Search found 1177 matches

by Dave Keenan
Wed Apr 12, 2023 6:42 pm
Forum: Linear Temperament notations
Topic: Notating 5-limit pental with added 7th harmonics
Replies: 15
Views: 3854

Re: Notating 5-limit pental with added 7th harmonics

This is incomplete, but hopefully it's enough so you understand what I have in mind. This would not be a general 255edo notation, but purely a pental-plus-7th-harmonics notation. D:!(: E:|): G:!): A:|(: C:\!): A:!(: B:|): D:!): E:|(: G:\!): E:!(: F:#::|): A:!): B:|(: D:\!): B:!(: C:#::|): E:!): F:#:...
by Dave Keenan
Wed Apr 12, 2023 2:59 pm
Forum: Linear Temperament notations
Topic: Notating 5-limit pental with added 7th harmonics
Replies: 15
Views: 3854

Re: Notating 5-limit pental with added 7th harmonics

Here's notating the easy parts of 255edo with uncontroversial sagittals, based on the complex 7-limit mappings. These sagittals all happen to correspond to even numbers of steps: D:!(: E:|): G:!): A:|(: C:\!): A:!(: B:|): D:!): E:|(: G:\!): E:!(: F:#::|): A:!): B:|(: D:\!): B:!(: C:#::|): E:!): F:#:...
by Dave Keenan
Wed Apr 12, 2023 1:34 pm
Forum: Linear Temperament notations
Topic: Notating 5-limit pental with added 7th harmonics
Replies: 15
Views: 3854

Re: Notating 5-limit pental with added 7th harmonics

If I had instead shown a redundant parenthesised top row: (104 155 206 2 53) We would obtain a different complex 7-limit pental mapping. In octave equivalent form: 0 0 2 0 0 1 5 -26 Octave specific: 5 5 -13 80 0 1 5 -26 Since this is arguably equally complex, we could refer to these as the +25g and ...
by Dave Keenan
Wed Apr 12, 2023 12:57 pm
Forum: Linear Temperament notations
Topic: Notating 5-limit pental with added 7th harmonics
Replies: 15
Views: 3854

Re: Notating 5-limit pental with added 7th harmonics

You clearly have a very good understanding of the system, so you should feel free to use whatever seems best to you. But the main problem I see with your proposal to set Archytas' comma to 5\255 is that the best approximation of the 7th harmonic is given by setting Archytas' comma and hence the righ...
by Dave Keenan
Tue Apr 11, 2023 11:19 am
Forum: Linear Temperament notations
Topic: Notating 5-limit pental with added 7th harmonics
Replies: 15
Views: 3854

Re: Notating 5-limit pental with added 7th harmonics

Welcome to the forum Roee. That is quite a puzzle. No sagittal notation has previously been devised for 255edo. After much investigation, the only viable solution I can find is to repurpose the left scroll :)|: , giving it a 7-limit (or perhaps 11-limit) definition, which I haven't worked out. The l...
by Dave Keenan
Wed Apr 05, 2023 3:06 pm
Forum: Just Intonation notations
Topic: Simplified "Stoic" Sagittal for 13-limit tonality diamond use
Replies: 73
Views: 45510

Re: Simplified "Stoic" Sagittal for 13-limit tonality diamond use

ndentonprotsack I finally got Dorico SE 4 installed correctly. I screwed it up the first time thanks to Steinberg's outdated and misleading installation video. The help has the following to say about Microtonal accidentals: Microtonal accidentals indicate pitches beyond the standard accepted chroma...
by Dave Keenan
Mon Apr 03, 2023 11:38 am
Forum: Just Intonation notations
Topic: Simplified "Stoic" Sagittal for 13-limit tonality diamond use
Replies: 73
Views: 45510

Re: Simplified "Stoic" Sagittal for 13-limit tonality diamond use

ndentonprotsack Hi Nick, That's great news. <pedantry warning> I'm not sure what you mean when you say your temperament has a "period of 12-edo", since 12-edo is a tuning containing many intervals whereas a period is a single interval. Do you mean it has a period of 1/12th of an octave, 1...
by Dave Keenan
Thu Feb 16, 2023 10:13 am
Forum: Just Intonation notations
Topic: Simplified "Stoic" Sagittal for 13-limit tonality diamond use
Replies: 73
Views: 45510

Re: Simplified "Stoic" Sagittal for 13-limit tonality diamond use

ndentonprotsack Hi Nick, Well we've both been busy for the past year. But maybe now we can finalise this, so I can make a SMuFL submission. Can you please confirm that: (a) You're still happy with the current outlines for the Stoic symbols, and (b) That the JSON metadata files have given the desire...
by Dave Keenan
Mon Nov 14, 2022 11:33 am
Forum: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19284

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: Mathematical theory
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5)
Replies: 38
Views: 19284

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)...