An appeal for suggestions

Some time ago John Chalmers posted te list about the book I recently
wrote. I expect that there will be many things that the people on this
list will think _should_ have been covered and weren't. So this is an
appeal to all people intrested in nonstandard tunings, to let me know
of anything in this category. There are two requirements: it should be
relevant to the topic of the book and it should be explainable at the
rather low level that I've written the book at (i. e., not require a
course in linear algebra or the like!)

I've already had some quite fruitful discussions by e-mail with three
people whose contributions are very much appreciated, but I'm certain
there are more of you out there whose input could help my book.

--- In tuning@yahoogroups.com, "Bruce R. Gilson" <brgster@...> wrote:
>
> Some time ago John Chalmers posted te list about the book
> I recently wrote. I expect that there will be many things that
> the people on this list will think _should_ have been covered
> and weren't. So this is an appeal to all people intrested in
> nonstandard tunings, to let me know of anything in this
> category. There are two requirements: it should be relevant
> to the topic of the book and it should be explainable at the
> rather low level that I've written the book at (i. e., not
> require a course in linear algebra or the like!)
>
> I've already had some quite fruitful discussions by e-mail
> with three people whose contributions are very much appreciated,
> but I'm certain there are more of you out there whose input
> could help my book.

Hi Bruce - thanks for this. Would you go so far as to loan
copies to reviewers here? In the past, I have simply purchased
all books related to tuning, but my house is now filling up,
and my bank account has lately been emptying out. :)
As always, feel free to contact me offlist.

-Carl

Bruce R. Gilson wrote:
> Some time ago John Chalmers posted te list about the book I recently > wrote. I expect that there will be many things that the people on this > list will think _should_ have been covered and weren't. So this is an > appeal to all people intrested in nonstandard tunings, to let me know > of anything in this category. There are two requirements: it should be > relevant to the topic of the book and it should be explainable at the > rather low level that I've written the book at (i. e., not require a > course in linear algebra or the like!) I don't have the book, so some of the things I mention might already be covered, but a couple of things I noticed looking through the index on Amazon: I didn't see any mention of maqam or raga scales (although there is one reference to Turkish music), or the pelog and slendro scales of Indonesian music. Clearly a book of this length can't go into much detail, but a few examples of applying mathematics to non-western tunings would be helpful.

There are mathematical properties relevant to "construction of musical scales" that don't require anything like linear algebra -- Myhill's property for instance is useful to know about (each interval class has two different sizes of interval), as is Rothenberg's propriety. Fokker's periodicity blocks can be mentioned in a discussion about commas. Different kinds of symmetry: a scale might be the same when inverted, or have identical tetrachords.

You do need some linear algebra to optimize RMS error, but simply calculating the RMS error of a scale is straightforward. It's a useful enough concept for regular temperament systems and tempered scales in general that it's probably worth a mention.

    Here is a relative easy scale concept.

Take a scale that
A) Divides 7-notes among 2 channels to make the harmony sound clearer

B) Divides them in such a way that you don't hear bin-aural beating (in simpler terms, so the tones don't seem to grind/fluctuate rapidly in volume against each other)

C) Shift the notes slightly in frequency so the mood of the tones feels the same IE all seven notes at once forms a very composed and relaxing sound (aesthetically pleasing; nothing to do with math)

Here is the scale (expressed in multiples of the root note frequency)

Left Channel -------------------------------Right Channel
1 (root tone)                                  1.112
1.23                                             1.328
1.48                                             1.6666
1.846                                           2 (octave/even numbered root tone)

    Note that for every even numbered octave up the root note (and all others) SWITCHES channels between left and right.
   Perhaps the best "newbie" thing about this scale...is the mood at feel are reminiscent of 12 tone 7 note scales...yet the ratios are a bit different and the flexibility (far as the number of chords which are legal) is much greater.

-Michael

--- On Mon, 10/13/08, Bruce R. Gilson <brgster@...m> wrote:
From: Bruce R. Gilson <brgster@...>
Subject: [tuning] An appeal for suggestions
To: tuning@yahoogroups.com
Date: Monday, October 13, 2008, 7:40 AM

Some time ago John Chalmers posted te list about the book I recently

wrote. I expect that there will be many things that the people on this

list will think _should_ have been covered and weren't. So this is an

appeal to all people intrested in nonstandard tunings, to let me know

of anything in this category. There are two requirements: it should be

relevant to the topic of the book and it should be explainable at the

rather low level that I've written the book at (i. e., not require a

course in linear algebra or the like!)

