Talk:Maximal evenness - Revision history

Mike Battaglia: 1 revision imported: Moving archived Wikispaces discussion to subpage

2018-10-01T18:02:39Z

1 revision imported: Moving archived Wikispaces discussion to subpage

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WikispacesArchive>Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-10-01T18:01:16Z

Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' <span style="color:#800000">''...

← Older revision		Revision as of 18:01, 1 October 2018
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	~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~		{{WSArchiveLink}}
	~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~

	~~<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.~~

	~~----~~

	~~== more general definition ==~~
	~~I added the slightly wrong example of the major scale in 12edo, according to the given definition, it should be the Locrian mode.~~

	~~What about the more general formula~~

	~~floor((i*edo+disp)/steps)~~

	~~with i and disp in the range [0,steps-1] ?~~

	~~- '''xenwolf''' January 10, 2014, 01:23:16 AM UTC-0800~~
	~~----~~

	~~== what is quasi-equal? ==~~
	I've noticed that folks tend to use the phrase "quasi-equal" in a less strict sense than "maximally even". This might be a good way to go, and I wonder how people feel about it. We could use QE to describe:

	~~1. Scales that are "close" to equal, leaving "close" subjective and context-sensitive.~~

	~~2. Scales where L:s is within a specific range.~~

	~~In my MOS investigations page, I noted a few different ranges of L:s and the consequences this has on chromatic alterations of the scale. In particular, there is:~~

	~~Case A: L/s<2. The chroma is smaller than the s step (c<s).~~

	~~Case B: L/s=2, ie. L=2s. The chroma and the small step are the same (c=s).~~

	~~Case C: L/s>2. The chroma is larger than the s step (c>s).~~

	~~Case A1: 2<L/s<3/2. The diminished step (s-c) is smaller than the chroma (d<c).~~

	~~Case A2: L/s=3/2. The diminished step and the chroma are the same (d=c).~~

	~~Case A3: 3/2<L/s<1. The diminished step is larger than the chroma (d>c).~~

	~~So I wonder if we want to reserve the term "quasi-equal" for Case A3, where 3/2<L/s<1. Is this a useful range to have a name for, and does it make sense to use this name for that?~~

	~~Another possibility is that QE could also include Case A2, where L/s = 3/2. What say ye?~~

	~~- '''Andrew_Heathwaite''' June 20, 2012, 07:46:18 AM UTC-0700~~
	~~----~~
	~~As I understand Mandelbaum's definition, it just says two intervals of adjacent size - I.e. L-s=1, nothing else.~~

	For "maximally even", there is an additional condition: that the intervals are distributed as evenly as possible. This means that, e.g., the melodic minor scale in 12edo is quasi-equal but not maximally even.

	~~- '''hstraub''' December 25, 2013, 08:56:08 AM UTC-0800~~
	~~----~~

	~~== Maximal Evenness ==~~
	~~These are exactly the same thing as maximally even scales, right?~~

	~~- '''keenanpepper''' November 26, 2011, 02:03:45 PM UTC-0800~~
	~~----~~
	Hm, looking now at the Wikipedia page for "Maximally Even," I think that is the case. I initially got the concept and phrase from Joel Mandelbaum's dissertation on 19-one equal temperament (which I think I read on the web, but I can't see to find now). I wasn't aware there was another phrase for this property.

	~~- '''Andrew_Heathwaite''' November 26, 2011, 07:01:11 PM UTC-0800~~
	~~----~~
	~~That sounds as if the claim in Wikipedia that Clough and Douthett were the first with the idea is false.~~

	~~- '''genewardsmith''' November 26, 2011, 07:04:31 PM UTC-0800~~
	~~----~~
	~~I would very much love to hear that Mandelbaum preceded Clough and Douthett with maximal evenness. Is that true?~~

	~~- '''mbattaglia1''' November 26, 2011, 09:04:16 PM UTC-0800~~
	~~----~~
	I am absolutely not making that claim! As far as I know, Mandelbaum only preceded Clough and Douthett in my own experience. I'll be the first to tell you that there's a lot I don't know about. As I said above, I'm pretty sure I found Mandelbaum's dissertation on the web somewhere, and if you can find it that might clear up the confusion a bit. I'm not attached to the phrase "quasi-equal," it's just the only one I knew about. If "maximal evenness" is more standard, it's no problem for me to start using it.

	~~- '''Andrew_Heathwaite''' November 27, 2011, 07:44:48 AM UTC-0800~~
	~~----~~
	~~Ok, here it is -- from 1961.~~

	~~http://www.anaphoria.com/mandelbaum.html~~

	~~- '''Andrew_Heathwaite''' November 27, 2011, 07:46:34 AM UTC-0800~~
	~~----~~
	~~Hmm, in which chapter of Mandelbaum's dissertation did you see the definition analogous to maximal evenness?~~

	~~- '''hstraub''' December 25, 2013, 02:55:07 AM UTC-0800~~
	~~----~~
	~~Chapter 14, page 4-5.~~

	~~- '''Andrew_Heathwaite''' December 25, 2013, 07:40:28 AM UTC-0800~~
	~~----~~
	"The systems considered here will all have in common that they are based on scales containing intervals as equal as is possible within a 19-tone system. ...as the diatonic scale in 12-tone equal temperament is composed only of the intervals 1/12 and 2/12 ... so all of the scales to be considered here contain a range of two intervals of adjacent size; the size of the intervals will depend on the number of tones in the scale. This is what is meant by the term 'quasi-equal' in the title of this supplement."

