Yahoo Tuning Groups Ultimate Backup mills-tuning-list 19-tone ruminations and 22-tone exhortations

Gregg Gibson wrote,

>}But to return to the matter of playing these in 12-tone equal. Yes, this
>}is of course possible, but the resulting modes conflate a number of
>}aurally distinct modes into single, neutral modes,
>
>Care to provide an example of a 12-tone mode which conflates two or more
>19-tone modes?
>
>}and lack much of the
>}distinct melodic character of the 19-tone versions.
>
>}For an example of what I mean, take the most common form of the minor
>}scale (on C for convenience):
>
>}C D Eb F G Ab B C
>
>}This can be played in 12-tone equal, but loses much of its piquancy
>}thereby. This is partly because the highly characteristic augmented tone
>}Ab-B is confounded with the minor third.
>
>True, but somehow even in 12-equal it never sounds like a minor third, always
>like a dissonant interval, in the context ofthis scale (except when a late
>Romantic composer is using the Ab minor chord). My high school music teacher
>played the harmonic minor scale, then the augmented second interval, and
>everyone in the class called the interval dissonant -- even though the very
>same interval, functioning as a minor third in another scale, was deemed
>consonant. Why is this so? Because tonal consonance is not merely an
>acoustical phenomenon -- it is also a function of musical grammar. The
>Western tonal grammar constructs consonant chords and intervals from
>alternate notes of the scale. Seconds, even augmented seconds, cannot
>function as harmonic consonances within this grammar.
>
>}Historically, the 'minor scale'
>}derived much of its attractiveness from the use of the mesotonic, which
>}preserves the augmented tone close to the just values (there are
>}several).
>
>I would argue that, if so, the most significant of these values is 7:6; the
>others are well beyond the 11-limit (I'm talking odd limit here) and
>therefore just intonantion is irrelevant. 19-equal conflates 7:6 with 8:7,
>and so if the augmented tone is to be heard as a particular ratio, 19-equal
>is a poor tuning for it. In 31-equal, however, the augmented tone is a very
>clear 7:6.
>
>}I have elsewhere referred to the fact that this is one of the
>}few respects in which 31-tone equal is melodically quite distinct from
>}12-tone equal. But 19-tone equal is still more distinct.
>
>Distinct from 12, yes; better -- well, the flexibility of interpreting the
>augmented tone as a minor third in late Romanic music is an advantage of
>12-tone that 19-tone does not posess, and the clear ratio-interpretation
>mentioned above is an advantage of 31.
>
>}Again, to give a better idea of exactly why one cannot adequately play
>}chromatic modes in 12-tone equal, let me offer up Yasser's old (but very
>}good) analogy between 12-tone equal and 7-tone equal. One can reproduce
>}the seven diatonic modes in 7-tone equal, but they are merged into a
>}single, neutral mode, for 7-tone equal has no semitones. This is very
>}much what occurs when a chromatic mode such as C D Eb F G Ab B C is
>}played in 12-tone equal - it is largely sterilized of its unique modal
>}flavor, because the two species of semitones are confounded.
>
>All the semitones in this mode are the same size in 19-equal: 2 degrees. And
>what modes are merged?
>
>}Paul E[]rlich asserts that 22-tone equal is the only path to escape
>}diatonicism.
>
>I only said it _may_ be the only path, and I explained why in a later post.
>
>}but 22-tone
>}equal is not a temperament at all, but a mere tuning artefact that
>}reproduces the worst defects of just intonation.
>
>But these "defects" (the non-vanishing of the syntonic comma) can only be
>seen as such in the context of diatonicism! Since we are speaking of escaping
>diatonicism, the relevant properties of a tuning system will be quite
>different.
>
>}Not that I wish to
>}question the validity of the just ratios as standards for musical
>}thought.
>}[...]
>}the enharmonic genus, where harmony is not an important element. This
>}involves the use of 1/3 tones, which are never written in our music, but
>}which fill the living rock melos of our people. No theorist should ever
>}presume to discount the importance of what the musically untutored
>}produce from their own melodic inspiration. They stand in need of our
>}guidance, but we also of theirs.
>
>Can you tell us what this genus looks like? Most of my favorite rock
>1/3-tones arise from the difference between a 7:6 and a whole tone; harmony
>is indeed an important element wherever such intervals arise. I suspect that
>22-equal, for instance, might even "work" for your enharmonic genus when its
>septimal basis is admitted. It certainly comes closer to the ancient Greek,
>quarter-tonal enharmonic genus, which by the way is yet another
>counter-example to your minimal melodic limen spec.
>
>}The 19-tone equal temperament _alone_ can give access to either of these
>}two genera [the "chromatic" -- really modes of 3 Western and 1 non-western
