Yahoo Tuning Groups Ultimate Backup tuning Alternatives to 12tET. Why?

Michael,

It seems to me that much of the traditional language and approach to questions of tuning still comes from the classical tradition of triadic harmony. Consequently, (IMNSVHO) it doesn't take into account the many beautiful dissonances that have become a natural consequence of the more complete 4-note '7th's' harmonies in modern jazz.

When the so-called 'blue' notes (minor 3rd, flat 5 and minor 7) began to appear in the melody against the major triads, they were eventually incorporated into the chords themselves. So instead of C, F and G7, we get C7, F7, G7 for the blues. Notice that the interval between the major 3 and minor 7 is a tritone (b5). If we move from C7 to F7, this tritone moves down a semitone while the 3-7 are inverted; 3-7 = E-Bb in C7 becomes 7-3 = Eb-A in F7. If we go through the cycle of fifths on a piano we get 11 decending tritones in the right hand while the left goes through the tonics C-F-Bb-Eb...Note also that we don't really need the fifths.

Next, apply the same cycle but restrict the notes to one major key (for eg, with only the white notes of the piano for C maj). Cma7, Fma7, Bm7(b5), Em7, Am7, Dm7, G7, Cma7.

From here we can begin to alter chords. Since any chord can be preceded by a 7 from its V position, then we can replace some of the m7 chords with a 7. Bm7(b5), E7, Am7 for eg.

Then comes all the chord substitutions. Since a 7(b5) is the same as a 7(b5) from its b5 (they have the same notes and are therefore only inversions of one another), E7(b5) = Bb7(b5) and we get Bm7(b5), E7, Am7. Continuing, Bm7(b5), E7, Am7, Ab7(b5), G7.
Or we could substitute the 7 with a 7(b9) which is the same as taking a diminished 7 chord from its b2, ma3, 5 or b7. Dm7, G7, Cma7 becomes Dm7, Ddim, Cma7. Or try G13(b9) = G-F-Ab-B-E, Cma7. Though this would be technically classified as a 'dissonance' it is probably *the* most beautiful substitution for the V7 in a major key.

Or for more rocky/funky music we can begin to introduce our 'nasty' chords. E7(#9), the Jimmy Hendrix chord, incorporated the major and minor thirds simultaneously. Better still, E13(#9) = E-G#-D-A(bb)-C# has two tritones and sounds great in context.

I am of course only scratching the surface. But I think that I've made my point that the b5th interval is absolutely indispensable to 12TET harmony. It appears everywhere within chords and between them. Being the sqrt2, it is the *only* interval to divide the 8ve equally. It is a '2tET'. To try to 'iron out' these dissonances is likely to destroy what is best about the music.

-Rick

🔗Daniel Forró <dan.for@...>

On 25 Apr 2010, at 7:46 PM, rick wrote:

>
> Michael,
>
> It seems to me that much of the traditional language and approach > to questions of tuning still comes from the classical tradition of > triadic harmony. Consequently, (IMNSVHO) it doesn't take into > account the many beautiful dissonances that have become a natural > consequence of the more complete 4-note '7th's' harmonies in modern > jazz.
>

Modern? Which years so you mean? All following harmonies are not so modern.
>
> When the so-called 'blue' notes (minor 3rd, flat 5
>

It is augmented fourth, in right spelling.

> and minor 7) began to appear in the melody against the major > triads, they were eventually incorporated into the chords > themselves. So instead of C, F and G7, we get C7, F7, G7 for the > blues.
>
Plus 9 chords as well, and of course 9+ chords as logical consequence (despite the fact that tonic 9+ chord must be spelled enharmonically not as minor third, but augmented second).

> Notice that the interval between the major 3 and minor 7 is a > tritone (b5).
>

Strictly spoken tritone means three whole tones distance, so it always must be augmented fourth only. Therefore is better to specify always when you talk about the interval of 6 halftones if it's augmented fourth or diminished fifth.

> If we move from C7 to F7, this tritone moves down a semitone while > the 3-7 are inverted; 3-7 = E-Bb in C7 becomes 7-3 = Eb-A in F7. If > we go through the cycle of fifths on a piano we get 11 decending > tritones in the right hand while the left goes through the tonics C-> F-Bb-Eb...Note also that we don't really need the fifths.
>
> Next, apply the same cycle but restrict the notes to one major key > (for eg, with only the white notes of the piano for C maj). Cma7, > Fma7, Bm7(b5), Em7, Am7, Dm7, G7, Cma7.
>
> From here we can begin to alter chords. Since any chord can be > preceded by a 7 from its V position, then we can replace some of > the m7 chords with a 7. Bm7(b5), E7, Am7 for eg.
>
> Then comes all the chord substitutions. Since a 7(b5) is the same > as a 7(b5) from its b5 (they have the same notes and are therefore > only inversions of one another),
>
Not true, they have different notes.

> E7(b5) = Bb7(b5)
>
E7/5- is E-G#-Bb-D
Bb7/5- is Bb-D-Fb-Ab

> and we get Bm7(b5), E7, Am7. Continuing, Bm7(b5), E7, Am7, Ab7(b5), > G7.
>
After 7/5- chord usually 7maj is used in similar progressions. Dominant 7th chord half tone down doesn't sound well here.

> Or we could substitute the 7 with a 7(b9) which is the same as > taking a diminished 7 chord from its b2, ma3, 5 or b7.
>
It's not the same, you should repeat your harmony lessons, but with better teacher or better books. Diminished 7th chords on different notes are always different. Only if you make inversions, they have the same notes in different permutations. In no case C7dim is the same chord as Eb7dim, D#7dim, Gb7dim, F#7dim, A7dim or B#7dim. Not on this planet :-) Exactly this difference in enharmonic spelling is used for one kind of modulation through 7dim chord.

> Dm7, G7, Cma7 becomes Dm7, Ddim,
>

If you mean G9- for the second chord, then you have to use G in bass and B7dim (in any inversion) as a chord. Not D7dim. They are definitely different chords. Try to forget standard keyboard for visualisation of chords. Or improve your imagination.

> Cma7. Or try G13(b9) = G-F-Ab-B-E, Cma7.
>

When we use 5-voice or 6-voice voicing, we usually keep it for all chords in the progression to avoid unison or octave doubling. Golden rule of a good arranger. So I would do C9/7maj as last chord, and when it should continue, also C9 would be possible. Imagine for example sax quartet plus bass.

> Though this would be technically classified as a 'dissonance' it is > probably *the* most beautiful substitution for the V7 in a major key.
>
> Or for more rocky/funky music we can begin to introduce our 'nasty' > chords. E7(#9), the Jimmy Hendrix chord, incorporated the major and > minor thirds simultaneously. Better still, E13(#9) = E-G#-D-A(bb)-> C# has two tritones and sounds great in context.
>

That's of course true, but strictly speaking G#-D is not tritone, but diminished fifth. Besides I see some very strange triple augmented third, not tritone. Tritone would be Abb-Db or G-C#. But for the chords which cross the border of thirdal harmony, or combine thirdal and quartal harmony, it's very often better to use the simplest way of writing, out of tonality, more like atonal way. So here you can write E-G#-D-G-C#.

Take the chord C-E-G-Bb-Eb-Ab-Db-Gb as an example. It should be written enharmonically properly in C major as C-E-G-Bb-D#-Ab-Db-F# (then it's easily recognizable as thirdal chord C13-/11+/9+/9-/7), but it's difficult to read and quartal structure of upper part is not well visible on the first sight.

>
> I am of course only scratching the surface. But I think that I've > made my point that the b5th interval is absolutely indispensable to > 12TET harmony. It appears everywhere within chords and between > them. Being the sqrt2, it is the *only* interval to divide the 8ve > equally. It is a '2tET'. To try to 'iron out' these dissonances is > likely to destroy what is best about the music.
>
> -Rick
>
Yes, it's really very nice and important interval for all lovers of symmetry in 12 tone system, me including. Its special unstable dissonance was always understood this way, in the middle age it was considered to be "a devil in music" (diabolus in musica) and avoided, even so, that whole concept of 1st/5th grade in old modes was heavily distorted by this, and later tritone always had to be resolved etc. It even become a symbol of something satanic, demonic (my theory is because tritone number is 6, and satanists like 666), and the first composer using this connotation was Carl Maria von Weber, later Mussorgski, Liszt, and mainly Skriabin (Satanic Poem, some sonatas... - he was obsessed by tritone and symmetry). Even until now you can hear tritone in every criminal film or horror ad nauseam as a symbol of evil, tension....