	~~- '''Andrew_Heathwaite''' December 25, 2013, 07:44:20 AM UTC-0800~~
	~~----~~
	~~Thanks. Indeed, what Mandelbaum calls "quasi-equal-interval-symmetrical" (QEIS) is, as far as I can see, exactly the same as maximally even. Quasi-equal alone is a little less.~~

	~~- '''hstraub''' December 25, 2013, 08:38:26 AM UTC-0800~~
	~~----~~
	~~Ah yes. Looking more closely at the text, I see that you are correct. Thanks for the clarification!~~

	~~- '''Andrew_Heathwaite''' December 25, 2013, 10:50:59 AM UTC-0800~~
	~~----~~

Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-09-20T07:00:40Z

← Older revision		Revision as of 07:00, 20 September 2018
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	= ARCHIVED WIKISPACES DISCUSSION BELOW =		= ARCHIVED WIKISPACES DISCUSSION BELOW =
	'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''		'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''

			<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.

	----		----

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

New page

= ARCHIVED WIKISPACES DISCUSSION BELOW =
'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
----

== more general definition ==
I added the slightly wrong example of the major scale in 12edo, according to the given definition, it should be the Locrian mode.

What about the more general formula

floor((i*edo+disp)/steps)

with i and disp in the range [0,steps-1] ?

- '''xenwolf''' January 10, 2014, 01:23:16 AM UTC-0800
----

== what is quasi-equal? ==
I've noticed that folks tend to use the phrase "quasi-equal" in a less strict sense than "maximally even". This might be a good way to go, and I wonder how people feel about it. We could use QE to describe:

1. Scales that are "close" to equal, leaving "close" subjective and context-sensitive.

2. Scales where L:s is within a specific range.

In my MOS investigations page, I noted a few different ranges of L:s and the consequences this has on chromatic alterations of the scale. In particular, there is:

Case A: L/s<2. The chroma is smaller than the s step (c<s).

Case B: L/s=2, ie. L=2s. The chroma and the small step are the same (c=s).

Case C: L/s>2. The chroma is larger than the s step (c>s).

Case A1: 2<L/s<3/2. The diminished step (s-c) is smaller than the chroma (d<c).

Case A2: L/s=3/2. The diminished step and the chroma are the same (d=c).

Case A3: 3/2<L/s<1. The diminished step is larger than the chroma (d>c).

So I wonder if we want to reserve the term "quasi-equal" for Case A3, where 3/2<L/s<1. Is this a useful range to have a name for, and does it make sense to use this name for that?

Another possibility is that QE could also include Case A2, where L/s = 3/2. What say ye?

- '''Andrew_Heathwaite''' June 20, 2012, 07:46:18 AM UTC-0700
----
As I understand Mandelbaum's definition, it just says two intervals of adjacent size - I.e. L-s=1, nothing else.

For "maximally even", there is an additional condition: that the intervals are distributed as evenly as possible. This means that, e.g., the melodic minor scale in 12edo is quasi-equal but not maximally even.

- '''hstraub''' December 25, 2013, 08:56:08 AM UTC-0800
----

== Maximal Evenness ==
These are exactly the same thing as maximally even scales, right?

- '''keenanpepper''' November 26, 2011, 02:03:45 PM UTC-0800
----
Hm, looking now at the Wikipedia page for "Maximally Even," I think that is the case. I initially got the concept and phrase from Joel Mandelbaum's dissertation on 19-one equal temperament (which I think I read on the web, but I can't see to find now). I wasn't aware there was another phrase for this property.

- '''Andrew_Heathwaite''' November 26, 2011, 07:01:11 PM UTC-0800
----
That sounds as if the claim in Wikipedia that Clough and Douthett were the first with the idea is false.

- '''genewardsmith''' November 26, 2011, 07:04:31 PM UTC-0800
----
I would very much love to hear that Mandelbaum preceded Clough and Douthett with maximal evenness. Is that true?

- '''mbattaglia1''' November 26, 2011, 09:04:16 PM UTC-0800
----
I am absolutely not making that claim! As far as I know, Mandelbaum only preceded Clough and Douthett in my own experience. I'll be the first to tell you that there's a lot I don't know about. As I said above, I'm pretty sure I found Mandelbaum's dissertation on the web somewhere, and if you can find it that might clear up the confusion a bit. I'm not attached to the phrase "quasi-equal," it's just the only one I knew about. If "maximal evenness" is more standard, it's no problem for me to start using it.

- '''Andrew_Heathwaite''' November 27, 2011, 07:44:48 AM UTC-0800
----
Ok, here it is -- from 1961.

http://www.anaphoria.com/mandelbaum.html

- '''Andrew_Heathwaite''' November 27, 2011, 07:46:34 AM UTC-0800
----
Hmm, in which chapter of Mandelbaum's dissertation did you see the definition analogous to maximal evenness?

- '''hstraub''' December 25, 2013, 02:55:07 AM UTC-0800
----
Chapter 14, page 4-5.

- '''Andrew_Heathwaite''' December 25, 2013, 07:40:28 AM UTC-0800
----
"The systems considered here will all have in common that they are based on scales containing intervals as equal as is possible within a 19-tone system. ...as the diatonic scale in 12-tone equal temperament is composed only of the intervals 1/12 and 2/12 ... so all of the scales to be considered here contain a range of two intervals of adjacent size; the size of the intervals will depend on the number of tones in the scale. This is what is meant by the term 'quasi-equal' in the title of this supplement."

- '''Andrew_Heathwaite''' December 25, 2013, 07:44:20 AM UTC-0800
----
Thanks. Indeed, what Mandelbaum calls "quasi-equal-interval-symmetrical" (QEIS) is, as far as I can see, exactly the same as maximally even. Quasi-equal alone is a little less.

- '''hstraub''' December 25, 2013, 08:38:26 AM UTC-0800
----
Ah yes. Looking more closely at the text, I see that you are correct. Thanks for the clarification!

- '''Andrew_Heathwaite''' December 25, 2013, 10:50:59 AM UTC-0800
----