Tuning-Math Digests messages 5677 - 5701

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Message: 5677

Date: Sun, 1 Dec 2002 22:25:29

Subject: Some 17-limit basis stuff

From: Gene W Smith

I was looking at what turns up when we take six successive 17-limit
superparticular commas, and it turns out that 72 is an outlier, in the
sense that it gets created ten times in this way; its nearest competition
is 764, which appears four times.

We get 72 from any successive six commas in this list

[385/384, 441/440, 442/441, 540/539, 561/560, 595/594, 625/624, 676/675] 

or this list

[625/624, 676/675, 715/714, 729/728, 833/832, 936/935, 1001/1000,
1089/1088] 

or this list:

[1089/1088, 1156/1155, 1225/1224, 1275/1274, 1701/1700, 1716/1715,
2058/2057]

The TM basis is this:

[169/168, 221/220, 225/224, 243/242, 273/272, 325/324]


We also have an interesting situation with 46, where two versions of the
46 et appear. We have
h46+v17:

[46, 73, 107, 129, 159, 170, 189]

This is defined by six contiguous commas in the list

[325/324, 351/350, 352/351, 364/363, 375/374, 385/384, 441/440]

and has basis

[52/51, 91/90, 121/119, 126/125, 169/168, 176/175]


We also have h46:

[46, 73, 107, 129, 159, 170, 188]

This is defined by six contiguous commas of the list

[256/255, 273/272, 289/288, 325/324, 351/350, 352/351, 364/363] 

or by the six commas

[2601/2600, 3025/3024, 4096/4095, 4225/4224, 4375/4374, 4914/4913]

It has basis

[91/90, 121/120, 126/125, 136/135, 154/153, 169/168]


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