Daniel Forro

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
>
> On 25 Apr 2010, at 7:46 PM, rick wrote:
>
> >
> > Michael,
> >
> > It seems to me that much of the traditional language and approach
> > to questions of tuning still comes from the classical tradition of
> > triadic harmony. Consequently, (IMNSVHO) it doesn't take into
> > account the many beautiful dissonances that have become a natural
> > consequence of the more complete 4-note '7th's' harmonies in modern
> > jazz.
> >
>
> Modern? Which years so you mean? All following harmonies are not so
> modern.
> >
> > When the so-called 'blue' notes (minor 3rd, flat 5
> >
>
> It is augmented fourth, in right spelling.

No Daniel, this is exactly the type of misunderstandings I'm talking about. It is a flat-fifth because it is *at the expense of the (perfect) fifth* meaning they should never appear together in this dominant, passing chord. 7(b5), mi7(b5) or half-dim, and dim7. This is distinct from the ma7(#11) which is a tonal chord and can appear with the fifth.
>
> > and minor 7) began to appear in the melody against the major
> > triads, they were eventually incorporated into the chords
> > themselves. So instead of C, F and G7, we get C7, F7, G7 for the
> > blues.
> >
> Plus 9 chords as well, and of course 9+ chords as logical consequence
> (despite the fact that tonic 9+ chord must be spelled enharmonically
> not as minor third, but augmented second).

Yes I get to that. 7(#9). Again it is called that because it cannot appear with the natural 9th. But of course the ear hears it as a minor third up an 8ve.
>
> > Notice that the interval between the major 3 and minor 7 is a
> > tritone (b5).
> >
>
> Strictly spoken tritone means three whole tones distance, so it
> always must be augmented fourth only. Therefore is better to specify
> always when you talk about the interval of 6 halftones if it's
> augmented fourth or diminished fifth.

Yes as I just mentioned. But of course I'm talking about the interval in itself, not from the root of any chord as yet.
>
> > If we move from C7 to F7, this tritone moves down a semitone while
> > the 3-7 are inverted; 3-7 = E-Bb in C7 becomes 7-3 = Eb-A in F7. If
> > we go through the cycle of fifths on a piano we get 11 descending
> > tritones in the right hand while the left goes through the tonics C-
> > F-Bb-Eb...Note also that we don't really need the fifths.
> >
> > Next, apply the same cycle but restrict the notes to one major key
> > (for eg, with only the white notes of the piano for C maj). Cma7,
> > Fma7, Bm7(b5), Em7, Am7, Dm7, G7, Cma7.
> >
> > From here we can begin to alter chords. Since any chord can be
> > preceded by a 7 from its V position, then we can replace some of
> > the m7 chords with a 7. Bm7(b5), E7, Am7 for eg.
> >
> > Then comes all the chord substitutions. Since a 7(b5) is the same
> > as a 7(b5) from its b5 (they have the same notes and are therefore
> > only inversions of one another),
> >
> Not true, they have different notes.
>
> > E7(b5) = Bb7(b5)
> >
> E7/5- is E-G#-Bb-D
> Bb7/5- is Bb-D-Fb-Ab

That's exactly the type of 'classical' thing I'm talking about which completely misses the point! In terms of practice, the ear hears the same 4 notes which is why one can be substituted for the other. Knowing this we can now cycle down chromatically. But if we imagine that these are not the same chord and then go about trying to 'tune' them differently then we are destroying that.
>
> > and we get Bm7(b5), E7, Am7. Continuing, Bm7(b5), E7, Am7, Ab7(b5),
> > G7.
> >
> After 7/5- chord usually 7maj is used in similar progressions.
> Dominant 7th chord half tone down doesn't sound well here.

First I didn't say dom7 semitone below but that if we go from V7 to I7 the tritone (b5) between the third and seventh degrees descend chromatically. Second, of course V7 to Ima7 sounds good. But V7 to I7 is in every single blues song ever written. It is *by definition* the blues. There are literally thousands of other examples one could cite.
>
> > Or we could substitute the 7 with a 7(b9) which is the same as
> > taking a diminished 7 chord from its b2, ma3, 5 or b7.
> >
> It's not the same, you should repeat your harmony lessons, but with
> better teacher or better books. Diminished 7th chords on different
> notes are always different. Only if you make inversions, they have
> the same notes in different permutations. In no case C7dim is the
> same chord as Eb7dim, D#7dim, Gb7dim, F#7dim, A7dim or B#7dim. Not on
> this planet :-) Exactly this difference in enharmonic spelling is
> used for one kind of modulation through 7dim chord.

Daniel, be nice. I've been a prof muso for 30 years. One must also keep in mind the practicalities of music. If I was to write double flats for your average jazz musician they'd laugh at the pretension. Plus it woud probably not be read very quickly. What I'm saying is this. Instead of G7, take G7(b9) = G-B-D-F-Ab. Notice that this is a Bdim7 over a G bass. Ah, but we can invert this dim chord simply by moving it up or down minor thirds. Since 'enharmonically' Abdim7 = Bdim7 = Ddim7 = Fdim7 then we can move to tonic C from any of these chords. More interesting still is the possibility for modulation it opens up. We could instead come out at tonics that are minor thirds away from C. Bach for eg did this all the time. Once again, if we think of these as being different because we simply wish to introduce different tunings for each chord then we are destroying it. [2^(1/4)]^4 = 2 is the best possible tuning for this chord because it is symmetric by definition. What we call the notes afterwards is only a matter of convention.
>
> > Dm7, G7, Cma7 becomes Dm7, Ddim,
> >
>
> If you mean G9- for the second chord, then you have to use G in bass
> and B7dim (in any inversion) as a chord. Not D7dim. They are
> definitely different chords. Try to forget standard keyboard for
> visualisation of chords. Or improve your imagination.
>
> > Cma7. Or try G13(b9) = G-F-Ab-B-E, Cma7.
> >
>
> When we use 5-voice or 6-voice voicing, we usually keep it for all
> chords in the progression to avoid unison or octave doubling. Golden
> rule of a good arranger. So I would do C9/7maj as last chord, and
> when it should continue, also C9 would be possible. Imagine for
> example sax quartet plus bass.

C9 is a dominant 7 chord with the 9th added. It is distinct from Cma9 which is a ma7 or Cadd9 which is simply a C triad with 9 added. As for voicings, I am a professional arranger. It's what I do.
>
> > Though this would be technically classified as a 'dissonance' it is
> > probably *the* most beautiful substitution for the V7 in a major key.
> >
> > Or for more rocky/funky music we can begin to introduce our 'nasty'
> > chords. E7(#9), the Jimmy Hendrix chord, incorporated the major and
> > minor thirds simultaneously. Better still, E13(#9) = E-G#-D-A(bb)-
> > C# has two tritones and sounds great in context.
> >
>
> That's of course true, but strictly speaking G#-D is not tritone, but
> diminished fifth. Besides I see some very strange triple augmented
> third, not tritone. Tritone would be Abb-Db or G-C#. But for the
> chords which cross the border of thirdal harmony, or combine thirdal
> and quartal harmony, it's very often better to use the simplest way
> of writing, out of tonality, more like atonal way. So here you can
> write E-G#-D-G-C#.
>
> Take the chord C-E-G-Bb-Eb-Ab-Db-Gb as an example. It should be
> written enharmonically properly in C major as C-E-G-Bb-D#-Ab-Db-F#
> (then it's easily recognizable as thirdal chord C13-/11+/9+/9-/7),
> but it's difficult to read and quartal structure of upper part is not
> well visible on the first sight.

