Just intonation subgroup/Mike's tips - Revision history

Fredg999: Remove blank lines, add lead section

2024-08-26T05:28:10Z

Remove blank lines, add lead section

← Older revision		Revision as of 05:28, 26 August 2024
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			This page contains an archived discussion between [[Chris Vaisvil]] and [[Mike Battaglia]] about [[just intonation subgroup]]s and [[regular temperament]]s.

	<pre>		<pre>
	On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <chrisvaisvil@gmail.com> wrote:		On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <chrisvaisvil@gmail.com> wrote:

Fredg999: Fredg999 moved page Just intonation subgroup/Mike's and Jake's tips to Just intonation subgroup/Mike's tips: Split page

2024-08-26T05:26:33Z

Fredg999 moved page Just intonation subgroup/Mike's and Jake's tips to Just intonation subgroup/Mike's tips: Split page

← Older revision	Revision as of 05:26, 26 August 2024
(No difference)

Fredg999: Move Jake's tips to another page (different topic), categories, misc. edits

2024-08-26T05:25:56Z

Move Jake's tips to another page (different topic), categories, misc. edits

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-== Mike's tips ==
 <pre>
 On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <chrisvaisvil@gmail.com> wrote:
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 -Mike</pre>
-== Jake's tips ==
+== See also ==
-<pre>
+* [[Equal-step tuning/Jake's tips]] (contains another archived discussion with Chris Vaisil)
-Jake
+[[Category:Guides]]

Fredg999: Add breadcrumb, use pre formatting tags to give the "archive" look (since that's what it is), add headers and force TOC (useful here despite only 2 headers)

2024-08-26T05:20:00Z

Add breadcrumb, use pre formatting tags to give the "archive" look (since that's what it is), add headers and force TOC (useful here despite only 2 headers)

← Older revision		Revision as of 05:20, 26 August 2024
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	{{delete\|Utterly unprofessional and unreadable format. If someone wants to keep this page they should make a lot of improvements explaining the page's motivation, what it discusses, why the reader might be interested, etc. Even the page's title is terrible.}}		{{breadcrumb}}
			__FORCETOC__

	On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil ~~<~~chrisvaisvil@gmail.com~~>~~		== Mike's tips ==
			<pre>
			On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <chrisvaisvil@gmail.com> wrote:

	~~wrote:~~		> For certain, no. I could only guess that subgroups are actually harmonic series prime limits.
	~~<br~~>~~>~~
	~~<br>>~~ For certain, no. I could only guess that subgroups are actually harmonic
	~~<br>>~~ series prime limits.

	Subgroups expand the concept of a prime limit. For instance, say you		Subgroups expand the concept of a prime limit. For instance, say you want the 7-limit, but you don't care about prime 5; you just want primes 2, 3, and 7. So that's the 2.3.7 subgroup. Or say that you want the 7-limit, but you don't care about 3/1 but you do care about 9/1. Then that's the 2.5.7.9 subgroup. Or, say that you want primes 2 and 3, and the composite interval 7/5; that's the 2.3.7/5 subgroup. The rule for any subgroup is that if you multiply or divide intervals, that's also in the subgroup. So for the 2.3.7 subgroup, 73 = 21/1 is in the subgroup, as is 7/(23) = 7/6. And for the 2.3.7/5 subgroup, 2/(7/5 * 7/5) = 50/49 is in the subgroup, and so on. They're infinite lattices of intervals.

	want the 7-limit, but you don't care about prime 5; you just want

	primes 2, 3, and 7. So that's the 2.3.7 subgroup. Or say that you want

	the 7-limit, but you don't care about 3/1 but you do care about 9/1.

	Then that's the 2.5.7.9 subgroup. Or, say that you want primes 2 and

	3, and the composite interval 7/5; that's the 2.3.7/5 subgroup.

	The rule for any subgroup is that if you multiply or divide intervals,

	that's also in the subgroup. So for the 2.3.7 subgroup, 7*3 = 21/1 is

	in the subgroup, as is 7/(2*3) = 7/6. And for the 2.3.7/5 subgroup,

	2/(7/5 * 7/5) = 50/49 is in the subgroup, and so on. They're infinite

	lattices of intervals.

	11-EDO happens to be a decent temperament for the 2.7.9.11 subgroup.		11-EDO happens to be a decent temperament for the 2.7.9.11 subgroup.
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	-Mike		-Mike

	Anyway, you asked about figuring out what steps in 11-EDO approximate		Anyway, you asked about figuring out what steps in 11-EDO approximate what intervals. So if 11-EDO supports the 2.7.9.11 subgroup, I can just give you the mappings for 2/1, 7/1, 9/1, and 11/1, and you can mix and match them to get what intervals you want, right. So for instance, 2/1 is 11 steps, 7/1 is 31 steps, 9/1 is 35 steps, and 11/1 is 38 steps. So then 11/9 is 38-35 = 3 steps. That should be enough information for you to get all the intervals.

	what intervals. So if 11-EDO supports the 2.7.9.11 subgroup, I can

	just give you the mappings for 2/1, 7/1, 9/1, and 11/1, and you can

	mix and match them to get what intervals you want, right. So for

	instance, 2/1 is 11 steps, 7/1 is 31 steps, 9/1 is 35 steps, and 11/1

	is 38 steps. So then 11/9 is 38-35 = 3 steps. That should be enough

	information for you to get all the intervals.

