Reply to Gregg Gibson

It is interesting that you began with a question about Arabic music.
Arabic modes use neutral seconds (which bisect minor thirds) and neutral
thirds (which bisect perfect fifths) which are not present in 19-equal.
So much for studying "all the modes melodically distinct to the ear!"
Septimal intervals, the next logical step in consonance after the
5-limit intervals in triads, are far better represented in 31-equal than
19-equal. If you really believe that the 31-equal dieses are too small
for use in melody, no one will force you to use them! Even avoiding
them, you will have more melodic variety than in 19-equal, plus you will
get much better 7-limit harmonies, far better 11-limit harmonies, and
even those Arabic modes (just add 1 to the size of each of the
heptatonic steps in an Arabic scale in 24-equal and you get a pretty
good 31-equal approximation).

22-equal, far from being worthless, has occupied me for the last six
years; see my paper at
http:/www-math.cudenver.edu/~jstarret/microtone.html under "Notes on
Microtonality." Worthless for diatonicism, maybe; for escaping the
diatonic hegemony, it may be our only hope. In a rare moment of
compositional inspiration, I wrote a piece where the top voice moves
down through 20 of the 22 tones. You can hear this on the Tuning-List
Tape. Despite the 54.5 cent steps, I can sing this melody in the shower
(but only if I clearly imagine the harmony).

>>Of the heptatonic modes, the familiar seven of the diatonic genus
>>have consonant chords on six of the seven degrees, as is universally
>>known. More subtly, every one of these degrees is part of at least one
>>consonant chord (actually, of at least two) within the untransposed
>>diatonic order. No other heptatonic modal genus has above four of its
>>seven degrees which are the roots of consonant chords within the genus,
>>all of whose degrees are included within at least one consonant chord.
>>These genera are four in number, including 28 modes. On C these are:
>
>>C D E F G Ab B C
>>C D E F G Ab Bb C
>>C Db E F Gb A Bb C
>>C D E F G# A B C
>
>This looks interesting, but it sounds like you're saying there are four of
>something that there are none of. Can you clarify please?
>
>Anyway, I recall someone posting about a psychology experiment back in the
>50s or 30s where subjects were trained to listen to melodies whose interval
>sizes were gradually decreased, over the course of months, to something like
>tenths of tones. The subjects became quite comformtable with these melodic
>sizes, could distinguish them quite clearly, and when exposed to conventional
>Western music again, found the intervals very large.
>
>Someone with a lot of 12-equal training is likely to consider two notes
>separated by 40 cents "the same", and two notes separated by 60 cents
>"different." It doesn't take a genius of psychology to explain that. However,
>both listeners and musicians are able to learn and enjoy considerably smaller
>intervals, as many on this list can attest from personal experience.


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From: DMB5561719
Subject: Re: Tuning into the FUTURE.
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>Out of boredom and final exam disorganization I hapted to open a copy of the
>Harvard Dictory of Music- albiet an older edition and turned to the enclosure
>about Just Intonation- and immediately realized why I haven't opened a copy of
>Harvard DM since undergraduate school- for holiday cheer check it out!

Yeah, a while back on the list, somebody or other arranged to collect
listers' replies to that definition, the two-word summary of which was "SAY
WHAT?!?".

Has anybody out there heard what, if anything, ever came of that?


SMTPOriginator: tuning@eartha.mills.edu
From: mr88cet@texas.net (Gary Morrison)
Subject: Re: More on the 19-tone Equal Temperament
PostedDate: 15-12-97 03:09:32
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