TWO TUNING digest 1192, GaryMo

TWO: ALL THE MUSIC IS MICROTONAL


At 02:02 PM 28/09/97 -0300, you wrote:
TUNING Digest 1192
----------------
>From: mr88cet@texas.net (Gary Morrison)
>To: tuning@eartha.mills.edu
>Subject: Re: All the music is microtonal
>Message-ID:
>
>> The real answer is 13, because they are 12 plus 1, such of the Octave. ...
>>8 means total notes and 12 means note-names (or structural notes if we
>>like).So to equalize concepts if we use 8/Oct we must use 13/Oct, and if we
>>use 12/Oct we must use 7/Oct.
>
> At the risk of being presumptuous, I think I can probably speak for most
>tuning enthusiasts when I say that you're far better off using 12 and 7
>than 13 and 8. In summary, you're asking for trouble when you count both
>beginning and ending notes (e.g., both upper and lower Cs in a C scale)
>when you also admit the possibility of repeating that pattern - using the
>upper C as the root of that same scale in the next octave.

If we see it from the STRICT Tuners point of view, that's right, and I
enter between "the most tuning enthusiasts" (Please Gary put me into the
list :-) ). Yes !!! this is the matter I have worked in my free-time for no
less than 30 years.
There are also others points of view.
- The 12 semitonic intervals are closed in 13 notes. This happens in the
note-book.
- In the piano, the white keys per Octave are 8.
- In the staff, in any key, we must count 8 notes to find the note-symbol of
a note one Octave appart.

>
> Ideally fifths would have been called fourths, unisons called zeros,
>octaves sevenths, thirds seconds, and so forth. That would ensure that
>intervals "add" correctly, like in the case of a fourth plus a third
>coming out to a sixth. Clearly 4+3=7 rather than 6.

As a mathematical concept all of this occur from the use of a Ordinal Scale
instead of a Scalar Scale. The Ordinal begins with 1 (one) and the Scalar
from 0 (zero). Ordinal comes from "orden" that means "order",



>If, historically speaking,
>we had recognized the (perfect) unison as a pitch difference of zero (which
>is after all exactly what it is) then fourths would have been called
>thirds, thirds called seconds, and sixths called fifths, and the result
>would have been correct: 3+2=5.
>

It seems there is a happy (or not) coincidence between the zero as a pitch
difference and the zero of the Scalar Scale. One physical, the other
mathematical. Ellis (Helmholtz p.13-d) define the concept of Intervals.

> But in the end our only option is to accept that the damage is done. We
>just use traditional interval nomenclatures as formal, conventional names,
>and attribute only very limited numerical meaning to them. Fourths,
>thirds, and sixths are just names; they could just as appropriately have
>been called johns, sarahs, and franks.
>
> So the fact that the etymology of the word octave suggests the number 8
>most of us view as largely inconsequential, because it really suggests 7
>diatonic steps, or 12, 19, or whatever chromatic steps.

The ordinal numbers (distances) such as Fourth, Fifth, Octave, are
Ordinals. NOTES are counted. And in the case of 7, 12, 19, INTERVALS (or
Chromatic notes) are counted.


Thanks Gary,

Eduardo
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