Yeah of course. #9 and #11 because 9 and 5 are taken. There are sometimes mitigating circumstances when arranging. Because horn players tend to read b's better than #'s and because it's on a 'need to know' basis, I'll often replace a # with a b if it will make it easier to read. Or for a #9 chord, I'll give one player a maj third and the other a minor etc...Some jazz composers have even discarded key signatures altogether because they like to modulate allot.
>
> >
> > I am of course only scratching the surface. But I think that I've
> > made my point that the b5th interval is absolutely indispensable to
> > 12TET harmony. It appears everywhere within chords and between
> > them. Being the sqrt2, it is the *only* interval to divide the 8ve
> > equally. It is a '2tET'. To try to 'iron out' these dissonances is
> > likely to destroy what is best about the music.
> >
> > -Rick
> >
> Yes, it's really very nice and important interval for all lovers of
> symmetry in 12 tone system, me including. Its special unstable
> dissonance was always understood this way, in the middle age it was
> considered to be "a devil in music" (diabolus in musica) and avoided,
> even so, that whole concept of 1st/5th grade in old modes was heavily
> distorted by this, and later tritone always had to be resolved etc.
> It even become a symbol of something satanic, demonic (my theory is
> because tritone number is 6, and satanists like 666), and the first
> composer using this connotation was Carl Maria von Weber, later
> Mussorgski, Liszt, and mainly Skriabin (Satanic Poem, some sonatas...
> - he was obsessed by tritone and symmetry). Even until now you can
> hear tritone in every criminal film or horror ad nauseam as a symbol
> of evil, tension....
>
> Daniel Forro

Yes another name for it was "old Nick". It's use in blues tends to sound sexy and mischievous. Even a social protest by the African Americans against puritanism. I've noticed lately in horror that they often use it with the ma7 in the melody.
>

🔗rick <rick_ballan@...>

Daniel said "If you mean G9- for the second chord, then you have to use G in bass and B7dim (in any inversion) as a chord. Not D7dim. They are definitely different chords. Try to forget standard keyboard for visualisation of chords. Or improve your imagination."

Rick> No I didn't mean G9 which is a G7 with natural 9th. I said G7(b9). Once again we see why 'enharmonic spelling' is NOT the correct language for atonality. B7dim and D7dim are absolutely NOT different chords. One is the inversion of the other. Misunderstandings like this is why we use the designations 0,1,2,...11 representing the N in 2^(N/12)instead of letters from the alphabet. Because the letters represent an old language based on tonality and lead to confusion. Since multiplying log's equals adding exponents, then intervals are determined by the operation of addition/subtraction. The correct mathematics is congruent modulo 12. Two intervals are inverse when they add to 12. Since 12 = 0 (mod 12) then inverses can also be written as negative. 3 + 9 = 12 = 0 are inverse, as are 3 + (-3) = 0. That is, 9 = -3 and 3 = -9 (mod 12).

Now look at Dim7 0:3:6:9. We might invert it as 0:-3:-6:-9. But this is 0:9:6:3. It has the same interval content. Another way of saying this is that every note is equally qualified to become *the root* 0. If 3 -> 0 then we get -3:0:3:6 = 9:0:3:6. 2nd inv 6->0 gives -6:-3:0:3 = 6:9:0:3 and finally 9->0 gives -9:-6:-3:0 = 3:6:9:0. So we see that Dim7 chords by definition *do not have a tonic*. This is because they are invariant with respect to inversion, yielding the same intervals from every point of view.

Getting back to the original problem, G7(b9) is equivalent to a Bdim7/G i.e. with a G bass. Ignoring the G altogether we get Bdim7 = Ddim7 = Fdim7 = Abdim7 which can now function as the V7 chord to a C tonic. However, by the same syllogistic logic, we could instead think of these as V7 to Eb, Gb or A, that is, minor thirds from C. Notice that we CAN use Eb or D# because these are new keys and no longer have nothing to do with C. A favourite of Bach's is to use this to come out in the relative minor of major key. For eg, Cmaj to G7 => G#dim7 => E7 to Amin.

As a final statement, this congruent modulo maths is the correct language for ANY truly equal temperament. The chromatic scale in 12 tET allows every note to become 0, which means that what we can play in one key can be played in any of the others. A true 17tET for eg would be 2^(N/17).

Advice: Get your facts right before attempting to criticise, and leave the insults.

-Rick

🔗Daniel Forró <dan.for@...>

Advice 1: read carefully what I have written. There's a "-" sign after my "G9". Together it makes "G9-". Because I'm well experienced in jazz theory I will never use chord sign system with "b" and "#" which works only for some chords. The only proper and universal system for all keys and chords is to use "+" and "-" signs for alterations. So if you want to teach me universal systems, you can learn this one as well and avoid using of flats and sharps in chord signs. You can write G9b or G(b9), that's OK, but if you write for example F#{b9} you will only show lack of knowledge, because there's no flat ninth interval in that chord. If you want to use accidentals, you must write properly F#9 and natural sign, because G# is changed to G, not to Gb. So it's not universal system. Capisco?

Advice 2: It's very surprising here on tuning group to find another person who doesn't understand about enharmonics and what it means for music theory. Don't argument with atonality, this has nothing to do with atonality. And don't argument with equal temperament, it doesn't exist in reality. Despite we have 12tone keyboard, 12tone system exists only in the score. And writing has its rules and distinguish between F and E# for example. There's a difference between Ab and G#, both in the score and in the real music practice. So if you want to stay in your darkness, you can. But once more I repeat: Bdim7, Ddim7, Fdim7 or Abdim7 are different chords because they have different notes (you can add even Cbdim7, E#dim7 and G#dim7 to your list). Here is your missed lesson:

Bdim7 = B-D-F-Ab
Ddim7 = D-F-Ab-Cc
Fdim7 = F-Ab-Cb-Ebb
Abdim7 = Ab-Cb-Ebb-Gbb

Of course each of them has its tonic chord, because they were created on VII grade of the scale. Tonic is always half tone up, and it can be major or minor.

All my life I fight with the ignorance of half educated music amateurs by explaining what's wrong, what's right. Lot of them learned something from me, forgot their funny theories and were happy, because they came to better understanding of music (this is not depending on the music style). Some not. Select your way. This is an advice, dear friend, not insult.

Daniel Forro

On 26 Apr 2010, at 5:38 PM, rick wrote:

>
> Daniel said "If you mean G9- for the second chord, then you have to > use G in bass and B7dim (in any inversion) as a chord. Not D7dim. > They are definitely different chords. Try to forget standard > keyboard for visualisation of chords. Or improve your imagination."
>
> Rick> No I didn't mean G9 which is a G7 with natural 9th. I said G7> (b9). Once again we see why 'enharmonic spelling' is NOT the > correct language for atonality. B7dim and D7dim are absolutely NOT > different chords. One is the inversion of the other. > Misunderstandings like this is why we use the designations > 0,1,2,...11 representing the N in 2^(N/12)instead of letters from > the alphabet. Because the letters represent an old language based > on tonality and lead to confusion. Since multiplying log's equals > adding exponents, then intervals are determined by the operation of > addition/subtraction. The correct mathematics is congruent modulo > 12. Two intervals are inverse when they add to 12. Since 12 = 0 > (mod 12) then inverses can also be written as negative. 3 + 9 = 12 > = 0 are inverse, as are 3 + (-3) = 0. That is, 9 = -3 and 3 = -9 > (mod 12).
>
> Now look at Dim7 0:3:6:9. We might invert it as 0:-3:-6:-9. But > this is 0:9:6:3. It has the same interval content. Another way of > saying this is that every note is equally qualified to become *the > root* 0. If 3 -> 0 then we get -3:0:3:6 = 9:0:3:6. 2nd inv 6->0 > gives -6:-3:0:3 = 6:9:0:3 and finally 9->0 gives -9:-6:-3:0 = > 3:6:9:0. So we see that Dim7 chords by definition *do not have a > tonic*. This is because they are invariant with respect to > inversion, yielding the same intervals from every point of view.
>
> Getting back to the original problem, G7(b9) is equivalent to a > Bdim7/G i.e. with a G bass. Ignoring the G altogether we get Bdim7 > = Ddim7 = Fdim7 = Abdim7 which can now function as the V7 chord to > a C tonic. However, by the same syllogistic logic, we could instead > think of these as V7 to Eb, Gb or A, that is, minor thirds from C. > Notice that we CAN use Eb or D# because these are new keys and no > longer have nothing to do with C. A favourite of Bach's is to use > this to come out in the relative minor of major key. For eg, Cmaj > to G7 => G#dim7 => E7 to Amin.
>
> As a final statement, this congruent modulo maths is the correct > language for ANY truly equal temperament. The chromatic scale in 12 > tET allows every note to become 0, which means that what we can > play in one key can be played in any of the others. A true 17tET > for eg would be 2^(N/17).
>
> Advice: Get your facts right before attempting to criticise, and > leave the insults.
>
> -Rick

