Ground's intro to tuning diversity - Revision history

Vector at 23:19, 5 August 2026

2026-08-05T23:19:09Z

← Older revision		Revision as of 23:19, 5 August 2026
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	If you're anything like me, you took them for granted for years. After all, why wouldn't you? No one has told you how these were chosen, that's just how music is. But the truth is, these notes are a centuries-long compromise based on lots of math and stylistic evolution. There are endless other valid ways to do it, some of which may sound a little odd at first, but it's just because you've only been exposed to one tuning system for most of your life. In order to fight this monopoly on music, it's important to step out of your comfort zone.		If you're anything like me, you took them for granted for years. After all, why wouldn't you? No one has told you how these were chosen, that's just how music is. But the truth is, these notes are a centuries-long compromise based on lots of math and stylistic evolution. There are endless other valid ways to do it, some of which may sound a little odd at first, but it's just because you've only been exposed to one tuning system for most of your life. In order to fight this monopoly on music, it's important to step out of your comfort zone.

			{{UserTag\|SS\|Vector\|cebaff\|"Monopoly" sounds too old-guard-xen-ish? idk. imo alternate tuning systems should be introduced the same way non-standard modes are, just as... an expansion of the musical repertoire}}

	== Diatonic tunings ==		== Diatonic tunings ==
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	}}		}}

	The diatonic scale works exactly as you'd expect. Because sharps and flats have been notated separately as a historical vestige, you could play any sheet music in 19edo if you wanted, but it sounds a little different. It's a bit softer and mellower, and the fifth is flat. It may sound jarring, or it may sound even better than 12edo. And because of these extra notes, there's a new scale related to diatonic that you've probably never heard before. This is '''semiquartal''', and instead of being mellower, it's harsher and has two extra small steps. It's full of this interval called the '''semifourth'''. As the name implies, it's half of a perfect fourth, and it's also halfway between a whole tone and a minor third. Just this adds so many new possibilities to fit intervals together to achieve new musical moods.		The diatonic scale works exactly as you'd expect. Because sharps and flats have been notated separately as a historical vestige, you could play any sheet music in 19edo if you wanted, but it sounds a little different. It's a bit softer and mellower, and the fifth is flat.

			{{UserTag\|SS\|Vector\|cebaff\|"Mellow" might be a xen-ism. Explain scale step ratios at least briefly.}}

			It may sound jarring, or it may sound even better than 12edo. And because of these extra notes, there's a new scale related to diatonic that you've probably never heard before. This is '''semiquartal''', and instead of being mellower, it's harsher and has two extra small steps. It's full of this interval called the '''semifourth'''. As the name implies, it's half of a perfect fourth, and it's also halfway between a whole tone and a minor third. Just this adds so many new possibilities to fit intervals together to achieve new musical moods.

	Now instead of adding 7 to 12edo, let's add 5. This gives us '''17edo''', and it's sort of a mirror image of 19edo:		Now instead of adding 7 to 12edo, let's add 5. This gives us '''17edo''', and it's sort of a mirror image of 19edo:
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	In 19edo, A# is below Bb; in 12edo, they're equal; and in 17edo, they're reversed with A# above Bb. 17edo is sort of a mirror image of 19edo. The diatonic scale is now harsher and more articulate, and the fifth is sharp, but there's a new scale called '''mosh''' that's softer. Mosh is full of '''neutral intervals''' such as the neutral third, halfway between a major and a minor third.		In 19edo, A# is below Bb; in 12edo, they're equal; and in 17edo, they're reversed with A# above Bb. 17edo is sort of a mirror image of 19edo. The diatonic scale is now harsher and more articulate, and the fifth is sharp, but there's a new scale called '''mosh''' that's softer. Mosh is full of '''neutral intervals''' such as the neutral third, halfway between a major and a minor third.

			{{UserTag\|SS\|Vector\|cebaff\|"sort of a mirror image of 19edo" is duplicated.}}

