Yahoo Tuning Groups Ultimate Backup mills-tuning-list re: pure?

Using Helmholtz as a reference (to what prime intervals are most
consonant) he calls a "natural" scale
C 1/1 0 cents
D 9/8 204
Eb 6/5 316
E 5/4 386
F 4/3 498 (inversion of 3/2)
G 3/2 702
Ab 8/5 814 (inv. maj3 5/4)
A 5/3 884 (inv. min3 6/5)
Bb 7/4 969
B 15/8 1088 (5/4 above G)

In regards to some postings on composing and using a more free
intonation (likely sticking to those just thirds above on all chords)
has there been much use of synths which have adjustable tuning maps for
different tonalities, or even for every chord?

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🔗alves@orion.ac.hmc.edu (Bill Alves)

>Bill Alves wrote,
>
>>Given that there are seven pitches in the diatonic set, there are thus
>>seven possible diatonic modes, of which major and minor are only two. I
>>don't see how they are different than the other diatonic modes.
>
PErlich wrote:

>They are very different. The tritone (the only exception in the
>classification of generic interval sizes according to 5-limit consonance)
>is disjoint from the tonic triad in only these modes.

Of course all the diatonic modes have their own peculiarities and hence
their musical uses. However, I was replying to a statement that major and
minor are not "modes" like the "church modes" but are instead "keys." I
don't think the fact that tonic triads in major and minor do not contain
one of the tritone pitches distinguish them enough to require a completely
different terminology. I posted my own defining characteristics of modes
which I feel encompass all diatonic modes. I said that major and minor are
not "different" in that they do not fall outside of that definition.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
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🔗Daniel Wolf <DJWOLF_MATERIAL@...>

Paul Erlich is quite right in identifying the qualitative difference thatmajor and minor have with respect to the other diatonic modes when placedin a polyphonic voice leading situation. Among other things, the placement
of the diminished fifth (_tritone_ ought to be saved for the pythagorean
729/512, on analogy with the ditone) allows for counterpoint with greaterfreedom for inverting voices, which becomes essential in tonal
counterpoint, canon, and fugue. However, _melodically_ these modes
function perfectly well when the melodic rules for the more traditional
modes are followed (that is - Major as combination of mixolydian and lydian
and minor as a combination dorian, phrygian and lydian). In fact, I thinka
good case could be made for hearing early works in Major or minor as a kind
of rapid _raga malaka_ where changes of harmony allow local melodic
fragments to shift from one modal melodic type to another.

Although the study of musical intonation provides fertile ground for
hearing these things flexibly, all too often the result is the opposite. I
heard a lecture a decade or so ago by a famous African American composer
and theorist who wanted to analyse _all music_ in terms of the lydian mode
because it was the one where the the tonic coincided with the lowest termin a series of fifths. I pointed out that this was fine as a model for
composition - and many fine compositions were made using his model - but
could not be applied analytically to all music. In simple voice leading,
the diminished fifth of the lydian mode would always resolve to the
dominant and the Bach example he used simply didn't do this. The good
professor responded: ''And that's where Bach went wrong...'' Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
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🔗Pieter Smit <PieterS@...>

🔗mr88cet@texas.net (Gary Morrison)

>Could somebody please explain modes (Dorian, Frigian, Aeolian, etc) to a
>newcomer on the list, or refer to literature explaining these?

These are the proverbial "church modes" used in Gregorian chant and more
recently in some forms of jazz, blues, and even a little in some popular
music. They are the scales you get when you between a given pitch and the
pitch an octave higher, but using only the white keys.

The scale from C to C using only white keys gives us the familiar
"major" scale, which is also called the "Ionian" mode. A to A using only
white keys gives you what we now call the "natural minor" mode, which is
also called the "Aolean" mode.

All told, these modes are called:

CDEFGABC Ionian mode (AKA major scale)
DEFGABCD Dorian mode
EFGABCDE Phrygian mode
FGABCDEF Lydian mode
GABCDEFG Mixolydian mode
ABCDEFGA Aolean mode (AKA natural minor)
BCDEFGAB Locrian mode

These modes also have a set of older Greek names, but I confess that I
don't know those names.

From: SMTP%"tuning@eartha.mills.edu" 29-MAY-1997 00:43:22.83
To: manuel.op.de.coul@ezh.nl
CC:
Subj: intemperate music

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🔗"Collins, Gordon" <CollinG@...>

Pieter Smit wrote:

>Could somebody please explain modes (Dorian, Frigian, Aeolian, etc) to a
>newcomer on the list, or refer to literature explaining these?

