User:VectorGraphics/intro to 5edo - Revision history

Lériendil: deploying new cat

2025-01-31T22:07:41Z

deploying new cat

← Older revision		Revision as of 22:07, 31 January 2025
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	\|}		\|}
	that's it. that's all of them. of course, there are more if you're willing to exceed the octave		that's it. that's all of them. of course, there are more if you're willing to exceed the octave

			[[Category:Method]]
			[[Category:Approaches to tuning systems]]

VectorGraphics at 03:22, 23 December 2023

2023-12-23T03:22:38Z

← Older revision		Revision as of 03:22, 23 December 2023
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	\|C,D,G		\|C,D,G
	\|minor triad		\|minor triad
	\|triad		\|sus triad
	\|-		\|-
	\|6		\|6
	\|C,E,G		\|C,E,G
	\|major triad		\|major triad
	\|triad		\|sus triad
	\|-		\|-
	\|7		\|7
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	\|C,E,A		\|C,E,A
	\|augmented triad		\|augmented triad
	\|triad		\|sus triad
	\|-		\|-
	\|11		\|11

VectorGraphics at 03:21, 23 December 2023

2023-12-23T03:21:03Z

← Older revision		Revision as of 03:21, 23 December 2023
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	one of the most important musical intervals is the 5th. here is the 5th. [0 720c] sound weird and dissonant? well, tough luck. hey, i remember saying this before. other intervals in 5edo include the fourth [0 480c], the second [0 240c], the seventh [0 960c], the octave [0 1200c], and that's it. there are no other intervals. ok, there's technically the unison but that's an interval in the same way multiplying by 1 is a multiplication. in fact, that's literally [[1/1\|what it is]]. what about thirds and sixths? there are none. well, kind of. you can use other intervals as thirds and sixths. let's call these notes C, D, E, G, and A, because those are the notes of the pentatonic scale, the other main scale that has 5 notes. F and B don't exist because 5edo actually breaks the way we name notes. you see, we name notes by stacking fifths. a fifth above C is, by definition, G. a fifth above G is D, then A, then E, and then B, but when you get to B in 5edo it turns out it is actually exactly the same note as C. similarly, sharps and flats are redundant because adding two more fifths to get to F# and C#, you will find that C# is in fact D. even if you tried to redefine sharps and flats to make sense in this context, the smallest step available IS that from C to D, so you can't.		one of the most important musical intervals is the 5th. here is the 5th. [0 720c] sound weird and dissonant? well, tough luck. hey, i remember saying this before. other intervals in 5edo include the fourth [0 480c], the second [0 240c], the seventh [0 960c], the octave [0 1200c], and that's it. there are no other intervals. ok, there's technically the unison but that's an interval in the same way multiplying by 1 is a multiplication. in fact, that's literally [[1/1\|what it is]]. what about thirds and sixths? there are none. well, kind of. you can use other intervals as thirds and sixths. let's call these notes C, D, E, G, and A, because those are the notes of the pentatonic scale, the other main scale that has 5 notes. F and B don't exist because 5edo actually breaks the way we name notes. you see, we name notes by stacking fifths. a fifth above C is, by definition, G. a fifth above G is D, then A, then E, and then B, but when you get to B in 5edo it turns out it is actually exactly the same note as C. similarly, sharps and flats are redundant because adding two more fifths to get to F# and C#, you will find that C# is in fact D. even if you tried to redefine sharps and flats to make sense in this context, the smallest step available IS that from C to D, so you can't.