	You can keep finding new tunings like this just by adding 7 and 5:		You can keep finding new tunings like this just by adding 7 and 5:
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	Being only a multiple of 5 does weird things. The fifth is very sharp, to the point that the semitones disappear and reading from 12edo sheet music doesn't sound right. It's possible to notate the result in many ways, but I'm using ups and downs notation with the little arrows altering the pitch by one step of the edo. Despite how alien this tuning is, the new chords actually sound pretty good. Instead of being based on a diatonic scale, it has several new ones including '''blackwood''' and '''pine''', which comes from a temperament called '''Porcupine'''. Instead of having whole tones and semitones like the other tunings discussed so far, there are actually two different intervals that take the function of a whole tone: the neutral second, halfway between a standard whole tone and semitone, and the semifourth, halfway between a standard whole tone and minor third. It's called a semifourth because it's half of a perfect fourth.		Being only a multiple of 5 does weird things. The fifth is very sharp, to the point that the semitones disappear and reading from 12edo sheet music doesn't sound right. It's possible to notate the result in many ways, but I'm using ups and downs notation with the little arrows altering the pitch by one step of the edo. Despite how alien this tuning is, the new chords actually sound pretty good. Instead of being based on a diatonic scale, it has several new ones including '''blackwood''' and '''pine''', which comes from a temperament called '''Porcupine'''. Instead of having whole tones and semitones like the other tunings discussed so far, there are actually two different intervals that take the function of a whole tone: the neutral second, halfway between a standard whole tone and semitone, and the semifourth, halfway between a standard whole tone and minor third. It's called a semifourth because it's half of a perfect fourth.

			{{UserTag\|SS\|Vector\|cebaff\|Additionally, if you tune a guitar to 15edo, it becomes isomorphic, because the major third created by stacking four perfect fifths becomes the same size as the perfect fourth.}}

	So we've discussed adding 7 and 5, but what about the other numbers? 6 ((7+5)/2), 8 (5+3), and 9 (7+2) can also be added to create even more unusual tunings. Let's look at 7 plus 9, '''16edo''':		So we've discussed adding 7 and 5, but what about the other numbers? 6 ((7+5)/2), 8 (5+3), and 9 (7+2) can also be added to create even more unusual tunings. Let's look at 7 plus 9, '''16edo''':
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	13edo is based on the '''oneirotonic''' scale, which has 8 notes rather than the diatonic 7. Of course, it's not really that simple, but there's a reason this scale is probably my favorite absolutely baffling piece of music theory. You may notice that C is lower than B and F is lower than E, and the sharps and flats are all very extreme. It may be prudent to abandon standard note names altogether and try something like this:		13edo is based on the '''oneirotonic''' scale, which has 8 notes rather than the diatonic 7. Of course, it's not really that simple, but there's a reason this scale is probably my favorite absolutely baffling piece of music theory. You may notice that C is lower than B and F is lower than E, and the sharps and flats are all very extreme. It may be prudent to abandon standard note names altogether and try something like this:

	1 1#/2b 2 3 3#/4b 4 4#/5b 5 6 6#/6b 7 7#/8b 8 1		1 1#/2b 2 3 3#/4b 4 4#/5b 5 6 6#/7b 7 7#/8b 8 1

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Inthar at 13:24, 12 February 2026

2026-02-12T13:24:34Z

← Older revision		Revision as of 13:24, 12 February 2026
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	There's no commonly accepted way to notate this one. Everything works out with a normal circle of fifths as long as you let Bb go on a white key. It could also be replaced with X as in my notation, or B and Bb could be replaced with H and B as in German notation.		There's no commonly accepted way to notate this one. Everything works out with a normal circle of fifths as long as you let Bb go on a white key. It could also be replaced with X as in my notation, or B and Bb could be replaced with H and B as in German notation.

	13edo is based on the '''oneirotonic''' scale, which has 8 notes rather than the diatonic 7. Of course, it's not really that simple, but there's a reason this scale is probably my favorite absolutely baffling piece of music theory. You may notice that C is lower than B and F is lower than E, and the sharps and flats are all very extreme. It may be prudent to abandon standard note names altogether and try something like:		13edo is based on the '''oneirotonic''' scale, which has 8 notes rather than the diatonic 7. Of course, it's not really that simple, but there's a reason this scale is probably my favorite absolutely baffling piece of music theory. You may notice that C is lower than B and F is lower than E, and the sharps and flats are all very extreme. It may be prudent to abandon standard note names altogether and try something like this:

	1 1#/2b 2 3 3#/4b 4 4#/5b 5 6 6#/6b 7 7#/8b 8 1		1 1#/2b 2 3 3#/4b 4 4#/5b 5 6 6#/6b 7 7#/8b 8 1

Inthar: /* The weird ones */

2026-02-12T13:11:46Z

The weird ones

← Older revision		Revision as of 13:11, 12 February 2026
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	}}		}}

	There's no commonly accepted way to notate this one. Everything works out with a normal circle of fifths as long as you let Bb go on a white key. It could also be replaced with X in my notation, or B and Bb could be replaced with H and B as in German notation.		There's no commonly accepted way to notate this one. Everything works out with a normal circle of fifths as long as you let Bb go on a white key. It could also be replaced with X as in my notation, or B and Bb could be replaced with H and B as in German notation.

