Search found 1099 matches

by Dave Keenan
Mon Nov 14, 2022 11:33 am
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 20
Views: 1836

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

Yes. I think one post a day would be plenty to take in. :-) Thank you for the correction. I have made the edit.
by Dave Keenan
Mon Oct 10, 2022 1:53 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 20
Views: 1836

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

I'm linking to this old post by Dan Stearns because it seems like it might be relevant. https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77465 There are other useful posts in that thread, such as this one with a list of noble and near-noble triads at its end (quoted below)...
by Dave Keenan
Sat Oct 08, 2022 7:41 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 20
Views: 1836

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

Here's a proposal for standard pairs of convergents (in green ) for approximating each noble using Mike Battaglia's geometric mean approximation scheme, with a "prime" basis of 2.3.5.7.11.13.2 χ .3 χ .5 χ .7 χ .11 χ .13 χ .17 χ where χ = ϕ/√5 ≈ 0.7236. Mike proved that this constant, for w...
by Dave Keenan
Fri Oct 07, 2022 10:32 am
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 20
Views: 1836

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

Choosing pairs of Rationals for the Geometric Mean Approximation Scheme The following table gives more insight into the process that led to the choices in the previous post, for approximating nobles by complex rationals. It is also useful in deciding which pairs of rationals to use in approximating...
by Dave Keenan
Thu Oct 06, 2022 10:23 am
Forum: Equal Division notations
Topic: Notating 37EDO
Replies: 10
Views: 7936

Re: Notating 37EDO

Here's a video of Joseph Monzo's The Kog Sisters, in 37ed2, showing how he notated it.
https://www.youtube.com/watch?v=QERRKsbbWUQ
by Dave Keenan
Wed Oct 05, 2022 9:11 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 20
Views: 1836

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

Approximating Nobles with Complex Rationals In discussions in the facebook thread , Mike Battaglia suggested approximating the nobles using phi-weighted geometric means. This would allow us to have only ordinary primes in our basis, but the entries in the vectors would become feudal integers instea...
by Dave Keenan
Sat Oct 01, 2022 12:23 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 20
Views: 1836

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

Modular Inverse I've attached an Excel spreadsheet with a formula that blew my mind the other day. In the feudal facebook thread, Mike Battaglia came up with a cool way of factoring an (almost*) arbitrary feudal integer into a product of nobles and units (assuming that's always possible, as I conje...
by Dave Keenan
Fri Sep 30, 2022 9:23 am
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 20
Views: 1836

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

Naming Nobles About that n7/4 or \(\text{n}\frac74\) notation for noble numbers shown in Figure 8 and Tables 14 and 15 . The small "n" can be considered the ennoblement function. When applied to any rational number, small "n" gives a unique noble number. Not to be confused with ...
by Dave Keenan
Thu Sep 29, 2022 6:26 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 20
Views: 1836

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

Thanks cmloegcmluin . It would have been strange if this thread did not contain at least one example of a feudal comma. You have given several. Clarifications I'd like to clarify a few things that have come up in email and facebook conversations: 1. It is so far only a conjecture , I don't have a pr...
by Dave Keenan
Fri Sep 23, 2022 9:17 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 20
Views: 1836

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

There is much discussion of this topic on the facebook group Xenharmonic Alliance - Mathematical Theory.

Many thanks to Mike Battaglia for these extensive discussions.