Search found 1177 matches

by Dave Keenan
Wed May 24, 2023 11:10 am
Forum: Notations for other tunings
Topic: Notation for Fibonacci tuning (Wilson's horogram #22)?
Replies: 27
Views: 15830

Re: Notation for Fibonacci tuning (Wilson's horogram #22)?

I get 700.3106 ¢ for the 12-generator fifth. That's (12 × n(1\2) ) mod 1200 ¢ = ((12 × n(1/2)) mod 1)×1200 ¢ = (12/ϕ² mod 1)×1200 ¢. I would expect a chain of 12 generators to give 13 notes, so I think you are missing a final G. I agree we need not be constrained by the Trojan capture zones, and sho...
by Dave Keenan
Tue May 23, 2023 12:38 pm
Forum: Notations for other tunings
Topic: Notation for Fibonacci tuning (Wilson's horogram #22)?
Replies: 27
Views: 15830

Re: Notation for Fibonacci tuning (Wilson's horogram #22)?

Brilliant. Yes, now that you mention it, the 144edo notation is the obvious solution. And 144 is a Fibonacci number. What is the largest MOS cardinality that can be notated with only the 144edo symbols without nominal crossings? I'm guessing 55, since 7×12 only gets you to 84.
by Dave Keenan
Fri May 12, 2023 11:24 am
Forum: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19222

Re: Noble frequency ratios as prime-count vectors in ℚ(√5)

Welcome to the Sagittal forum, Mike. @battaglia01

See the text beginning "A fundamental prime is" near the middle of this post:
viewtopic.php?p=4606#p4606
by Dave Keenan
Thu May 11, 2023 2:26 pm
Forum: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19222

Re: Noble frequency ratios as prime-count vectors in ℚ(√5)

Mike Battaglia, You asked on this facebook thread : "One question for רועי סיני and Dave Keenan - I think in some recent post, we determined that the "canonical" versions of each feudal prime are not necessarily the two that are closest together, right? I had thought we determined tha...
by Dave Keenan
Mon May 01, 2023 12:54 am
Forum: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19222

Re: Noble frequency ratios as prime-count vectors in ℚ(√5)

Dave KeenanAuthor Here's a specific proposal for how to approximate the 32 simplest nobles using higher primes. https://forum.sagittal.org/viewtopic.php?p=4625#p4625 Noble frequency ratios as prime-count vectors in ℚ(√5) - Page 2 - The Sagittal forum FORUM.SAGITTAL.ORG Noble frequency ratios as prim...
by Dave Keenan
Mon May 01, 2023 12:53 am
Forum: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19222

Re: Noble frequency ratios as prime-count vectors in ℚ(√5)

Mike BattagliaAdmin FWIW, I was originally thinking about all of the nobles you can generate from the 5-limit being this very large dimensional space - what was it, like 150-dimensions or something, just for the 5-limit? I'm not sure how it compares if you only want to add one or two nobles. But the...
by Dave Keenan
Mon May 01, 2023 12:47 am
Forum: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19222

Re: Noble frequency ratios as prime-count vectors in ℚ(√5)

Dave KeenanAuthor Mike Battaglia Paul Erlich Cmloegcmluin Xenharmonic Feisbeuk Steve Martin Here is a table/plot of my new preferred feudal primes — those that ensure that all rationals and the maximum number of nobles (all but 2 on each level of the Stern-Brocot tree) can be factorised without need...
by Dave Keenan
Mon May 01, 2023 12:38 am
Forum: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19222

Re: Noble frequency ratios as prime-count vectors in ℚ(√5)

Dave KeenanAuthor We need a UFD to make the whole monzo thing work. Right? Reply 31 wEdited Mike BattagliaAdmin OK, well, I'm not sure what to say - it seems like you are mostly just defending what you already have... I think it's all interesting and was trying to explore a little bit further. All I...
by Dave Keenan
Mon May 01, 2023 12:20 am
Forum: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19222

Re: Noble frequency ratios as prime-count vectors in ℚ(√5)

[I've pasted the fully-expanded current contents of the related facebook thread below (as 5 posts), because I'm tired of having to click "See more" and "View more replies" all the time to find the recent gems (proofs and counterexamples) by רועיסיני (Roee Sinai), hilted below.] D...
by Dave Keenan
Fri Apr 28, 2023 11:01 pm
Forum: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19222

Re: Noble frequency ratios as prime-count vectors in ℚ(√5)

Thank you! I have now added asterisk notes to both of the posts you mentioned, which link to your post above.