Ground's intro to tuning diversity - Revision history

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
Line 97:		Line 97:
	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.

	{{#invoke:Halberstadt_SVG\|render		{{#invoke:Halberstadt_SVG\|render

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
Line 19:		Line 19:

	== 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)

	{{#invoke:Halberstadt_SVG\|render		{{#invoke:Halberstadt_SVG\|render

Inthar at 01:47, 9 February 2026

2026-02-09T01:47:01Z

← Older revision		Revision as of 01:47, 9 February 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.

			== 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 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:

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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''':