## Base 180

This forum examines bases larger than or equal to sixty / five dozen / pentanunqual

# Base 180

Dozens Demigod
Double sharp
Dozens Demigod
Joined: Sep 19 2015, 11:02 AM

Dozens Demigod
Double sharp
Dozens Demigod
Joined: Sep 19 2015, 11:02 AM

Dozens Demigod
icarus
Dozens Demigod
Joined: Apr 11 2006, 12:29 PM
Very good! Added. Wrestling with some work and will add some bases as requested soon.

Dozens Demigod
Double sharp
Dozens Demigod
Joined: Sep 19 2015, 11:02 AM
icarus @ Nov 2 2017, 09:19 PM wrote: Very good! Added. Wrestling with some work and will add some bases as requested soon.
Please, do take your time: we all want to see them done perfectly!

I have some time this weekend and will try to get another few done. I have {64} in the works and should be able to finish it shortly.

Dozens Demigod
wendy.krieger
Dozens Demigod
Joined: Jul 11 2012, 09:19 AM
Base 180 joins 10, 45, 117, in that the 'db' scale is also a useful scale covering all of the regulars. The logs of 2, 3, and 5 are 0;24, 0;38 and 0;56. This gives 2 steps per semitone. 180 is 90 semitones.

Base 117 gives the logs of 3 and 13 are ;27 and ;63 resp

Base 45 gives 3, 5, 7 at 13, 19, and 23. This scale is quite handy for sorting the 3-5-7 numbers, and goes a good deal towards explaining base 105 has quite sizable gaps in the log-wheel despite having three prime divisors.

Base 10 gives 2, 5 at 3, 7. So log 2 = 0.3, log 5 = 0.7

Base 17 has e at 0;6 b17, which is quite unusual.

Among the reciprocal pairs we find 13.60 v 13.90 Yes, 13,75 sq gives 1,00,01,45. cf b12 346, 368 gives 357²=100121, and base 40 with 6.10 * 6.16, where 6.13 gives 1,0,0,9.
Twelfty is 120 dec, as 12 decades. V is teen, the '10' digit, E is elef, the '11' digit. A place is occupied by two staves (digits).
Digits group into 2's and 4's, and . , are comma points, : is the radix.
Numbers writen with a single point, in twelfty, like 5.3, means 5 dozen and 3. It is common to push 63 into 5.3 and viki verka.
Exponents (in dec): E = 10^x, Dx=12^x, H=120^x, regardless of base the numbers are in.