	anyway, back to theory. let's use all five notes of the scale for now, because they kind of sound like a pentatonic scale. remember when I said thirds didn't exist? well, you can still do a kind of triadic harmony by using what are basically sus4 and sus2 chords. i.e. [0 480c 720c] and [0 240c 720c]. note that these are inversions of each other, unlike normal major and minor chords, so it's important that you establish your root note, otherwise you can accidentally use the wrong chord. or is it the same chord in a different context? i dunno. but 5edo is actually small enough that you can actually categorize ~~and name~~ every single chord or scale spanning up to an octave - there are 16 of them, and 7 up to inversions.		anyway, back to theory. let's use all five notes of the scale for now, because they kind of sound like a pentatonic scale. remember when I said thirds didn't exist? well, you can still do a kind of triadic harmony by using what are basically sus4 and sus2 chords. i.e. [0 480c 720c] and [0 240c 720c]. note that these are inversions of each other, unlike normal major and minor chords, so it's important that you establish your root note, otherwise you can accidentally use the wrong chord. or is it the same chord in a different context? i dunno. but 5edo is actually small enough that you can actually categorize every single chord or scale spanning up to an octave - there are 16 of them, and 7 up to inversions.
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
Line 58:		Line 58:
	\|9		\|9
	\|C,D,A		\|C,D,A
	\|~~first inversion of the diminished triad~~		\|
	\|diminished triad		\|diminished triad
	\|-		\|-
Line 68:		Line 68:
	\|11		\|11
	\|C,D,E,A		\|C,D,E,A
	\|~~first inversion of the diminished seventh~~		\|
	\|diminished seventh		\|diminished seventh
	\|-		\|-
	\|12		\|12
	\|C,G,A		\|C,G,A
	\|~~second inversion of the diminished triad~~		\|
	\|diminished triad		\|diminished triad
	\|-		\|-
	\|13		\|13
	\|C,D,G,A		\|C,D,G,A
	\|~~second inversion of the diminished seventh~~		\|
	\|diminished seventh		\|diminished seventh
	\|-		\|-
	\|14		\|14
	\|C,E,G,A		\|C,E,G,A
	\|~~third inversion of the diminished seventh~~		\|
	\|diminished seventh		\|diminished seventh
	\|-		\|-

VectorGraphics: Created page with "5edo is the smallest edo. that's technically not true, but it's the smallest one that you didn't just get because you bought 12edo from EA and they ripped you off. one of th..."

2023-12-23T03:19:27Z

Created page with "5edo is the smallest edo. that's technically not true, but it's the smallest one that you didn't just get because you bought 12edo from EA and they ripped you off. one of th..."

New page

5edo is the smallest edo. that's technically not true, but it's the smallest one that you didn't just get because you bought 12edo from EA and they ripped you off.

one of the most important musical intervals is the 5th. here is the 5th. [0 720c] sound weird and dissonant? well, tough luck. hey, i remember saying this before. other intervals in 5edo include the fourth [0 480c], the second [0 240c], the seventh [0 960c], the octave [0 1200c], and that's it. there are no other intervals. ok, there's technically the unison but that's an interval in the same way multiplying by 1 is a multiplication. in fact, that's literally [[1/1|what it is]]. what about thirds and sixths? there are none. well, kind of. you can use other intervals as thirds and sixths. let's call these notes C, D, E, G, and A, because those are the notes of the pentatonic scale, the other main scale that has 5 notes. F and B don't exist because 5edo actually breaks the way we name notes. you see, we name notes by stacking fifths. a fifth above C is, by definition, G. a fifth above G is D, then A, then E, and then B, but when you get to B in 5edo it turns out it is actually exactly the same note as C. similarly, sharps and flats are redundant because adding two more fifths to get to F# and C#, you will find that C# is in fact D. even if you tried to redefine sharps and flats to make sense in this context, the smallest step available IS that from C to D, so you can't.

anyway, back to theory. let's use all five notes of the scale for now, because they kind of sound like a pentatonic scale. remember when I said thirds didn't exist? well, you can still do a kind of triadic harmony by using what are basically sus4 and sus2 chords. i.e. [0 480c 720c] and [0 240c 720c]. note that these are inversions of each other, unlike normal major and minor chords, so it's important that you establish your root note, otherwise you can accidentally use the wrong chord. or is it the same chord in a different context? i dunno. but 5edo is actually small enough that you can actually categorize and name every single chord or scale spanning up to an octave - there are 16 of them, and 7 up to inversions.
{| class="wikitable"
|+
!ID
!Notes
!Name
!Inversion class
|-
|0
|C
|unison
|unison
|-
|1
|C,D
|second
|second
|-
|2
|C,E
|fourth
|fourth
|-
|3
|C,D,E
|diminished triad
|diminished triad
|-
|4
|C,G
|fifth
|fourth
|-
|5
|C,D,G
|minor triad
|triad
|-
|6
|C,E,G
|major triad
|triad
|-
|7
|C,D,E,G
|diminished seventh
|diminished seventh
|-
|8
|C,A
|seventh
|second
|-
|9
|C,D,A
|first inversion of the diminished triad
|diminished triad
|-
|10
|C,E,A
|augmented triad
|triad
|-
|11
|C,D,E,A
|first inversion of the diminished seventh
|diminished seventh
|-
|12
|C,G,A
|second inversion of the diminished triad
|diminished triad
|-
|13
|C,D,G,A
|second inversion of the diminished seventh
|diminished seventh
|-
|14
|C,E,G,A
|third inversion of the diminished seventh
|diminished seventh
|-
|15
|C,D,E,G,A
|entire scale
|scale
|}
that's it. that's all of them. of course, there are more if you're willing to exceed the octave