	13edo is based on the '''oneirotonic''' scale, which has 8 notes rather than the diatonic 7. Of course, it's not really that simple, but there's a reason this scale is probably my favorite absolutely baffling piece of music theory. You may notice that C is lower than B and F is lower than E, and the sharps and flats are all very extreme. It may be prudent to abandon standard note names altogether and try something like:		13edo is based on the '''oneirotonic''' scale, which has 8 notes rather than the diatonic 7. Of course, it's not really that simple, but there's a reason this scale is probably my favorite absolutely baffling piece of music theory. You may notice that C is lower than B and F is lower than E, and the sharps and flats are all very extreme. It may be prudent to abandon standard note names altogether and try something like:

Inthar: /* The weird ones */

2026-02-12T13:10:25Z

The weird ones

← Older revision		Revision as of 13:10, 12 February 2026
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	This tuning is '''antidiatonic''', which means that the fifth is so flat that it flips the sharps and flats, which now change the pitch in opposite directions. The antidiatonic scale is made up of 2 large and 5 small steps rather than the 5 large and 2 small steps in the diatonic scale. You can actually read 12edo sheet music in this tuning, and it will warp all the major intervals to minor and vice versa. It sounds pretty weird, but I actually love how gritty and dark it is, and how it's absolutely full of neutral seconds.		This tuning is '''antidiatonic''', which means that the fifth is so flat that it flips the sharps and flats, which now change the pitch in opposite directions. The antidiatonic scale is made up of 2 large and 5 small steps rather than the 5 large and 2 small steps in the diatonic scale. You can actually read 12edo sheet music in this tuning, and it will warp all the major intervals to minor and vice versa. It sounds pretty weird, but I actually love how gritty and dark it is, and how it's absolutely full of neutral seconds.

	It's possible to split the large steps into a neutral second and an even smaller step, resulting in a 9-note scale called '''armotonic'''. I like to notate this with a version of my own notation that extends the circle of fifths for 8 and 9-note scales. It adds two new letters in this case, XFCGDAEBY. Let's also fix the sharps and flats ~~again~~:		It's possible to split the large steps into a neutral second and an even smaller step, resulting in a 9-note scale called '''armotonic'''. I like to notate this with a version of my own notation that extends the circle of fifths for 8 and 9-note scales. It adds two new letters in this case, XFCGDAEBY. Let's also fix the sharps and flats:

	A A#/Bb B X X#/Cb C C#/Db D D#/Eb E E#/Yb Y F F#/Gb G G#/Ab (A)		A A#/Bb B X X#/Cb C C#/Db D D#/Eb E E#/Yb Y F F#/Gb G G#/Ab (A)

Inthar: /* The weird ones */

2026-02-12T13:09:50Z

The weird ones

← Older revision		Revision as of 13:09, 12 February 2026
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	This tuning is '''antidiatonic''', which means that the fifth is so flat that it flips the sharps and flats, which now change the pitch in opposite directions. The antidiatonic scale is made up of 2 large and 5 small steps rather than the 5 large and 2 small steps in the diatonic scale. You can actually read 12edo sheet music in this tuning, and it will warp all the major intervals to minor and vice versa. It sounds pretty weird, but I actually love how gritty and dark it is, and how it's absolutely full of neutral seconds.		This tuning is '''antidiatonic''', which means that the fifth is so flat that it flips the sharps and flats, which now change the pitch in opposite directions. The antidiatonic scale is made up of 2 large and 5 small steps rather than the 5 large and 2 small steps in the diatonic scale. You can actually read 12edo sheet music in this tuning, and it will warp all the major intervals to minor and vice versa. It sounds pretty weird, but I actually love how gritty and dark it is, and how it's absolutely full of neutral seconds.

	It's possible to split the large steps into a neutral second and an even smaller step, resulting in a 9-note scale called '''armotonic'''. I like to notate this with a version of my own notation that extends the circle of fifths for 8 and 9-note scales. It adds two new letters in this case, XFCGDAEBY. ~~Doing this actually fixes~~ the sharps and flats again:		It's possible to split the large steps into a neutral second and an even smaller step, resulting in a 9-note scale called '''armotonic'''. I like to notate this with a version of my own notation that extends the circle of fifths for 8 and 9-note scales. It adds two new letters in this case, XFCGDAEBY. Let's also fix the sharps and flats again:

	A A#/Bb B X X#/Cb C C#/Db D D#/Eb E E#/Yb Y F F#/Gb G G#/Ab (A)		A A#/Bb B X X#/Cb C C#/Db D D#/Eb E E#/Yb Y F F#/Gb G G#/Ab (A)

Inthar: /* The weird ones */

2026-02-12T13:06:29Z

The weird ones

← Older revision		Revision as of 13:06, 12 February 2026
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	A ^A vB/vC B/C ^B/^C vD D ^D vE/vF E/F ^E/^F vG G ^G vA (A)		A ^A vB/vC B/C ^B/^C vD D ^D vE/vF E/F ^E/^F vG G ^G vA (A)

	B and C are the same note, and so are E and F. ~~Since F and B are on the most extreme ends of the circle of fifths, they are left out:~~		B and C are the same note, and so are E and F.