🔗genewardsmith <genewardsmith@...>

🔗cameron <misterbobro@...>

🔗Daniel Forró <dan.for@...>

🔗Marcel de Velde <m.develde@...>

🔗Michael <djtrancendance@...>

🔗Daniel Forró <dan.for@...>

On 26 Apr 2010, at 11:39 PM, Michael wrote:

>
>
> Daniel>
> "Bdim7 = B-D-F-Ab
> Ddim7 = D-F-Ab-Cc
> Fdim7 = F-Ab-Cb-Ebb
> Abdim7 = Ab-Cb-Ebb-Gbb"
>
> Trying to make sure I understand this...
> Since CEGB has each note in the 7th chord spaced one letter apart, > chords based on other roots must follow the same pattern.

Exactly, Michael. You've got it right. If you want to have 7th chord, it must follow in theory and in the score triadic structure, that means if you remove all accidentals, basic note names must follow triadic pattern (with gap between neighboring notes). Then even if you will add to each basic note any accidental including double ones, and create quite different chords sounding far from basic seventh chord, they will be always called seventh chord (with alterations of course).

> Thus, for example, D F A-flat B can not exist both because there > is not letter gap between A and B and because the interval from D > to C-flat is actually different pitch wise than the interval from D > to B in, say, meantone (since rotation by fifths forward vs. > backward to create all tones produces slightly different intervals)?

Of course D-F-Ab-B exist, but it is an inversion of seventh chord, because it hasn't triadic structure. In such case you can try its inversions until you come to triadic structure. This can be considered as basic shape chord. So here: F-Ab-B-D not triadic, Ab-B-D-F not triadic, B-D-F-Ab triadic, so we found its basic shape and can analyse it as dim7 on VII grade of C major or C minor key.
Of course with some chords is more difficult to reveal their triadic structure, as some notes are missing, or they have quartal structure, or combination of thirdal or quartal. In my personal harmonic theory I count also with secondal structure of chords, clusters, there are more possibilities and all three types can be mixed. For example diatonic C major scale can create secondal chord C-D-E-F-G-A-B (plus another 6 inversions), or thirdal C-E-G-B-D-F-A (plus 6 inversions), or quartal C-F-B-E-A-D-G (plus 6 inversions). Of course it's possible to add black keys and build maximally 12tone chromatic chords.

> Also, the only time C-flat exactly equals B pitch-wise is in > 12TET, correct?

We can say so as a simplification about pitch and about key on standard keyboard, but notes in the scores are different as well as theoretical consequences, like resolution. But in the reality they can be tuned differently depending on the vertical and horizontal music context. At least there's some purely psychological difference. There are people with synesthesia, and Ab minor definitely looks differently in the score then G# minor. It can have some impact on the musician performing from the score, especially when he knows something more about harmony, modulations etc. Notation has some rules, and clever composers of tonal and extended tonal music used it intentionally and logically, not randomly. It has some reason why some composition is written in Ab minor and another one in G# minor. And it has also some reason why it's written in Ab minor and not in G minor. Sometimes the reason is practical - tuning of instruments, easier fingering, sometimes it's pure magic why it's so. But when you do transposition, composition can lose its character.

Even in atonal music it's possible to recognize educated and careful composer from somebody with less historical background just from the way how the score is written.

>
> >"And writing has its rules and distinguish between F and E# for > example. There's a difference
> between Ab and G#, both in the score and in the real music practice. "
> Correct me if I'm wrong, but again is it true E# and F are the > same pitch in 12TET,

yes and no

> but mean to different things in composition and different intervals > in different tunings?

Yes.

> So what advantage of understanding do you get "even" under 12TET by > using enharmonic equivalents (beside, say, that the are not two > different notes listed under the same letter)?

It has sense for understanding of older music which was based on this, in understanding modulations. Such knowledge is good for composing and arranging - to write logical setting of the chords, good voicing. In the end it has advantages for performers, as logically written score is easily to read, as basic chord structure is easily to recognize on the first sight.

Daniel Forro

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:

> "Don't attempt to argue by bringing up "equal temperament", something that does not really exist in practice. Despite the existence of the 12-tone keyboard, the system of 12 equal tones exists only in the score".
>
> That's proofread, and very obviously what was said. And completely valid- outside of mechanical and electronic renditions, literal 12-tET is only achieved by tortuous means, if at all.

Daniel first brings up keyboard instruments, which are sometimes accurately tuned in 12 equal, and then goes on to say that despite the manifest existence of 12 equal in the real world, it doesn't exist in the real world. That kind of self-contradiction is nonsensical. Moreover, the context was a discussion of 12 tone serialism, where performance practice takes 12 equal as an ideal, and often get close to achieving that ideal. Saying that serial music ought to be interpreted in terms which employ a distincton between enharmonic equivalents is either a manifestation of extreme ignorance or some kind of fantaicism.

Finally, those electronic renditions in 12 equal you remark on, because of such features as midi files and their default tuning, the tuning usually used in computer games and sometimes on ringtones, and so forth, are actually very common. So Daniel was not only spouting drivel about how serialism should be analyzed, he was clearly dead wrong about the world we live in.

> A basic understanding of the physics of wind instruments for example gives some indication of the "natural" discrepancy between 12-tET and performable, er, performance.

Stick your head out the damned window. A basic knowledge of the world we live in shows it does have 12 equal in it.

🔗Chris Vaisvil <chrisvaisvil@...>

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

Man, I remember when I learned all this stuff from the keyboardist in my high school band. He used to get so mad at me and the other guitarist for mixing sharps and flats in one key...didn't make a difference to us if you called it C# or Db, it just meant 4th fret on the A string, we had no idea why the same note had two names! We used to use what to us were just "weird chords" but he had a proper name (and note spelling) for all of them. Everything I know about music theory I learned from that guy or this list.

But yeah, when I learned that note names don't just tell you where to put your fingers but actually tell you how each note relates to each other note, and how each chord relates to the tonic, it was kind of a breakthrough for me. Those old theoreticians that developed the "common practice" were pretty clever!

I used to think that in microtonality, if one abandons meantone/pythagorean-based metatunings, knowledge of common-practice convention would be worthless. Notating Blackwood Decatonic music forces one to do ALL MANNER of enharmonic-juggling gymnastics to preserve common-practice spellings. And just TRY notating 8-note Father temperament using common-practice spellings...not so easy when a fourth equals a third, is it? But I'm realizing that the rationale BEHIND common-practice conventions is still valid: chord spellings ought to indicate relationships between notes, not just be arbitrary designations of pitch. So whatever new naming conventions people may come up with, it's important to preserve the spirit of the common practice, if not the letter of it (pun intended!) And this you can take from someone with no music "schooling" at all!

