What's the definition of ♯/♭?

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Dannyu NDos
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Joined: Sat Sep 25, 2021 10:01 am

What's the definition of ♯/♭?

Post by Dannyu NDos »

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.

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cmloegmcluin
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Re: What's the definition of ♯/♭?

Post by cmloegmcluin »

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 :b: 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.

Dannyu NDos
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Re: What's the definition of ♯/♭?

Post by Dannyu NDos »

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.
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.

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cmloegmcluin
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Re: What's the definition of ♯/♭?

Post by cmloegmcluin »

Ah, I see! Yes, depending on the EDO, :#: and :b: 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.

FloraC
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Re: What's the definition of ♯/♭?

Post by FloraC »

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.

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