>altered diatonic scales --
>}and the "enharmonic" -- yet to be fully described by Gregg]
>
>We shall see. I have already mentioned that your 28 "chromatic" modes are
>well-represented in 22-equal.
>
>}just as it alone gives adequate access to the diatonic
>}genus.
>
>While 22-equal does not give adequate access to the diatonic genus, 19-tone
>is far from the only tuning that does. The vast majority of music that we
>hear today serves as proof that 12-equal is more than "adequate." 31-equal we
>have already been discussing, but there's one more in-between: 26-equal. Its
>harmonies are about as good as those in 12-equal, and the unusual structure
>of the scale (tones 4 units wide, semitones 3 units wide) is not that hard to
>get used to with the proper harmony. What's more, the tritone is distinct
>from the half-octave -- in C major, the B sounds like an 11th harmonic over
>an F major chord -- a clear, surprising, and unique effect. Combining two
>diatonic scales a half-octave apart leads to a 14-tone set where all the
>consonant triads in one diatonic scale have their septimal completion in the
>other diatonic scale. The point is that there are many avenues for exploring
>the diatonic genus, all with their advantages and disadvantages.
>
>}This follows from the principle of the melodic limen, and from
>}the incredibly close harmonic congruence between just intonation and the
>}19-tone equal. I have not leisure here to treat this in the depth that
>}it deserves, but would like to observe something that I do not believe
>}has ever been clearly noticed before. If the consonances of the senario
>}are each taken as new tonics, we arrive at 19 just intervals within the
>}octave:
>
>}1:1 25:24 16:15 10:9 9:8 16:15 5:4 32:25 4:3 25:18 36:25 3:2 25:16 8:5
>} 5:3 16:9 9:5 15:8 48:25 2:1
>
>}These are the intervals that singers can actually sound accurately
>}singing pure consonances, although there is some debate concerning the
>}ability to reliably distinguish between the commatically separated
>}species of tones. Of these, the 19-tone equal merges the minor and major
>}tones, and also the two species of minor seventh, and intercalates the
>}augmented tone/diminished third and the augmented sixth/diminished
>}seventh.
>
>Thus the "incredibly close harmonic congruence" is not a congruence, or
>one-to-one mapping at all -- it is a mere numerical coincidence. By
>contradistinction, the many highly symmetrical just schemes that intend to
>represent the 22-sruti system of India do form a one-to-one mapping with
>22-equal; that is, all consonant intervals in both are represented by the
>same number of steps. Similarly, the 22-tone just septimal tuning used by Ben
>Johnston in his 4th string quartet is similarly congruent to 22-equal.
>
>
>Graham Breed wrote,
>
>}I haven't investigated Paul Erlich's decatonic
>}modes enough to decide if they can be treated as 10 pitch classes.
>}I don't like the theory because it clings to the idea of diatonic
>}harmony -- that all notes used in harmony must belong to the same key.
>}I'd rather work out a chord sequence, and fit a melody to it. Or,
>}define a melodic mode, write a tune in it, and harmonise it
>}chromatically.
>
>You can't deny that most Western music derives much of its beauty and
>contrapuntal versatility from having both vertical and horizontal sonorities
>taken from the same pitch set. These pitch sets have characteristic dissonant
>intervals which allow a "tonic" to be defined and when the pitch set changes,
>so does the tonic. In this way non-diatonic notes can anticipate a change of
>tonality before that tonality also arrives.
>
>Moreover, the pitch sets in question have a certain structure which allows
>consonance and dissonance, which alone at best are only relative acoustical
>qualities, to achieve absolute grammatical significance. The reality of this
>is proved by the paradox of the augmented second which I mention above. The
>same interval can be heard as a dissonance or a consonance depending on
>whether it functions as a second or a third in the scale.
>
>My decatonic scales in 22-equal provide a way of extending Western
>compositional techniques so that 7-limit tetrads, both otonal ("major") and
>utonal ("minor") may function instead of 5-limit triads as the basic
>consonant harmonies. A dodecatonic, 9-limit system is also present in
>22-equal, but it is purely modal -- the conditions for a tonal style are not
>fulfilled. Additionally, the consonance of 9-limit utonal pentads is
>questionable under certain timbral and inversional circumstances, while that
>of 11-limit otonal hexads is quite clear, so the symmetry between major and
>minor seems to completely break down beyond the 7-limit.

SMTPOriginator: tuning@eartha.mills.edu
From: Adam Silverman
Subject: Re: Partch thesis
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19-tone ruminations and 22-tone exhortations

🔗"Paul H. Erlich" <PErlich@...>

🔗"Jonathan M. Szanto" <jszanto@...>