-Igs

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
>
> On 26 Apr 2010, at 11:39 PM, Michael wrote:
>
> >
> >
> > Daniel>
> > "Bdim7 = B-D-F-Ab
> > Ddim7 = D-F-Ab-Cc
> > Fdim7 = F-Ab-Cb-Ebb
> > Abdim7 = Ab-Cb-Ebb-Gbb"
> >
> > Trying to make sure I understand this...
> > Since CEGB has each note in the 7th chord spaced one letter apart,
> > chords based on other roots must follow the same pattern.
>
> Exactly, Michael. You've got it right. If you want to have 7th chord,
> it must follow in theory and in the score triadic structure, that
> means if you remove all accidentals, basic note names must follow
> triadic pattern (with gap between neighboring notes). Then even if
> you will add to each basic note any accidental including double ones,
> and create quite different chords sounding far from basic seventh
> chord, they will be always called seventh chord (with alterations of
> course).
>
>
> > Thus, for example, D F A-flat B can not exist both because there
> > is not letter gap between A and B and because the interval from D
> > to C-flat is actually different pitch wise than the interval from D
> > to B in, say, meantone (since rotation by fifths forward vs.
> > backward to create all tones produces slightly different intervals)?
>
>
> Of course D-F-Ab-B exist, but it is an inversion of seventh chord,
> because it hasn't triadic structure. In such case you can try its
> inversions until you come to triadic structure. This can be
> considered as basic shape chord. So here: F-Ab-B-D not triadic, Ab-B-
> D-F not triadic, B-D-F-Ab triadic, so we found its basic shape and
> can analyse it as dim7 on VII grade of C major or C minor key.
> Of course with some chords is more difficult to reveal their triadic
> structure, as some notes are missing, or they have quartal structure,
> or combination of thirdal or quartal. In my personal harmonic theory
> I count also with secondal structure of chords, clusters, there are
> more possibilities and all three types can be mixed. For example
> diatonic C major scale can create secondal chord C-D-E-F-G-A-B (plus
> another 6 inversions), or thirdal C-E-G-B-D-F-A (plus 6 inversions),
> or quartal C-F-B-E-A-D-G (plus 6 inversions). Of course it's possible
> to add black keys and build maximally 12tone chromatic chords.
>
>
> > Also, the only time C-flat exactly equals B pitch-wise is in
> > 12TET, correct?
>
> We can say so as a simplification about pitch and about key on
> standard keyboard, but notes in the scores are different as well as
> theoretical consequences, like resolution. But in the reality they
> can be tuned differently depending on the vertical and horizontal
> music context. At least there's some purely psychological difference.
> There are people with synesthesia, and Ab minor definitely looks
> differently in the score then G# minor. It can have some impact on
> the musician performing from the score, especially when he knows
> something more about harmony, modulations etc. Notation has some
> rules, and clever composers of tonal and extended tonal music used it
> intentionally and logically, not randomly. It has some reason why
> some composition is written in Ab minor and another one in G# minor.
> And it has also some reason why it's written in Ab minor and not in G
> minor. Sometimes the reason is practical - tuning of instruments,
> easier fingering, sometimes it's pure magic why it's so. But when you
> do transposition, composition can lose its character.
>
> Even in atonal music it's possible to recognize educated and careful
> composer from somebody with less historical background just from the
> way how the score is written.
>
> >
> > >"And writing has its rules and distinguish between F and E# for
> > example. There's a difference
> > between Ab and G#, both in the score and in the real music practice. "
> > Correct me if I'm wrong, but again is it true E# and F are the
> > same pitch in 12TET,
>
> yes and no
>
>
> > but mean to different things in composition and different intervals
> > in different tunings?
>
> Yes.
>
> > So what advantage of understanding do you get "even" under 12TET by
> > using enharmonic equivalents (beside, say, that the are not two
> > different notes listed under the same letter)?
>
> It has sense for understanding of older music which was based on
> this, in understanding modulations. Such knowledge is good for
> composing and arranging - to write logical setting of the chords,
> good voicing. In the end it has advantages for performers, as
> logically written score is easily to read, as basic chord structure
> is easily to recognize on the first sight.
>
> Daniel Forro
>
>
> >
>

🔗cameron <misterbobro@...>

The conversation I saw was about notation of functional tall chords, read by humans. Most literally 12-tET music doesn't have a human-readable score at all, or has one as a kind of byproduct. Like you said, midi information. That's not what was being discussed. So, :-P

Rick is correct that different kinds of performers have different standards and expectations. Jazz musicians can notate "wrong" by strict functional standards because the functions that make it "jazz" are imparted by oral tradition.

-Cameron Bobro

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
>
>
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
>
> > "Don't attempt to argue by bringing up "equal temperament", something that does not really exist in practice. Despite the existence of the 12-tone keyboard, the system of 12 equal tones exists only in the score".
> >
> > That's proofread, and very obviously what was said. And completely valid- outside of mechanical and electronic renditions, literal 12-tET is only achieved by tortuous means, if at all.
>
> Daniel first brings up keyboard instruments, which are sometimes accurately tuned in 12 equal, and then goes on to say that despite the manifest existence of 12 equal in the real world, it doesn't exist in the real world. That kind of self-contradiction is nonsensical. Moreover, the context was a discussion of 12 tone serialism, where performance practice takes 12 equal as an ideal, and often get close to achieving that ideal. Saying that serial music ought to be interpreted in terms which employ a distincton between enharmonic equivalents is either a manifestation of extreme ignorance or some kind of fantaicism.
>
> Finally, those electronic renditions in 12 equal you remark on, because of such features as midi files and their default tuning, the tuning usually used in computer games and sometimes on ringtones, and so forth, are actually very common. So Daniel was not only spouting drivel about how serialism should be analyzed, he was clearly dead wrong about the world we live in.
>
> > A basic understanding of the physics of wind instruments for example gives some indication of the "natural" discrepancy between 12-tET and performable, er, performance.
>
> Stick your head out the damned window. A basic knowledge of the world we live in shows it does have 12 equal in it.
>

🔗genewardsmith <genewardsmith@...>

🔗cameron <misterbobro@...>

🔗Mike Battaglia <battaglia01@...>

> Advice 1: read carefully what I have written. There's a "-" sign
> after my "G9". Together it makes "G9-". Because I'm well experienced
> in jazz theory I will never use chord sign system with "b" and "#"
> which works only for some chords. The only proper and universal
> system for all keys and chords is to use "+" and "-" signs for
> alterations.

Then the correct way to write it would be G7(-9), analogous to G7(b9).
Nobody would write G9b, because it doesn't make sense. Note as well
the the minus sign (-) and the plus sign (+) are often used to denote
minor and augmented chords respectively, so that C-9 means Cm9 and C+9
means Caug9.

> So if you want to teach me univers l systems, you can
> learn this one as well and avoid using of flats and sharps in chord
> signs. You can write G9b or G(b9), that's OK, but if you write for
> example F#{b9} you will only show lack of knowledge, because there's
> no flat ninth interval in that chord.

Cmon, you're just making stuff up now :) We're dealing with a musical
notation that is almost a century old at this point, I think it's here
to stay.

> Advice 2: It's very surprising here on tuning group to find another
> person who doesn't understand about enharmonics and what it means
> for music theory.

You are again making stuff up. This is a convention in jazz and, as
I've said, it's been around for over a century. You need to learn how
people are communicating, not say how they "should" be communicating.

> So if you want to stay in your darkness, you can. But once more I
> repeat: Bdim7, Ddim7, Fdim7 or Abdim7 are different chords because
> they have different notes (you can add even Cbdim7, E#dim7 and G#dim7
> to your list). Here is your missed lesson:
>
> Bdim7 = B-D-F-Ab
> Ddim7 = D-F-Ab-Cc
> Fdim7 = F-Ab-Cb-Ebb
> Abdim7 = Ab-Cb-Ebb-Gbb

The diesis has been tempered out for almost three centuries now.
Should we use the same logic to insist that meantone spelling itself
is wrong, and that E and E- are different notes, and hence should be
spelled as such?

-Mike

🔗Daniel Forró <dan.for@...>

On 27 Apr 2010, at 5:54 AM, Mike Battaglia wrote:

>
> Then the correct way to write it would be G7(-9), analogous to G7(b9).
> Nobody would write G9b, because it doesn't make sense. Note as well
> the the minus sign (-) and the plus sign (+) are often used to denote
> minor and augmented chords respectively, so that C-9 means Cm9 and C+9
> means Caug9.
>
>
Mike, my reason to write "-" and "+" signs after the number has exactly that reason to avoid understanding it as belonging to the chord root, and to spare writing parentheses. You see well there's a difference between C-9 and C9-. And I start from the highest number to see the most important information about ambitus, size of the chord, first. So my way, like C13-/11+/7maj is logical and consistent. I don't use "-" for minor chord, because it is not alteration, it is just a basic feature of that chord. So I kept Cmi.

