Re: You asked for comments

Hi Charles,

Regarding "Representing Meantone Tunings with Nowitzkian Note Names
('NNN')" (http://nowitzky.hypermart.net/justint/nnnmt.htm), thanks for your
comments!

At 01:26 PM 5/18/00 +0100, you wrote:
>The concept of measuring all meantone-type tunings benchmarked from
>"integer frequency ratios" makes something very simple unnecessarily
>complicated.

Well, I don't wanna complicate something, unless it helps shed some light
in the process. As a matter of fact, the complexity of "integer frequency
ratios" helped inspire Nowitzkian Note Names. For example, a IV, V, I
progression (5-Limit Just Intonation):

"integer frequency ratios":
IV: 4/3 5/3 2/1
V: 3/2 15/8 9/4
I: 1/1 5/4 3/2

Nowitzkian Note Names:
IV: 5F 4A 5C
V: 5G 4B 5D
I: 5C 4E 5G

Instead of obscuring relationships in ratios, I believe my notation makes
the similarity of the three major triads above glaringly obvious (without
losing the accuracy that the ratios provide).

>To describe any meantone, all you need to specify is:
>
>1. Octave Ratio
>2. size of Large interval (L) (II) (as ratio, cents, or whatever unit of
>measurement you wish e.g. Savant etc.)
>
>The naming of intervals and specific notes then becomes musically
>obvious once you set a frequency to notename reference. e.g. A4=440Hz.

I agree that my notation is "overkill" in some situations. If I want
someone to perform a piece in "1/4 Comma Meantone", I wouldn't want to put
a Comma Number in front of each note on the page. I'd specify the tuning
up at the top of the page, up there with the key signature and time
signature. Using your suggestion above, I believe it would be specified as:

1. Octave ratio: 2/1
2. Large Interval: 5^(1/4)
(that's the fourth root of 5, = approx. 1.495)
i.e., it's a just fifth, flattened a fourth of a comma:
3/2/((81/80)^1/4)
(it's irrational, so I can't give you a ratio)

But as a tool for understanding how 1/4 Comma Meantone works - how it
disburses the Comma evenly over four slightly flattened fifths - I believe
my notation helps elucidate it. Here's the cycle of slightly flattened
fifths:

frequency "ratios":
5/4 = 1.25
5^(3/4)/2 = approx. 1.672
5^(1/2)/2 = approx. 1.118
5^(1/4) = approx. 1.495
1/1 = 1

Nowitzkian Note Names:
4 E
4 1/4 A
4 1/2 D
4 3/4 G
5 C

So instead of getting lost in fourth-roots and octave-equivalance issues,
Nowitzkian Note Names simply show a reduction of 1/4 comma as you go up the
cycle.

>You did ask for comments ;-)

And don't think I don't appreciate 'em ;) Thanks again,

--Mark

P.S.: Now I gotta go see if I can represent a LucyTuned scale in "NNN"...

+-------------------------------------------------------
| Mark Nowitzky
| email: nowitzky@alum.mit.edu
| www: http://nowitzky.hypermart.net
| "If you haven't visited Mark Nowitzky's home
| page recently, you haven't missed much..."
+-------------------------------------------------------
_____________________________________________
NetZero - Defenders of the Free World
Click here for FREE Internet Access and Email
http://www.netzero.net/download/index.html

I see your point.
You may find that the way that I have used with orchestras and choirs helpful.

I tell them that: " A is as usual i.e.440 hz.
For each step of fifths from A you should sound the note 4.5 cents flatter than
12tET. i.e. E is 4.5 flatter, B is 9 flatter,
F# is 13.5 flatter, etc.

For steps of fourths from A play the notes sharper by the same 4.5 cents per
step. i.e. D is 4.5 cents sharper, G is 9 cents sharper etc."

They seem to grasp the idea, and run with it without too much trouble, once
they have adjusted their open strings or reset their reference pitches.

>Hi Charles,
>
>Regarding "Representing Meantone Tunings with Nowitzkian Note Names
>('NNN')" (http://nowitzky.hypermart.net/justint/nnnmt.htm), thanks for your

>comments!
>
>At 01:26 PM 5/18/00 +0100, you wrote:
>>The concept of measuring all meantone-type tunings benchmarked from
>>"integer frequency ratios" makes something very simple unnecessarily
>>complicated.
>
>Well, I don't wanna complicate something, unless it helps shed some light
>in the process. As a matter of fact, the complexity of "integer frequency

>ratios" helped inspire Nowitzkian Note Names. For example, a IV, V, I
>progression (5-Limit Just Intonation):
>
> "integer frequency ratios":
> IV: 4/3 5/3 2/1
> V: 3/2 15/8 9/4
> I: 1/1 5/4 3/2
>
> Nowitzkian Note Names:
> IV: 5F 4A 5C
> V: 5G 4B 5D
> I: 5C 4E 5G
>
>Instead of obscuring relationships in ratios, I believe my notation makes
>the similarity of the three major triads above glaringly obvious (without
>losing the accuracy that the ratios provide).
>
>>To describe any meantone, all you need to specify is:
>>
>>1. Octave Ratio
>>2. size of Large interval (L) (II) (as ratio, cents, or whatever unit of
>>measurement you wish e.g. Savant etc.)
>>
>>The naming of intervals and specific notes then becomes musically
>>obvious once you set a frequency to notename reference. e.g. A4=440Hz.
>
>I agree that my notation is "overkill" in some situations. If I want
>someone to perform a piece in "1/4 Comma Meantone", I wouldn't want to put

>a Comma Number in front of each note on the page. I'd specify the tuning
>up at the top of the page, up there with the key signature and time
>signature. Using your suggestion above, I believe it would be specified as:

>
> 1. Octave ratio: 2/1
> 2. Large Interval: 5^(1/4)
> (that's the fourth root of 5, = approx. 1.495)
> i.e., it's a just fifth, flattened a fourth of a comma:
>3/2/((81/80)^1/4)
> (it's irrational, so I can't give you a ratio)
>
>But as a tool for understanding how 1/4 Comma Meantone works - how it
>disburses the Comma evenly over four slightly flattened fifths - I believe

>my notation helps elucidate it. Here's the cycle of slightly flattened
>fifths:
>
> frequency "ratios":
> 5/4 = 1.25
> 5^(3/4)/2 = approx. 1.672
> 5^(1/2)/2 = approx. 1.118
> 5^(1/4) = approx. 1.495
> 1/1 = 1
>
> Nowitzkian Note Names:
> 4 E
> 4 1/4 A
> 4 1/2 D
> 4 3/4 G
> 5 C
>
>So instead of getting lost in fourth-roots and octave-equivalance issues,
>Nowitzkian Note Names simply show a reduction of 1/4 comma as you go up the

>cycle.
>
>>You did ask for comments ;-)
>
>And don't think I don't appreciate 'em ;) Thanks again,
>
>--Mark
>
>P.S.: Now I gotta go see if I can represent a LucyTuned scale in "NNN"...

>
>
>+-------------------------------------------------------
>| Mark Nowitzky
>| email: nowitzky@alum.mit.edu
>| www: http://nowitzky.hypermart.net
>| "If you haven't visited Mark Nowitzky's home
>| page recently, you haven't missed much..."
>+-------------------------------------------------------
>_____________________________________________
>NetZero - Defenders of the Free World
>Click here for FREE Internet Access and Email
>http://www.netzero.net/download/index.html
>
>
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