Hi everyone. I'm new to sagittal notation.
What's the definition of ♯/♭ used in sagittal notation?
It seems ♯ is to approximate the just chromatic semitone, 25/24.
Why not the Pythagorean one, 2187/2048? Since C to G is to approximate 3/2, a Pythagorean interval, it seems inconsistent to define ♯ as 25/24, a 5-limit interval. C to D approximates 9/8, and in most times, C to E approximates 81/64, rather than 5/4.
What's the definition of ♯/♭?
- cmloegcmluin
- Site Admin
- Posts: 1700
- Joined: Tue Feb 11, 2020 3:10 pm
- Location: San Francisco, California, USA
- Real Name: Douglas Blumeyer (he/him/his)
- Contact:
Re: What's the definition of ♯/♭?
Hi @Dannyu NDos! Welcome to the Sagittal forum. I hope you can get all the info you need, and have some fun and interesting conversations here.
In Sagittal, and are the Pythagorean semitone, 2187/2048.
You can find this information, and a lot more, here: https://sagittal.org/Sagittal-SMuFL-Map.pdf
Out of curiosity, how did you come to the conclusion that it seemed to be 25/24? I would like to help prevent other people from coming to the same misconception.
In Sagittal, and are the Pythagorean semitone, 2187/2048.
You can find this information, and a lot more, here: https://sagittal.org/Sagittal-SMuFL-Map.pdf
Out of curiosity, how did you come to the conclusion that it seemed to be 25/24? I would like to help prevent other people from coming to the same misconception.
-
- Posts: 3
- Joined: Sat Sep 25, 2021 10:01 am
Re: What's the definition of ♯/♭?
It seemed to be 25/24 in meantone EDOs such as 19edo or 31edo. 25/24 is approximated by 1\19 and 2\31, while Pythagorean chromatic semitone is approximated by 2\19 and 3\31.cmloegmcluin wrote: ↑Sat Sep 25, 2021 10:35 am Out of curiosity, how did you come to the conclusion that it seemed to be 25/24? I would like to help prevent other people from coming to the same misconception.
- cmloegcmluin
- Site Admin
- Posts: 1700
- Joined: Tue Feb 11, 2020 3:10 pm
- Location: San Francisco, California, USA
- Real Name: Douglas Blumeyer (he/him/his)
- Contact:
Re: What's the definition of ♯/♭?
Ah, I see! Yes, depending on the EDO, and may also represent 25/24. But the primary comma is 2187/2048. Meaning, in the absence of other information, that's what one should assume it represents. Let me know if that raises any other questions.
Re: What's the definition of ♯/♭?
In 19edo and 31edo both 25/24 and 2187/2048 are represented by 1\19 and 2\31 respectively because 81/80 is tempered out. Mind you, the 2187/2048 is understood as a stack of seven of 3/2's instead of using the direct approximation.