> Cmon, you're just making stuff up now :) We're dealing with a musical
> notation that is almost a century old at this point, I think it's here
> to stay.
>

That's true, but it was derived from classical music theory. There's no reason to brake old good rules and argument it's new style which doesn't need it.
> You are again making stuff up. This is a convention in jazz and, as
> I've said, it's been around for over a century. You need to learn how
> people are communicating, not say how they "should" be communicating.
>

There are more chord sign system in use in jazz, different fakebooks use different one.
One of my activity is teaching music, so I must to learn people how they should communicate properly and show them about the mistakes they do. Every field of human activity has some development, and it should go from the simple to the more complex, from the wrong to the better.
> The diesis has been tempered out for almost three centuries now.
> Should we use the same logic to insist that meantone spelling itself
> is wrong, and that E and E- are different notes, and hence should be
> spelled as such?
>
> -Mike

Music theory and notation unfortunately has some rules, so we should keep them as much as possible. They have their reason. But of course there's a lot of strange spellings even in the works of great classical masters. Therefore there are critical editions done by musicologist who should repair such errors.
Concerning the notation of extended tonality, modality or 12tone seriality - of course it doesn't need to keep the rules for tonality, as sometimes it's difficult to decide the function of the chord, and how it should be written in the score, for example if to write F#7 chord or Gb7. Then priority is readability of individual chords (if there are chords) and logical context. Before F would be better to write Gb7 (generally in flat keys and chords with flats context), before G or D - F#7 (generally in "#" keys and chords). Of course there are many chords combining flats and sharps. In atonal music sometimes the decision is difficult and almost everything is possible, but double accidentals are not necessary. We can write both F# or Gb before Dmi.
System using numbers for all chromatic notes can be used for serial and 12tone music, but it has also some disadvantages - there's no reason to start always from C as this music has no center, another problem are double character numbers 10, 11 and 12 which complicate the reading and can cause errors. When I compose such music, which is very often, and make preparation material, I use note names, that's easy. But I use numbers for interval sizes, with "-" sign indicating direction down.

Daniel Forro

🔗Mike Battaglia <battaglia01@...>

> > Cmon, you're just making stuff up now :) We're dealing with a musical
> > notation that is almost a century old at this point, I think it's here
> > to stay.
>
> That's true, but it was derived from classical music theory. There's
> no reason to brake old good rules and argument it's new style which
> doesn't need it.

That might have applied 100 years ago. At this point, these other
conventions are also themselves "old good rules." It's hardly a "new"
style. It's not that hard, and I'm sure you can understand it. If
you're in F#, and you play a "flat nine" over it, you take the G# and
apply the "flattening" operator to it. If you "flatten" a "sharpened"
note, you end up with the natural. Very simple. If you sharpen a note
that's already sharp, it becomes doubly sharp. Easy.

It may be your "preference" to apply a different set of naming
conventions to different notes. That's fine. But for you to say that
you're right and everyone else is "wrong" is a bit arrogant and
slightly misguided. You aren't talking about a bunch of deviant
children who didn't learn theory properly. You're talking about naming
conventions that are a century old now, and have evolved from people
who most certainly advanced music theory past the older "common
practice" norms. If you don't like it - you should have spoken up 100
years ago :)

> Music theory and notation unfortunately has some rules, so we should
> keep them as much as possible. They have their reason. But of course
> there's a lot of strange spellings even in the works of great
> classical masters. Therefore there are critical editions done by
> musicologist who should repair such errors.

I think you missed my point. My point was that you are insisting that
12-tet is still meantone, and hence that different enharmonically
equivalent chords (C E G# vs C E Ab, or C Eb Gb Bbb vs C Eb Gb A) are
aurally different. I'm thus asking then if, by the same logic,
meantone is really 5-limit JI, and hence chords like C Eb G and C F Bb
Eb G are different, and if one of the Eb's should be notated as Eb+ or
Eb\ or something like that.

-Mike

🔗Daniel Forró <dan.for@...>

On 27 Apr 2010, at 8:49 AM, Mike Battaglia wrote:

> That might have applied 100 years ago. At this point, these other
> conventions are also themselves "old good rules."
>
They can't be good if they are done wrong way.

> It's hardly a "new"
> style. It's not that hard, and I'm sure you can understand it. If
> you're in F#, and you play a "flat nine" over it, you take the G# and
> apply the "flattening" operator to it. If you "flatten" a "sharpened"
> note, you end up with the natural. Very simple. If you sharpen a note
> that's already sharp, it becomes doubly sharp. Easy.
>
>
To use terms like "flatten" and "sharpen" here is inaccurate, because it evokes using of flats and sharps which is not always true. Better is to use neutral terms like "raising" and "lowering", or "shift up", "shift down".
Don't forget there are three stages - flat, natural and sharp. When you go from flat up, it's not sharpening, because there's no sharp sign used but natural. When you go from sharp down, it's not flattening, because there's no flat sign, but natural. (Maybe you could call it "naturalising".) This is my point. Therefore I use universal "+" meaning rising up, and "-" for lowering down. Easy.

> It may be your "preference" to apply a different set of naming
> conventions to different notes. That's fine. But for you to say that
> you're right and everyone else is "wrong" is a bit arrogant and
> slightly misguided. You aren't talking about a bunch of deviant
> children who didn't learn theory properly. You're talking about naming
> conventions that are a century old now, and have evolved from people
> who most certainly advanced music theory past the older "common
> practice" norms.
>
This is exactly what I doubt.
>
> I think you missed my point. My point was that you are insisting that
> 12-tet is still meantone, and hence that different enharmonically
> equivalent chords (C E G# vs C E Ab, or C Eb Gb Bbb vs C Eb Gb A) are
> aurally different. I'm thus asking then if, by the same logic,
> meantone is really 5-limit JI, and hence chords like C Eb G and C F Bb
> Eb G are different, and if one of the Eb's should be notated as Eb+ or
> Eb\ or something like that.
>
> -Mike
I was not talking about microtonality or meantone, just about pure 12ET. For me is no problem to think in 12ET and use enharmonics. I see no problem in it, no contradiction, because I have started my formal music education on piano. And because I'm zen-buddhist, for us nothing is impossible. When I see black, I see in the same time white :-) It's just another koan.

Daniel Forro

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

> > That might have applied 100 years ago. At this point, these other
> > conventions are also themselves "old good rules."
> >
> They can't be good if they are done wrong way.

Well, I'm a Zen Buddhist, and to me, things like this can't be wrong.
When I hear that it's "wrong," I see at the same time that it's
"right" :-) It's just another koan

:-)

> To use terms like "flatten" and "sharpen" here is inaccurate, because
> it evokes using of flats and sharps which is not always true.

It doesn't confuse anyone that I ever talk to... :) It's pretty clear:
when you "sharpen" a note that is already "flattened," it becomes
"natural." If you're talking about generic intervals (9th, 7th, etc)
the meaning is clear. I have never come up against any confusion from
it.

> This is my point. Therefore I use
> universal "+" meaning rising up, and "-" for lowering down. Easy.

That's fine, and to avoid confusion you can do that. But to tell
everyone else that the other way is "wrong" or that it means they
"don't understand basic music theory" is wrong.

> > I think you missed my point. My point was that you are insisting that
> > 12-tet is still meantone, and hence that different enharmonically
> > equivalent chords (C E G# vs C E Ab, or C Eb Gb Bbb vs C Eb Gb A) are
> > aurally different. I'm thus asking then if, by the same logic,
> > meantone is really 5-limit JI, and hence chords like C Eb G and C F Bb
> > Eb G are different, and if one of the Eb's should be notated as Eb+ or
> > Eb\ or something like that.
>
> I was not talking about microtonality or meantone, just about pure
> 12ET. For me is no problem to think in 12ET and use enharmonics. I
> see no problem in it, no contradiction, because I have started my
> formal music education on piano. And because I'm zen-buddhist, for us
> nothing is impossible. When I see black, I see in the same time
> white :-) It's just another koan.

In "pure" 12-et, there is no difference between F# and Gb. You made a
specific psychoacoustic claim - which is that in 12-tet, although F#
and Gb "round off" to the same note, that they will be perceived
differently, and thus the "spelling" should reflect this. I am asking
if you think the same applies to meantone and 5-limit just intonation.