The New Grove Dictionary of Music and Musicians has an excellent description
under "Mode". See also under "Tonality" for more on the difference between
modes and keys.

Several of the articles in Music Theory Online also illuminate the
distinction. Look around in http://boethius.music.ucsb.edu/mto/mtohome.html

Standard books on Western music history *ought* to have good descriptions,
but many I've seen are very sparse on the pre-Baroque era.

Discussions tend to get thwarted by different usages of the word "mode". For
example, Bill Alves appears to view modes as little more than types of
scales. (They are very often described as such when an author is trying to
be brief, perhaps the cause of the growing general impression that that's all
there is to them.) Daniel Wolf sees modes in certain patterns of
harmonization. I use the term as the composers themselves did when
indicating that a composition is composed *in* a particular mode, as
(for example) Merulo did with his toccatas. I believe this is how other
Medieval and Renaissance writers used the term as well. This is analogous to
saying that a Mozart piano sonata is *in* the key of C Major, but as the
above articles show, there is an important musical difference.

My comment that started this off would be expressed more accurately, I think,
as: Very few, if any, (Western classical) works have been written *in* a mode
in the era of 12TET.

Gordon Collins

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🔗Daniel Wolf <DJWOLF_MATERIAL@...>

Gordon Collins wrote:

''Daniel Wolf sees modes in certain patterns of harmonization. ''

This is not so. Rather: I hear particular patterns of harmonization as a
consequence of melodic modes. As Bill Alves says, Major and minor are modes
of the common diatonic collection just as well as any others. Their
historical prominence in the common practice era - as opposed to the
prominence of other modes in other eras - is attributable to the particular
suitability of the intervallic arrangement to harmonizations which can
project the first degree of the major scale as a tonic over the duration of
a piece. This is a fairly Schekerian statement, but as I noted in earlierpostings, I am also quite open to simultaneous interpretations of a work
where local melodic behavior is suggestive of other modes - a ''Raga
Malaka'' interpretation. Please note that my definition here is based upon
major to allow for the characteristic ambiguity of the minor, which pivots
between its own distinctive modal identity and one based upon the parallel
major scale with chromatic modifications. The difficulty represented by this misunderstanding is similar to the
problem that mid-Rennaisance theorists in had dealing with the definitionof modes when not all voices in a polyphonic setting started or ended on
the final of the mode. Just because the thickened texture allowed for
chords with more pitches, doesn't mean that a piece whose bass is in d
dorian will have an alto in f lydian when the alto starts and ends on f. A
close study of that alto voice will probably reveal motion that is
uncharacteristic of a lydian melody. Counterpoint did indeed change the
modes, but the distinctiveness of the modes was determinative in how
actually counterpoint functioned.

In the common practice era, the rise of Major and minor corresponded
generally with the substitution of transposition for modulation (in the
sense of changing the melodic mode) as a means of generating tonal variety
over the duration of a piece, with the melodic contrast between minor andMajor leading to two distinct ways of coloring harmonic progressions thatwere functionally identical. This was accompanied by a general change in
the texture, towards a more homophonic arrangement of the voices, or rather
one in which the inner voices were decidedly subservient to the outer. The
striking cross relationships in Bach chorale harmonizations are one example
of this. The net result is that although the material resources of these
modes at the local level of a piece were not substantially different fromthose of earlier musics, the experience was quite distinct.

What, however, does this have directly do with tuning? I am afraid that the
more I ponder the music of the common practice era, the closer I come to
concluding that ''tonal music'' was composed with increasing disregard for
precise tuning. And the increasingly indistinct tuning was used to
represent or imply an increasingly broad harmonic language with unlimitedtransposition. Twelve tone and serial musics may even be worse off; a good
friend of mine recalls visting the studios of many composers in the fifties
- Boulez, Stockhausen, Nono among them - and all of them had out-of-tune
pianos. The first broadcast of the complete _Lulu_ featured intermissionswith George Perle playing analytical examples on an instrument where almost
every pitch had vibrato due to mistuned strings. In contrast, older musicis terribly sensitive to tuning. Simply playing dorian as d to d' on a just
major C scale won't work due to the comma shy fifth d - a; in pythagoreanthe opposite is often the case due to the ditone above the tonic,
resolution to which is demanded by the diminished fifth b - f. (A
discussion of the benefits and disadvantages of out-of-tuneness might be
worthwhile for this list...).