I've already had some quite fruitful discussions by e-mail with three

people whose contributions are very much appreciated, but I'm certain

there are more of you out there whose input could help my book.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
>
> I don't have the book, so some of the things I mention might
> already be covered, but a couple of things I noticed looking
> through the index on Amazon: I didn't see any mention of maqam or
> raga scales (although there is one reference to Turkish music), or
> the pelog and slendro scales of Indonesian music. Clearly a book of
> this length can't go into much detail, but a few examples of ern
> applying mathematics to non-west tunings would be helpful.

On the one hand, I agree with you that it would be useful to have
this information in the book. On the other, I haven't found a good
write-up that I could use as a source. The one book on the Arabic
maqamat I own deals with them in a 12-ET approzimation; I'm sure that
is an oversimplification, but I don't know what the correct
descriptions are. I once had a book (by Danielou?) on South Indian
scales, but I no longer have it in an easily accessible location, and
it's been years since I read the material, so I can't reconstruct it.
And while I've seen reference to the two Indonesian scales, I've only
seen lists of cents intervals, not the theory behind how these
intervals were derived. So I'm not dismissing your post, but rather
asking for directions on where I can find the material.

> There are mathematical properties relevant to "construction of
> musical scales" that don't require anything like linear algebra --
> Myhill's property for instance is useful to know about (each
> interval class has two different sizes of interval), as is
> Rothenberg's propriety. Fokker's periodicity blocks can be
> mentioned in a discussion about commas. Different kinds of
> symmetry: a scale might be the same when inverted, or have
> identical tetrachords.

You've actually mentioned there a few items I don't have a lot of
familiarity with. So on these I'll accept them as suggestions, but
pending some study on my part to determine their suitability.

> You do need some linear algebra to optimize RMS error, but simply
> calculating the RMS error of a scale is straightforward. It's a
> useful enough concept for regular temperament systems and tempered
> scales in general that it's probably worth a mention.

That can probably be included. It's a useful suggestion.

Thank you.

Bruce R. Gilson wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>> >> I don't have the book, so some of the things I mention might >> already be covered, but a couple of things I noticed looking >> through the index on Amazon: I didn't see any mention of maqam or >> raga scales (although there is one reference to Turkish music), or >> the pelog and slendro scales of Indonesian music. Clearly a book of >> this length can't go into much detail, but a few examples of ern >> applying mathematics to non-west tunings would be helpful.
> > On the one hand, I agree with you that it would be useful to have > this information in the book. On the other, I haven't found a good > write-up that I could use as a source. The one book on the Arabic > maqamat I own deals with them in a 12-ET approzimation; I'm sure that > is an oversimplification, but I don't know what the correct > descriptions are. I once had a book (by Danielou?) on South Indian > scales, but I no longer have it in an easily accessible location, and > it's been years since I read the material, so I can't reconstruct it. > And while I've seen reference to the two Indonesian scales, I've only > seen lists of cents intervals, not the theory behind how these > intervals were derived. So I'm not dismissing your post, but rather > asking for directions on where I can find the material. I don't have any books that go over the maqam tradition in much detail -- a brief summary of the Persian _dastgah_ system in William P. Malm's _Music Cultures of the Pacific, the Near East, and Asia_, but there have been some web site links posted recently in this group that may be relevant. http://www.maqamworld.com/ is the main one that comes to mind, although the maqamat are notated as quarter-tones. Others here may have some better sources. Malm's book also goes over the basics of the Indian shruti system, but I know I've seen more detail in other sources.

I think the interesting point about the Indonesian scales is not the specific cents values of the intervals (which vary considerably from one place to another), but the practice of detuning two sets of instruments to beat at a specific rate, and the variable detuning of the octaves.

>> There are mathematical properties relevant to "construction of >> musical scales" that don't require anything like linear algebra -- >> Myhill's property for instance is useful to know about (each >> interval class has two different sizes of interval), as is >> Rothenberg's propriety. Fokker's periodicity blocks can be >> mentioned in a discussion about commas. Different kinds of >> symmetry: a scale might be the same when inverted, or have >> identical tetrachords.
> > You've actually mentioned there a few items I don't have a lot of > familiarity with. So on these I'll accept them as suggestions, but > pending some study on my part to determine their suitability.

I've learned most of what I know about these properties from the Scala help files and associated files that come with the program, as well as from this list. http://www.xs4all.nl/~huygensf/scala/

Also on periodicity blocks specifically, http://www.sonic-arts.org/td/erlich/intropblock1.htm