Talk:Hobbit - Revision history

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	~~== OETES ==~~

	Is there a reason this norm with no calculator available and a wiki page full of complex matrix nonsense (including a pseudoinverse thing that literally has essentially no arithmetic method of determining it) is chosen over any other formulation of octave-equivalent mapped interval complexity? I can think of a couple ways to formalize it to be honest that don't involve that.
	~~-- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 02:13, 13 November 2025 (UTC)~~

VectorGraphics: /* OETES */ new section

2025-11-13T02:13:48Z

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			== OETES ==

			Is there a reason this norm with no calculator available and a wiki page full of complex matrix nonsense (including a pseudoinverse thing that literally has essentially no arithmetic method of determining it) is chosen over any other formulation of octave-equivalent mapped interval complexity? I can think of a couple ways to formalize it to be honest that don't involve that.
			-- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 02:13, 13 November 2025 (UTC)

Xenwolf: Xenwolf moved page Talk:Hobbits to Talk:Hobbit: singular rule for better linking

2021-01-07T06:53:14Z

Xenwolf moved page Talk:Hobbits to Talk:Hobbit: singular rule for better linking

← Older revision	Revision as of 06:53, 7 January 2021
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Mike Battaglia: 1 revision imported: Moving archived Wikispaces discussion to subpage

2018-10-01T18:02:37Z

1 revision imported: Moving archived Wikispaces discussion to subpage

← Older revision	Revision as of 18:02, 1 October 2018
(No difference)

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">''...

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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.~~

	~~----~~

	~~== Can we explain these things in English as well? ==~~
	~~It would be a nice thing to not immediately assault the reader with PhD mathematical treatise-speak when they learn about scale classification....~~

	~~Granted are two points:~~

	~~1) Much scale research goes on on the (various) Yahoo tuning lists. The research is valuable and discoveries are made, etc.~~

	~~2) Potentially, many of these discoveries are of musical value.~~

	~~BUT---if we care/want musicians to even tinker with these concepts, we will scare them away with talks of "vals" and "monzos"...to the outsider, these are simply neologisms.~~

	~~Just a thought. The xenwiki is setup as a resource, one would hope, for musicians, and not simply for PhD mathematicians.~~

	~~Best,~~

	~~AKJ~~

	~~- '''akjmicro''' March 07, 2011, 01:01:50 PM UTC-0800~~
	~~----~~
	~~I agree with you. I tried to force a definition of val, monzo by adding links to (future) wiki pages, but this will not improve the readability.~~

	~~As I've learned, some notations are very efficient, but some of them I cannot decode at all. Maybe some examples for these techniques will suffice for the non-mathematician of us.~~

	~~Best regards,~~

	~~Wolf~~

	~~- '''xenwolf''' March 07, 2011, 11:53:22 PM UTC-0800~~
	~~----~~
	~~Here's an outline for how I think the page can be improved. Unfortunately the details will need to be filled in by Gene.~~

	In 2001 it was discovered that [MOS] scales correspond to rank 2 regular temperamnts. For a regular temperament of arbitrary rank, there is a corroseponding hobbit scale (named for their relationship to [dwarf scales]). Examples may be found on the [Scalesmith] page.

	~~Definition~~

	Given a regular tempearment, we first find an equal temperament [val] v which supports it. Next, we define an [octave equivalent seminorm] for the temperament. This seminorm applies to monzos and sends any comma of the temperament, and also the octave, to zero. It measures the complexity of the octave-equivalent pitch class to which a monzo belongs. For example, in meantone temperament, the OE seminorm of 3/2 is <u>_ and of 3/1 is </u>_ and of 25/16 is ___. Roughly speaking, the hobbit is the scale consisting of the lowest OE complexity for each scale step mapped to the integer i by v (see [epimorphic] for details).

	~~In the rank 2 case, the hobbit for v is identical to the MOS for v because...~~

	~~Examples~~

	~~Consider the 7-note hobbit for meantone temperament ... yields the familiar diatonic scale (MOS)...~~

	~~Next, consider the 22-note hobbit for minerva temperament...~~

	~~Details~~

	~~Denoting the OE seminorm...~~

	~~- '''clumma''' March 08, 2011, 10:16:42 PM UTC-0800~~
	~~----~~
	~~Wow, I cannot edit this. Useless.~~

	~~- '''clumma''' March 08, 2011, 10:17:22 PM 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.''' ''...

2018-09-20T07:00:35Z

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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.'''
----

== Can we explain these things in English as well? ==
It would be a nice thing to not immediately assault the reader with PhD mathematical treatise-speak when they learn about scale classification....

Granted are two points:

1) Much scale research goes on on the (various) Yahoo tuning lists. The research is valuable and discoveries are made, etc.

2) Potentially, many of these discoveries are of musical value.

BUT---if we care/want musicians to even tinker with these concepts, we will scare them away with talks of "vals" and "monzos"...to the outsider, these are simply neologisms.

Just a thought. The xenwiki is setup as a resource, one would hope, for musicians, and not simply for PhD mathematicians.

Best,

AKJ

- '''akjmicro''' March 07, 2011, 01:01:50 PM UTC-0800
----
I agree with you. I tried to force a definition of val, monzo by adding links to (future) wiki pages, but this will not improve the readability.

As I've learned, some notations are very efficient, but some of them I cannot decode at all. Maybe some examples for these techniques will suffice for the non-mathematician of us.

Best regards,

Wolf

- '''xenwolf''' March 07, 2011, 11:53:22 PM UTC-0800
----
Here's an outline for how I think the page can be improved. Unfortunately the details will need to be filled in by Gene.

In 2001 it was discovered that [MOS] scales correspond to rank 2 regular temperamnts. For a regular temperament of arbitrary rank, there is a corroseponding hobbit scale (named for their relationship to [dwarf scales]). Examples may be found on the [Scalesmith] page.

*Definition*

Given a regular tempearment, we first find an equal temperament [val] v which supports it. Next, we define an [octave equivalent seminorm] for the temperament. This seminorm applies to monzos and sends any comma of the temperament, and also the octave, to zero. It measures the complexity of the octave-equivalent pitch class to which a monzo belongs. For example, in meantone temperament, the OE seminorm of 3/2 is <u>_ and of 3/1 is </u>_ and of 25/16 is ___. Roughly speaking, the hobbit is the scale consisting of the lowest OE complexity for each scale step mapped to the integer i by v (see [epimorphic] for details).

In the rank 2 case, the hobbit for v is identical to the MOS for v because...

*Examples*

Consider the 7-note hobbit for meantone temperament ... yields the familiar diatonic scale (MOS)...

Next, consider the 22-note hobbit for minerva temperament...

*Details*

Denoting the OE seminorm...

- '''clumma''' March 08, 2011, 10:16:42 PM UTC-0800
----
Wow, I cannot edit this. Useless.

- '''clumma''' March 08, 2011, 10:17:22 PM UTC-0800
----