Search found 1207 matches

by Dave Keenan
Thu Nov 21, 2024 9:47 am
Forum: Just Intonation notations
Topic: Decimal point in EDA values
Replies: 3
Views: 211

Re: Decimal point in EDA values

I think I cracked it: They are intended to be a short way to specify (other?) capture zones for the symbols: the apotome fraction lower bound for upward pointing symbol is the "EDA value" minus a half, divided by the EDA steps (i.e. \(\frac{v-\frac12}s\)), and for downward pointing symbols the same ...
by Dave Keenan
Wed Nov 20, 2024 10:08 pm
Forum: Linear Temperament notations
Topic: Ennealimmal
Replies: 13
Views: 623

Re: Ennealimmal

I thought the reason for the post was that you wanted me to explain more fully what I mean when I assign modular generator counts to periods and how I think about the subject. Yes, please. Feel free to ignore my suggestions. I want to understand how you see it. Maybe I need to see some lattice ...
by Dave Keenan
Wed Nov 20, 2024 7:35 pm
Forum: Just Intonation notations
Topic: Decimal point in EDA values
Replies: 3
Views: 211

Re: Decimal point in EDA values

Good questions. George chose those numbers. But I'm pretty sure the part after the decimal point was intended as an approximate decimal-fraction part of a number of steps, not merely a distinguishing or ordering mark. You can see in George's original version of the JI Calculator spreadsheet , that ...
by Dave Keenan
Sun Nov 17, 2024 1:30 pm
Forum: Linear Temperament notations
Topic: Ennealimmal
Replies: 13
Views: 623

Re: Ennealimmal

I think it's probably better to start a new one, or maybe even two (although they could be separate posts on the same thread): One about general notation guidelines I found helpful for notating linear temperaments, and one about the problems and my approach to them when dealing with temperaments ...
by Dave Keenan
Sat Nov 16, 2024 5:38 pm
Forum: Linear Temperament notations
Topic: Ennealimmal
Replies: 13
Views: 623

Re: Ennealimmal

I thought I understood, but perhaps I don't. If you can work out a general theory of chain-of-fifths-plus-microtonal-accidentals notations for rank 2 temperaments, that would be wonderful. Particularly if it could be derived from a mapping for the temperament. It should preferably use the standard ...
by Dave Keenan
Fri Nov 15, 2024 2:06 pm
Forum: Linear Temperament notations
Topic: Ennealimmal
Replies: 13
Views: 623

Re: Ennealimmal

I get it now. I think you are confusingly overloading the words "generator" and "complexity". I think we can do better than either of the two ways you addressed it, but I don't want to spend the time to set out examples in detail. So I'll just give the most important points. 1. I think there is no ...
by Dave Keenan
Fri Nov 15, 2024 10:45 am
Forum: Mathematical theory
Topic: Fractions that you're not allowed to (or choose not to) reduce, like musical time signatures
Replies: 9
Views: 1526

Re: Fractions that you're not allowed to (or choose not to) reduce them, like musical time signatures

... formal fractions ... I think "formal fractions" is an excellent name. Obvious now that you've given it. Captures the idea perfectly. And from a non-native English speaker. Well done. I don't understand or find any use for Douglas's ideas of locking just the numerator, or just the denominator ...
by Dave Keenan
Wed Nov 13, 2024 10:53 pm
Forum: Linear Temperament notations
Topic: Ennealimmal
Replies: 13
Views: 623

Re: Ennealimmal

Yes, the number of accidentals needed in a chain of fifths notation for a rank-2 temperament is exactly the complexity of the fifth in that temperament ... How are you defining, or calculating, the complexity of a given interval in a given temperament? Thanks for the Evo notation. I agree it offers ...
by Dave Keenan
Tue Nov 12, 2024 3:35 pm
Forum: Linear Temperament notations
Topic: Ennealimmal
Replies: 13
Views: 623

Re: Ennealimmal

That staff showing an 18 note scale where every note has a different accidental is like a parody of a chain-of-fifths notation. It's the kind of thing that is likely to scare anyone away from ever considering Sagittal notation. But it's not Sagittal's fault. And it's not your fault. I spent several ...
by Dave Keenan
Sun Nov 10, 2024 1:45 pm
Forum: Linear Temperament notations
Topic: Notating 5-limit pental with added 7th harmonics
Replies: 23
Views: 18036

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

This is all good thinking. I prefer :~|::|: to :)|\\: in the 255edo notation. You have convinced me that we should create symbols with the following codepoints and names: Spartan Sagittal multi-shaft accidentals [using unused values near the end of the existing section ]: U+E336 ...