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tuning-math

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  • Members: 191
  • Category: Mathematics
  • Founded: May 21, 2001
  • Language: English
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7-limit MT reduced bases for ets   Message List  
Reply Message #3151 of 20696 |
9: [21/20, 27/25, 128/125]
10: [25/24, 28/27, 49/48]
12: [36/35, 50/49, 64/63]
15: [28/27, 49/48, 126/125]
19: [49/48, 81/80, 126/125]
22: [50/49, 64/63, 245/243]
27: [64/63, 126/125, 245/243]
31: [81/80, 126/125, 1029/1024]
41: [225/224, 245/243, 1029/1024]
68: [245/243, 2048/2025, 2401/2400]
72: [225/224, 1029/1024, 4375/4374]
99: [2401/2400, 3136/3125, 4375/4374]
130: [2401/2400, 3136/3125, 19683/19600]
140: [2401/2400, 5120/5103, 15625/15552]

For any prime limit, we could consider the most characteristic linear
temperament of a particular et to be the one leaving off the last member of the
MT reduced basis. It is interesting to note that the characteristic linear
temperament of 99 and 130 is the same. Of course we can do the same for planar
temperaments, etc.




Sat Feb 2, 2002 3:31 am

genewardsmith
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Message #3151 of 20696 |
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9: [21/20, 27/25, 128/125] 10: [25/24, 28/27, 49/48] 12: [36/35, 50/49, 64/63] 15: [28/27, 49/48, 126/125] 19: [49/48, 81/80, 126/125] 22: [50/49, 64/63,...
genewardsmith Offline Send Email Feb 2, 2002
3:31 am

... I accidentally left off 171: [2401/2400, 4375/4374, 32805/32768] Wouldn't want to do that--look at those three high-powered commas!...
genewardsmith Offline Send Email Feb 2, 2002
3:34 am

... This is seriously cool. ... Does it have to be prime (not odd) limit? -Carl...
clumma Offline Send Email Feb 2, 2002
4:07 am

... Fraid so. It occurs to me another fun game to play with these is to find the corresponding Fokker blocks....
genewardsmith Offline Send Email Feb 2, 2002
4:41 am

... Or better yet, the most compact blocks where ratio odd-limit measures distance from a central 1/1 (this is what I refer to as the van Prooijen metric)....
paulerlich Offline Send Email Feb 2, 2002
7:26 am

... Yeah, Carl, these are _tuning system building_ considerations and not _simultaneous consonance_ considerations....
paulerlich Offline Send Email Feb 2, 2002
7:24 am

... linear temperament of a particular et to be the one leaving off the last member of the MT reduced basis. Let's follow up on that: 9: 21/20 ^ 27/25 = [2, 3,...
Gene Ward Smith
genewardsmith Offline Send Email
Nov 3, 2003
8:20 pm
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