As to the general question of the survival of other modes in the tonal era:
Sibelius's _Seventh_, or any of Debussy's lydian works should be sufficient
- if late - counter-examples to the thesis that modal writing just stopped.

I wish to acknowlege that Harry Powers - author of the New Grove article on
''Mode and Melodic Type'' - greatly influenced my thinking on these issues
during his guest professorship at my graduate school. My definition of key
does differ from his but does so by going to a fairly radical reduction (a
group of seven consecutive members from a chain of fifths, with chromaticsubstitutions in the minor borrowed from the parallel Major). I find thisdefinition will be true for a wider repertoire than that defined in Groveand also one that is closer to the practices of notating and keyboarding,which are certainly signs and symptoms of the conceptual framework
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🔗alves@orion.ac.hmc.edu (Bill Alves)

Sorry for the delayed response, but Gordon Collins wrote:

>Discussions tend to get thwarted by different usages of the word "mode". For
>example, Bill Alves appears to view modes as little more than types of
>scales. (They are very often described as such when an author is trying to
>be brief, perhaps the cause of the growing general impression that that's all
>there is to them.)

This is not true. I outlined my defining characteristics reasonably
clearly, I think. A scale is a representation of the pitches in a mode
arranged in ascending or descending order from tonic to tonic. (There are
also, of course, non-modal scales like the "chromatic scale" and
"whole-tone scale.")

As for whether a mode is "little more than" what can be representated by a
scale, that all depends on the time and place and what one supposes a scale
represents. As I said, in different times and places, the concept of mode
might also include a range, characteristic melodic motives, and so on.

I had earlier written:

>>Well, right now I have my synth tuned in a very interesting 11-limit
>>lattice, and when I play the white keys from C to C it certainly doesn't
>>sound like any kind of major scale I would recognize.
>
>What you've got there is not a major scale. But a major scale is a major
>scale is a major scale whether a whole tone is 9/8, 10/9, (5/4)^(1/2),
>2^(1/6), or something in between.
>
>Or whether the scale is 1/1 9/8 44/35 4/3 3/2 176/105 66/35 2/1.

My point was to counter an earlier claim I had thought you made:

>The distinction between n-limit JI, x-comma meantone, well-temperament, and
>12TET is *totally irrelevant* to the definition of modes and scales!

with a counter-example. Of course it's not a major scale, because the
tuning system no longer makes it recognizably diatonic.

>Your idea of "recognizably diatonic" is interesting, and deserves
>quantification. As in, "What is the ideal and how far from it can a scale be
>to be recognized as diatonic?"
>
Yes, it would be interesting to quantify such an effect (like Blackwood),
but I'm not a psychologist, so I'll have to leave it to someone else.

>But treating 3-limit JI and 12TET as variations within the same tuning
>system.... Well, I have the definite impression that most list contributors
>consider them to be fundamentally different.
>
As would I, but I never claimed that pythagorean and 12TET were
"variations" of the same tuning system. I think that subsets of both can
reasonably represent diatonic modes.

>The point is, those augmented sixth chord arcana are more important *to
>understanding the music* than are the details of the tuning.

I think that all depends on the music. I think the value of tuning
knowledge for the understanding of music is greatly underrated in general.
(As Lou Harrison says: You haven't heard a piece until you've heard it in
the tuning that the composer intended or expected.) An intimate knowledge
of augmented sixth chords is likewise pretty useless in the understanding
of Partch, Indian music, or medieval music (even in the Renaissance and
Baroque augmented sixth chords are not that important).

My snide reference was meant to be a jab at conventional college "music
theory" curricula, which are really common-practice harmony courses --
courses that thus concentrate nearly exclusively on one dimension of one
type of music. To those students who unquestionably accept 12TET as the
words of the Prophet, an understanding of tuning systems is, I think, just
as valuable as how to resolve a Neapolitan sixth chord, if not more so.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
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re: pure?

🔗matt rocker <Matthew.D.Rocker-1@...>

🔗alves@orion.ac.hmc.edu (Bill Alves)

🔗Daniel Wolf <DJWOLF_MATERIAL@...>

🔗Pieter Smit <PieterS@...>

🔗mr88cet@texas.net (Gary Morrison)

🔗"Collins, Gordon" <CollinG@...>

🔗Daniel Wolf <DJWOLF_MATERIAL@...>

🔗alves@orion.ac.hmc.edu (Bill Alves)