19 equal and modal genera

> Bill Alves (quoted by Paul Ehrlich) made a very interesting comment to
> the effect that the four chromatic modal genera (scales) comprising 28
> modes, that I have discovered and posted:
>
> C D E F G A B C
> C D E F G Ab B C
> C D E F G Ab Bb C
> C Db E F Gb A Bb C
>
> can be played in the 12-tone equal.

More importantly, they are all distinct in 12 equal, as are the other 6:

C D Eb F G Ab A C C Eb E F G A Bb C
C C# E F G G# A C C Eb Fb F G Ab Cb C
C C# E F F# G A C C Eb F Gb G Ab Cb C

There are also come chords within these scales that work in 12 equal,
but not 19 equal. I can find no opposing example. With 12 pitch
classes, then, the harmonic vocabulary is enhanced, with no reduction
in the number of genera that fulfil Gregg's criteria. This is a
strange argument for 19 equal. Gregg's replies are unconvincing:

> ... but the resulting modes conflate a number of
> aurally distinct modes into single, neutral modes, and lack much of the
> distinct melodic character of the 19-tone versions.

Which modes cease to be distinct? Of course, the melodic character
will be different in different tunings, but that is not to say one is
superior to the others. In good old 31 equal, you get the added bonus
of septimal chords, consonant or otherwise.

The other arguments are all specifically about 12 equal, and not the
infinity of meantone temperaments in which the genera also work.


To the more general argument:

> Hence, 19-tone equal gives rise to a powerful contrast between
> consonance and dissonance, both melodically and harmonically speaking.
> The effect is to give music a kind of elastic, forward impetus quite
> unknown in the 12-tone equal, which has a more static, uncertain
> esthetic.

This is a good description of 19 equal. I can see the relevance to
rock music, but some of us like a bit more subtlety. The consonances
are acceptable. but not that good. Minor triads have a uniquely
bright sound, which may be a result of the good minor third. The
dissonances something to behold.

> The prinicipal
> temperaments are 12- 19- 31- 43- 50- & 55-tone equal.

Gregg's dislike of non-meantone temperaments is well established. As
an existentialist, I cannot agree, because I use and will continue to
use such temperaments. However, his neglect of non-equal temperaments
is so far unjustified. The obvious scale he's overlooking is
LucyTuning, whose 54 cent diesis is at the bottom of the melodic limen.
As the difference between 19 equal and LucyTuning is well below a
melodic limen, melodies will presumably remain distinctive after the
transition. Singers should be able to make the distinctions if they
are trained with 19 pitch classes. The advantage is that both melodies
and harmonies sound a lot better -- but there I go with my opinions
again. So, Gregg, how about it?


Now, I'd just like to clear this up:

> To give some idea of just how immense this universe is - and remember
> these are _real_, usable resources, not purely theoretical, aurally
> imperceptible variations - compare the number of modes (I here use the
> term loosely merely to indicate a collection of seven notes used in a
> melody) consisting of 12 notes taken 7 at a time:
>
> nCr where n = 12 & r = 7
> = 792
> with the number of modes consisting of 19 notes taken 7 at a time:
> nCr where n = 19 & r = 7
> = 50,388

Really, you should define modes relative to a tonic, so the numbers
get smaller. With 12, you're choosing 6 from 11, which gives 462
modes. 19C6 is 12376. The contrast is still striking. Including
all the transpositions, you get 462*12=5544 and 12376*19=235144.


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From: mr88cet@texas.net (Gary Morrison)
Subject: Re: Reply 3 to Graham Breed
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>If the man on the street wanted music in other
>temperaments than 12, don't you think he would have asked for it by now?

Well, that's one way to put it!

I think it's fair to say that the music scene in general asks for new
tunings, but as for whether 19 is the best way to go ... Well, I think we
have to sell 19 and many other tunings for their possibilities that can't
be realized in 12.


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From: Gregg Gibson
Subject: Number of pitches used in melodies
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