-Mike

🔗Daniel Forró <dan.for@...>

On 27 Apr 2010, at 12:15 PM, Mike Battaglia wrote:
>
> It doesn't confuse anyone that I ever talk to... :) It's pretty clear:
> when you "sharpen" a note that is already "flattened," it becomes
> "natural." If you're talking about generic intervals (9th, 7th, etc)
> the meaning is clear. I have never come up against any confusion from
> it.
>
OK, I will apply for English lesson course with genewardsmith. I can teach him about 30 another languages if he is interested.

> > This is my point. Therefore I use
> > universal "+" meaning rising up, and "-" for lowering down. Easy.
>
> That's fine, and to avoid confusion you can do that. But to tell
> everyone else that the other way is "wrong" or that it means they
> "don't understand basic music theory" is wrong.
>
In my opinion it's wrong. I have right to have opinions and tell them, whether you like it or not. And you have right to think that I'm wrong and tell it to me. I didn't force you to accept my opinion. And I didn't say you don't understand basic music theory.
> > I was not talking about microtonality or meantone, just about pure
> > 12ET. For me is no problem to think in 12ET and use enharmonics. I
> > see no problem in it, no contradiction, because I have started my
> > formal music education on piano. And because I'm zen-buddhist, > for us
> > nothing is impossible. When I see black, I see in the same time
> > white :-) It's just another koan.
>
> In "pure" 12-et, there is no difference between F# and Gb.
>
There is no difference on piano keyboard, and on some instruments even in the sound, but there is a difference in writing music in the score. Gb minor chord must be written as Gb-Bbb-Db, not as F#-Gx-Db or Gb-A-C#. Is this so difficult to understand?
> You made a
> specific psychoacoustic claim - which is that in 12-tet, although F#
> and Gb "round off" to the same note, that they will be perceived
> differently, and thus the "spelling" should reflect this. I am asking
> if you think the same applies to meantone and 5-limit just intonation.
>
> -Mike
I didn't say they will be perceived differently and spelling should reflect it. I have said they will look differently in the score, it has deep reason why it should be distinguished in the score and why enharmonics should be used. That's all I can say to it.

Daniel Forro

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗Daniel Forró <dan.for@...>

🔗rick <rick_ballan@...>

Ah Daniel, last post you said that I need to have the "imagination to think off the keyboard". Below you say that "12tET exists only in the score". But if you actually read some of my recent posts you'll see that its all about the mathematics of wave theory.

As for "jazz theory", well I'm an actual bonefide jazz musician. A guitarists in fact. It's my job. Throwing a minus sign after a G9 is NOT, I repeat NOT, the correct way to write G7(b9). Why? Because when reading a chart jazz musicians only have a split second to recognise a chord. G9 is a G7 add (natural) 9. If I was to put - after it would go unnoticed. And we all know how 'nice' a G9 would sound with a G7(b9). Remember, jazz is an improvised music that is played with *other musicians*. This needs a common, not private, language.

"Don't argument with atonality, this has nothing to do with atonality". Well I will argument with atonality. The congruent modulo 12 doesn't exist "only on the score". If we ask "which interval equals the 8ve when multiplied by itself?", this becomes a math problem I^2 = 2. It has one and only one solution, I = sqrt2 or 2^(1/2). Observe that [2^(1/2)]/1 = 2/[2^(1/2)] = [2^(1/2)]. Thus the interval gives itself under 8ve inversion. And it is in a manner of speaking a '2tET'. Now if we "imagine" that from C to F# (say) there can be two F#'s, say another called "Gb", and detune according to some comma problem that came from elsewhere, then we are destroying this symmetry. We would then need to create two C's to redress the imbalance, B# for eg, and the problem would spiral out of control.

As I said, the language of enharmonics comes out of questions of tonality, ironing out commas, and so on. It is not particularly well suited for all of those symmetric, passing chords which are necessarily atonal because they don't have a tonic. This

"Bdim7 = B-D-F-Ab
> Ddim7 = D-F-Ab-Cc
> Fdim7 = F-Ab-Cb-Ebb
> Abdim7 = Ab-Cb-Ebb-Gbb"

treats the alphabet notes B, D, F, Ab as if they were 'tonics'. What, are you saying the C E G is a C major but E G C is some type of E? Of course these chords are just inversions of one another. But these are not Bmaj, Dmaj etc...Since all intervals bear the same relation to every other, then the chord is atonal and the assumption that the bottom note is the tonic or root is ill founded. Mathematically this solves the problem "what interval gives the 8ve when multiplied by itself 4 times?". I^4 = 2 has one and only one solution, I = 2^(1/4). In contrast the letter name system is biased toward tonality from the very beginning. Your naming system above is superfluous and overcomplicated. It is certainly not customary in jazz circles.

-Rick

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
> Advice 1: read carefully what I have written. There's a "-" sign
> after my "G9". Together it makes "G9-". Because I'm well experienced
> in jazz theory I will never use chord sign system with "b" and "#"
> which works only for some chords. The only proper and universal
> system for all keys and chords is to use "+" and "-" signs for
> alterations. So if you want to teach me universal systems, you can
> learn this one as well and avoid using of flats and sharps in chord
> signs. You can write G9b or G(b9), that's OK, but if you write for
> example F#{b9} you will only show lack of knowledge, because there's
> no flat ninth interval in that chord. If you want to use accidentals,
> you must write properly F#9 and natural sign, because G# is changed
> to G, not to Gb. So it's not universal system. Capisco?
>
> Advice 2: It's very surprising here on tuning group to find another
> person who doesn't understand about enharmonics and what it means
> for music theory. Don't argument with atonality, this has nothing to
> do with atonality. And don't argument with equal temperament, it
> doesn't exist in reality. Despite we have 12tone keyboard, 12tone
> system exists only in the score. And writing has its rules and
> distinguish between F and E# for example. There's a difference
> between Ab and G#, both in the score and in the real music practice.
> So if you want to stay in your darkness, you can. But once more I
> repeat: Bdim7, Ddim7, Fdim7 or Abdim7 are different chords because
> they have different notes (you can add even Cbdim7, E#dim7 and G#dim7
> to your list). Here is your missed lesson:
>
> Bdim7 = B-D-F-Ab
> Ddim7 = D-F-Ab-Cc
> Fdim7 = F-Ab-Cb-Ebb
> Abdim7 = Ab-Cb-Ebb-Gbb
>
> Of course each of them has its tonic chord, because they were created
> on VII grade of the scale. Tonic is always half tone up, and it can
> be major or minor.
>
> All my life I fight with the ignorance of half educated music
> amateurs by explaining what's wrong, what's right. Lot of them
> learned something from me, forgot their funny theories and were
> happy, because they came to better understanding of music (this is
> not depending on the music style). Some not. Select your way. This is
> an advice, dear friend, not insult.
>
> Daniel Forro
>
>
> On 26 Apr 2010, at 5:38 PM, rick wrote:
>
> >
> > Daniel said "If you mean G9- for the second chord, then you have to
> > use G in bass and B7dim (in any inversion) as a chord. Not D7dim.
> > They are definitely different chords. Try to forget standard
> > keyboard for visualisation of chords. Or improve your imagination."
> >
> > Rick> No I didn't mean G9 which is a G7 with natural 9th. I said G7
> > (b9). Once again we see why 'enharmonic spelling' is NOT the
> > correct language for atonality. B7dim and D7dim are absolutely NOT
> > different chords. One is the inversion of the other.
> > Misunderstandings like this is why we use the designations
> > 0,1,2,...11 representing the N in 2^(N/12)instead of letters from
> > the alphabet. Because the letters represent an old language based
> > on tonality and lead to confusion. Since multiplying log's equals
> > adding exponents, then intervals are determined by the operation of
> > addition/subtraction. The correct mathematics is congruent modulo
> > 12. Two intervals are inverse when they add to 12. Since 12 = 0
> > (mod 12) then inverses can also be written as negative. 3 + 9 = 12
> > = 0 are inverse, as are 3 + (-3) = 0. That is, 9 = -3 and 3 = -9
> > (mod 12).
> >
> > Now look at Dim7 0:3:6:9. We might invert it as 0:-3:-6:-9. But
> > this is 0:9:6:3. It has the same interval content. Another way of
> > saying this is that every note is equally qualified to become *the
> > root* 0. If 3 -> 0 then we get -3:0:3:6 = 9:0:3:6. 2nd inv 6->0
> > gives -6:-3:0:3 = 6:9:0:3 and finally 9->0 gives -9:-6:-3:0 =
> > 3:6:9:0. So we see that Dim7 chords by definition *do not have a
> > tonic*. This is because they are invariant with respect to
> > inversion, yielding the same intervals from every point of view.
> >
> > Getting back to the original problem, G7(b9) is equivalent to a
> > Bdim7/G i.e. with a G bass. Ignoring the G altogether we get Bdim7
> > = Ddim7 = Fdim7 = Abdim7 which can now function as the V7 chord to
> > a C tonic. However, by the same syllogistic logic, we could instead
> > think of these as V7 to Eb, Gb or A, that is, minor thirds from C.
> > Notice that we CAN use Eb or D# because these are new keys and no
> > longer have nothing to do with C. A favourite of Bach's is to use
> > this to come out in the relative minor of major key. For eg, Cmaj
> > to G7 => G#dim7 => E7 to Amin.
> >
> > As a final statement, this congruent modulo maths is the correct
> > language for ANY truly equal temperament. The chromatic scale in 12
> > tET allows every note to become 0, which means that what we can
> > play in one key can be played in any of the others. A true 17tET
> > for eg would be 2^(N/17).
> >
> > Advice: Get your facts right before attempting to criticise, and
> > leave the insults.
> >
> > -Rick
>

