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Important 7-limit commas?

🔗Gene Ward Smith <gwsmith@svpal.org>

4/13/2005 12:34:30 AM

Here is a list of 7-limit commas, under 50 cents in size and within a
Hahn radius of 7 of unity, in order of TOP error of the corresponding
temperament times the fourth power of the Hahn radius. There are five
limit commas on this list, but they are being evaluated from a seven
limit point of view, and hence do not show well. The first two on the
list vanish in ennealimmal, 50/49 and 49/48 are identified, and
1029/1024 and 225/224 are identified. The schisma shows up as
important in the five limit. Hence, asking for symbols for 49/48 or
50/49, 36/35, 126/125, and 225/224 or 1029/1024 seems justified in
terms of their importance, if you believe this analysis.

2401/2400, 4375/4374, 50/49, 49/48, 36/35, 126/125, 1029/1024, 225/224,
6144/6125, 1728/1715, 3136/3125, 65625/65536, 64/63, 128/125, 875/864,
15625/15552, 81/80, 245/243, 5120/5103, 3125/3087, 16875/16807, 525/512,
1029/1000, 4000/3969, 3125/3072, 686/675, 2048/2025, 2430/2401, 250/243,

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

4/14/2005 1:16:39 AM

Gene,

You wrote:
________________________________________________________________________
Date: Wed, 13 Apr 2005 07:34:30 -0000

Here is a list of 7-limit commas, under 50 cents in size and within a
Hahn radius of 7 of unity, in order of TOP error of the corresponding
temperament times the fourth power of the Hahn radius. There are five
limit commas on this list, but they are being evaluated from a seven
limit point of view, and hence do not show well. The first two on the
list vanish in ennealimmal, 50/49 and 49/48 are identified, and
1029/1024 and 225/224 are identified. The schisma shows up as
important in the five limit. Hence, asking for symbols for 49/48 or
50/49, 36/35, 126/125, and 225/224 or 1029/1024 seems justified in
terms of their importance, if you believe this analysis.

2401/2400, 4375/4374, 50/49, 49/48, 36/35, 126/125, 1029/1024, 225/224,
6144/6125, 1728/1715, 3136/3125, 65625/65536, 64/63, 128/125, 875/864,
15625/15552, 81/80, 245/243, 5120/5103, 3125/3087, 16875/16807, 525/512,
1029/1000, 4000/3969, 3125/3072, 686/675, 2048/2025, 2430/2401, 250/243,
________________________________________________________________________

Gene, some questions:
1. What's the rationale for choosing the fourth power of the Hahn radius?

2. Saying " ... asking for symbols for ... seems justified in terms of their
importance,
if you believe this analysis" suggests both:
A. that you can conceive of alternative analyses (What are they?), and
B. that you still prefer THIS analysis (Why do you?).

Regards,
Yahya

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