FIXES ISSUE #4018 More default EDOs for temperament

[omsuneri]

By these changes user can experience some of the most common Equal temperaments

1. Equal 5EDO : A system that divides the octave into 5 equal parts It is used in certain traditional and experimental musical contexts Instruments that can be easily adapted to 5EDO tuning include Panpipes, Native American Flutes, xylophones, marimbas in African and Asian, Fretted string instruments, etc.

2. Equal 7EDO : A system that divides the octave into 7 equal parts it is sometimes used in experimental music and can be explored on various adaptable instruments like synthesisers, violins, violas, cellos, guitar, keyboards. etc.

3. Equal 19EDO : A system that divides the octave into 19 equal parts. several types of instruments can be adapted or built to use this tuning, particularly in experimental and microtonal music contexts and can be experienced by instruments like fretless violins, fretless cellos, fretless basses, fretless guitars, etc.

4. Equal 31EDO : A system that divides the octave into 31 equal parts several types of instruments can be adapted or built for this tuning like Custom-built guitars and basses Microtonal guitars can be used to experience this.

[walterbender]

@pikurasa I have some questions about this. Let's find a time to discuss.
@omsuneri curious with 5EDO why the notes are assigned the way they are. For example, with Perfect 5th is a G4 and not a C5? Same applies to the other temperaments.

[omsuneri]

@walterbender actually for perfect 5 interval we have G4 for every another temperament we have in the the menu.

[walterbender]

Yes. I don't understand why. Maybe @pikurasa can explain it to me.

[pikurasa]

The interval names that we have are best suited for 12EDO.

With fewer than 12 pitches in an EDO, we could map to the nearest 12EDO interval, but for more than 12 pitches in an EDO, the resolution is higher, so we need to have additional qualifiers (hence "ups" and "downs" systems).

For now, we could map to the nearest 12EDO interval, based on its proximity. Later, we would need to implement something like ups and downs qualifiers.

[walterbender]

+1 But also, don't want to do the same for the letter names?

[omsuneri]

@walterbender so should I do changes in this commit or you can create some new issue for that.

[walterbender]

We may need to change some of the interval assignments you made. Let's wait to discuss in more detail with @pikurasa

[pikurasa]

@omsuneri I tested your branch.

The EDOs sound good, however it seems that you calculated their values through ratios rather than exponents.

Notice how when you export 12EDO from the temperament widget, you get math of 2^(x/12) where x is a chromatic pitch in the scale.

You want to do the same for the other EDOs as well, so:

• 5 EDO = 2^(x/5)
• 7 EDO = 2^(x/7)
• 19 EDO = 2^(x/19)
• 31 EDO = 2^(x/31)

This is important because, although the difference may be imperceptible on a certain level, the definition of EDO is basically that you arrive at the temperament through exponents rather than ratios. So we want users to see this congruently throughout.

This video shows my test on commit 6706865:

temperament-test-2-2024-10-01_14.04.51.zip

[omsuneri]

@pikurasa but in musicutils.js you can see that i had created the temperament using the pow function only and dont know why this strange thinga happens with the new temperaments well let me check it once again also @walterbender is asking for some changes in intervals that i had created could please refer those too so in order to resolve that too

[omsuneri]

@pikurasa @walterbender the thing of 2 to the power for the interval ratio instead of the division type is resolved have a look over this
temperament-test-2-2024-10-01_14.04.51.zip
should i raise a new commit for this

[pikurasa]

For naming intervals of any temperament other than 12EDO, @omsuneri and I discussed doing the following:

• Find the nearest 12EDO pitch, use that as its letter name (e.g. A, B, C, and with sharp/flat)
• Calculate the difference from nearest 12EDO pitch in cents and append that to the name with (+/- [value-in-cents]) where + is used when it is higher than the 12EDO pitch and - is used when it is higher than the 12EDO pitch.

As a reference, this is similar to how we are naming pitch names for custom temperament.