	-Mike		-Mike

	OK, so rather than write all of that out in English, though, we can		OK, so rather than write all of that out in English, though, we can just use a simple notation. So if 2/1 is 11 steps, 7/1 is 31 steps, 9/1 is 35 steps, and 11/1 is 38 steps, then we can just condense all that as follows:

	~~just use a simple notation. So if 2/1 is~~ 11 ~~steps, 7/1 is~~ 31 ~~steps,~~		<11 31 35 38\|

	9/1 ~~is 35 steps,~~ and 11/1 is ~~38 steps~~, ~~then~~ we can ~~just condense all~~		where it's understood in this particular case that the coefficients represent how many steps map to 2/1, 7/1, 9/1 and 11/1, respectively. This is called a val, and this is why we use them; so we can figure out how many steps every interval maps to. So 9/7 in the above case is 35-31 = 4 steps.

	~~that as follows:~~		-Mike</pre>

	~~<11 31 35 38\|~~		== Jake's tips ==
			<pre>
	~~where it~~'s ~~understood in this particular case that the coefficients~~		Chris Vaisvil said:

	~~represent how many steps map to 2/1, 7/1, 9/1 and 11/1, respectively.~~

	~~This is called a val, and this is why we use them; so we can figure~~

	~~out how many steps every interval maps to. So 9/7 in the above case is~~

	~~35-31~~ = ~~4 steps.~~

	~~-Mike~~

	~~Chris Vaisvil~~ said:		> As someone pretty ignorant of tuning theory I wish there was a table that said

	~~<br~~>~~> As someone pretty ignorant of tuning theory I wish there was a table that said~~		> If you play scale (tuning) steps 0:4:8:10 in 11 edo you will come close to approximating a harmonic series chord of 0:3:6:7
	~~<br>>~~
	~~<br>>~~ If you play scale (tuning) steps 0:4:8:10 in 11 edo you will come close to
	~~<br>>~~ approximating a harmonic series chord of 0:3:6:7

	There's an easy way to do that in Scala.		There's an easy way to do that in Scala.
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	Jake		Jake
			</pre>

Fredg999: Fredg999 moved page N00b page to Just intonation subgroup/Mike's and Jake's tips: Clarify title, move to (pseudo-)subpage

2024-08-26T04:57:28Z

Fredg999 moved page N00b page to Just intonation subgroup/Mike's and Jake's tips: Clarify title, move to (pseudo-)subpage

← Older revision	Revision as of 04:57, 26 August 2024
(No difference)

Lériendil: removed from categories (nominated for deletion)

2024-08-26T03:04:00Z

removed from categories (nominated for deletion)

← Older revision		Revision as of 03:04, 26 August 2024
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	Jake		Jake

	~~[[Category:11edo]]~~
	~~[[Category:Chords]]~~
	~~[[Category:Guides]]~~
	~~[[Category:Newbie]]~~
	~~[[Category:Simple]]~~
	~~[[Category:Start]]~~
	~~[[Category:Subgroup]]~~

Godtone: nominate for deletion

2024-07-27T18:21:04Z

nominate for deletion

← Older revision		Revision as of 18:21, 27 July 2024
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			{{delete\|Utterly unprofessional and unreadable format. If someone wants to keep this page they should make a lot of improvements explaining the page's motivation, what it discusses, why the reader might be interested, etc. Even the page's title is terrible.}}

	On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <chrisvaisvil@gmail.com>		On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <chrisvaisvil@gmail.com>

Fredg999 category edits: Moving from Category:Howto to Category:Guides using Cat-a-lot

2023-05-02T04:57:44Z

Moving from Category:Howto to Category:Guides using Cat-a-lot

← Older revision		Revision as of 04:57, 2 May 2023
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	[[Category:11edo]]		[[Category:11edo]]
	[[Category:Chords]]		[[Category:Chords]]
	[[Category:~~Howto~~]]		[[Category:Guides]]
	[[Category:Newbie]]		[[Category:Newbie]]
	[[Category:Simple]]		[[Category:Simple]]
	[[Category:Start]]		[[Category:Start]]
	[[Category:Subgroup]]		[[Category:Subgroup]]

Keenan Pepper: AFAIK this doesn't contain a Scala file - not sure why it's here at all really

2020-12-04T22:22:58Z

AFAIK this doesn't contain a Scala file - not sure why it's here at all really

← Older revision		Revision as of 22:22, 4 December 2020
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	[[Category:Howto]]		[[Category:Howto]]
	[[Category:Newbie]]		[[Category:Newbie]]
	~~[[Category:Pages with Scala files]]~~
	[[Category:Simple]]		[[Category:Simple]]
	[[Category:Start]]		[[Category:Start]]
	[[Category:Subgroup]]		[[Category:Subgroup]]

Keenan Pepper: Moving from Category:Scala to Category:Pages with Scala files using Cat-a-lot

2020-12-04T22:16:53Z

Moving from Category:Scala to Category:Pages with Scala files using Cat-a-lot

← Older revision		Revision as of 22:16, 4 December 2020
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	[[Category:Howto]]		[[Category:Howto]]
	[[Category:Newbie]]		[[Category:Newbie]]
	[[Category:Scala]]		[[Category:Pages with Scala files]]
	[[Category:Simple]]		[[Category:Simple]]
	[[Category:Start]]		[[Category:Start]]
	[[Category:Subgroup]]		[[Category:Subgroup]]