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Inthar: /* Diatonic tunings */

2026-02-12T12:55:55Z

Diatonic tunings

← Older revision		Revision as of 12:55, 12 February 2026
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	== Diatonic tunings ==		== Diatonic tunings ==
	Let's take a look at the piano keyboard. 12 keys per octave, and the steps between them are all the same size. We call that '''12edo''', short for 12 equal divisions of the octave. There are 7 white keys and 5 black keys. For reasons that aren't important to explain now, 7 and 5 are very important numbers to our diatonic musical practice, with the major and minor scales, and the circle of fifths. So we can add 7 to 12edo and get '''19edo'''. With these extra notes, suddenly sharps and flats aren't the same anymore:		Let's take a look at the piano keyboard. 12 keys per octave, and the steps between them are all the same size. We call that '''12edo''', short for 12 equal divisions of the octave. There are 7 white keys and 5 black keys. For reasons that aren't important to explain now, 7 and 5 are very important numbers to our diatonic musical practice, with the major and minor scales and the circle of fifths. So we can add 7 to 12edo and get '''19edo'''. With these extra notes, suddenly sharps and flats aren't the same anymore:

	A A# Bb B B#/Cb C C# Db D D# Eb E E#/Fb F F# Gb G G# Ab (A)		A A# Bb B B#/Cb C C# Db D D# Eb E E#/Fb F F# Gb G G# Ab (A)

Inthar: /* Diatonic tunings */

2026-02-12T12:55:24Z

Diatonic tunings

← Older revision		Revision as of 12:55, 12 February 2026
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	== Diatonic tunings ==		== Diatonic tunings ==
	Let's take a look at the piano keyboard. 12 keys per octave, and the steps between them are all the same size. We call that '''12edo''', short for 12 equal divisions of the octave. There 7 white keys and 5 black keys. For reasons that aren't important to explain now, 7 and 5 are very important numbers to our diatonic musical practice, with the major and minor scales, and the circle of fifths. So we can add 7 to 12edo and get '''19edo'''. With these extra notes, suddenly sharps and flats aren't the same anymore:		Let's take a look at the piano keyboard. 12 keys per octave, and the steps between them are all the same size. We call that '''12edo''', short for 12 equal divisions of the octave. There are 7 white keys and 5 black keys. For reasons that aren't important to explain now, 7 and 5 are very important numbers to our diatonic musical practice, with the major and minor scales, and the circle of fifths. So we can add 7 to 12edo and get '''19edo'''. With these extra notes, suddenly sharps and flats aren't the same anymore:

	A A# Bb B B#/Cb C C# Db D D# Eb E E#/Fb F F# Gb G G# Ab (A)		A A# Bb B B#/Cb C C# Db D D# Eb E E#/Fb F F# Gb G G# Ab (A)

Inthar: /* The Weird Ones */

2026-02-09T07:48:49Z

The Weird Ones

← Older revision		Revision as of 07:48, 9 February 2026
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	All of these tunings are also great, but you can also do more interesting things that will truly test your comfort zone.		All of these tunings are also great, but you can also do more interesting things that will truly test your comfort zone.

	== The ~~Weird Ones~~ ==		== The weird ones ==

	Let's take a look at a tuning that's just 3 times 5, '''15edo''':		Let's take a look at a tuning that's just 3 times 5, '''15edo''':

Inthar at 02:02, 9 February 2026

2026-02-09T02:02:18Z

← Older revision		Revision as of 02:02, 9 February 2026
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	It's possible to split the large steps into a neutral second and an even smaller step, resulting in a 9-note scale called '''armotonic'''. I like to notate this with a version of my own notation that extends the circle of fifths for 8 and 9-note scales. It adds two new letters in this case, XFCGDAEBY. Doing this actually fixes the sharps and flats again:		It's possible to split the large steps into a neutral second and an even smaller step, resulting in a 9-note scale called '''armotonic'''. I like to notate this with a version of my own notation that extends the circle of fifths for 8 and 9-note scales. It adds two new letters in this case, XFCGDAEBY. Doing this actually fixes the sharps and flats again:

			A A#/Bb B X X#/Cb C C#/Db D D#/Eb E E#/Yb Y F F#/Gb G G#/Ab (A)

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