🔗genewardsmith <genewardsmith@...>

🔗rick <rick_ballan@...>

But Michael, your statement "chords based on other roots" is mistaken from the very beginning because the dim7 chord HAS NO ROOTS, necessarily. What is written below is neither a 'B', 'D', 'F' or "Ab' necessarily but all and none of them at once. In themselves they do not have a key and so we can't decide in advance what key to write them in. Even if we take a progression like Cma7 C#dim7 Dmi7 Ddim7, the dim's are not really in the key of C major. The C# is used because it substitutes A7(b9) which is leading to the D minor. But in itself it isn't really in that key. You're both confusing tonal 'landing' chords with atonal 'floating' ones.

-Rick

🔗Mike Battaglia <battaglia01@...>

31 I think would be far superior to 19. The fact that the fifths are
significantly flat in both 19/31 is enough to drive me nuts with all
of my pseudo-hip stacked fifth/fourth voicings, but I could probably
get used to it. I had a very fruitful conversation with Paul Erlich
about the intersection of tuning theory and jazz a month ago, and it
left me believing the following two theses:

1) "Jazz," in the sense of the term being a description of a genre of
music, is really suited for 12-equal. There are a lot of comma pumps
and "puns" taken advantage of in 12-equal that don't exist in other
temperaments. For example, as you no doubt know, 12-equal (or some
kind of 12-tone circulating temperament) is the only tuning in which
meantone, pajara, and dominant are all "modalities," and their
importance to jazz is listed, IMO, in that order.

Figuring out ii-V-I's without meantone is basically guaranteed to give
you nightmares. The other two could probably be worked out a little
bit more easily. Also, the fact that b9's and #9's approximate 17:16
and 19:16 very well in 12-equal implies some other higher-limit
temperaments that I'm not sure have names right now. But we should
give them names.

2) "Jazz," in a more broad, philosophical sense, is more of a
philosophy that could be "run" on any tuning. Consider the following:

Historically speaking, after plowing into meantone a bit more than was
done common practice music (building off of some of the harmonic ideas
in the late-Romantic era), jazz started to become more about a
systematic exploration of other rank-2 temperaments consistent with
12-equal.
- The concept of tritone substitution, for example, strongly implies a
tempering out of 50/49.
- The use of the blues in 12-tet general could imply an equivocation
between 19/16 and 6/5 (and 7/6 and 32/27 too (and 75/64 if you're
exceptionally clever)).
- The use of the mixolydian mode in particular to play the blues
implies a tempering out of 64/63, and all of the "sus7->dom7"
interplay over the blues reflects this a lot. From a purely perceptual
standpoint, I feel that Thelonious Monk, for example, tended to use
this tempering more to imply ratios of 7 (and 19), and other post-bop
composers (such as Wayne Shorter) used it to imply ratios of 5.
- We then saw an even more substantial re-exploration of meantone by
exploring "modal" music and the use of various modes as the basis for
a tonality (what Paul Erlich refers to as "dynamic tonality," I
believe, although I disagree with his notion that only Dorian and
Mixolydian can display this tendency).
- We then also started to see other rank 2 temperaments consistent
with 12-equal being explored, namely the augmented temperament (as
displayed in Giant Steps) and the diminished temperament (this could
be said to have been explored prior to this with the use of the
octatonic scale as well).
- A nice "ultra-modern" sound is to explore the "#1" interval while
keeping the natural 1 in the scale as well, and although I have no
scientific theory backing this up, I think the equivocation between
this and 17/16 is being taken advantage of at times. The same applies
with the #2 and 19/16.

Not all of these developments are really particular to jazz (Debussy
and Ravel were screwing around with a lot of these ideas decades
prior), but the point is: if you gave jazz musicians a 31-tet
instrument, they'd go nuts. They'd also go nuts with an instrument
tuned to mavila. I do think equal temperaments are probably going to
be somewhat important here though.

-Mike

On Tue, Apr 27, 2010 at 2:40 AM, genewardsmith
<genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> > --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>
> > Now if we "imagine" that from C to F# (say) there can be two F#'s, say another called "Gb", and detune according to some comma problem that came from elsewhere, then we are destroying this symmetry. We would then need to create two C's to redress the imbalance, B# for eg, and the problem would spiral out of control.
> >
> > It's not spiraling out of control, it's just spiraling out of 12 equal.
> >
>
> Paul Erlich got me thinking that 22 would be a good division for jazz, but now I'm wondering if anyone has done meantone jazz. I would think 19 would be fine for jazz.
>
>

🔗cameron <misterbobro@...>

I agree that 31 would be superior, quartal and quintal sonorities being the first objection to 19, sonorities stronger in 31 but still weaker than in 12.

But for many kinds of "jazz" or dare I say jazz-like music, I think it's nuts that 31 hasn't been in full swing for years. An extended (11-limit I guess it would be) quarter-comma modality of 31 is "the" system for schmoooov, as far as I know. And ii-V-I "IS" quarter-comma meantone, it's the most direct demonstration of the fourth-root-of 5 nature of the "fifth", and only in quarter-comma is this progression "perfect".

There are disadvantages for some styles. For example the near-Just nature of quarter-comma meantone means tall chords tend to melt together a lot more than they do in 12-tET, so 7+ note chords often don't have any more zing than 4 note chords do in 12, more of a thicker timbre on a simpler chord effect.

In fact, I noodled out a little example of this effect some time ago, hm...

http://dl.kibla.org/dl.php?filename=ItsSoHardLordXampl.wav

the palilogic riff is from a tune of mine (you can hear it going, in 5 beats with the word "hard" syncopated, "it's so...hard, Lord" over and over again). I wouldn't call this jazz, I'm not a jazz musician, but hopefully it might demonstrate that the tuning would be excellent for a number of different jazz styles.

-Cameron Bobro

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> 31 I think would be far superior to 19. The fact that the fifths are
> significantly flat in both 19/31 is enough to drive me nuts with all
> of my pseudo-hip stacked fifth/fourth voicings, but I could probably
> get used to it. I had a very fruitful conversation with Paul Erlich
> about the intersection of tuning theory and jazz a month ago, and it
> left me believing the following two theses:
>
> 1) "Jazz," in the sense of the term being a description of a genre of
> music, is really suited for 12-equal. There are a lot of comma pumps
> and "puns" taken advantage of in 12-equal that don't exist in other
> temperaments. For example, as you no doubt know, 12-equal (or some
> kind of 12-tone circulating temperament) is the only tuning in which
> meantone, pajara, and dominant are all "modalities," and their
> importance to jazz is listed, IMO, in that order.
>
> Figuring out ii-V-I's without meantone is basically guaranteed to give
> you nightmares. The other two could probably be worked out a little
> bit more easily. Also, the fact that b9's and #9's approximate 17:16
> and 19:16 very well in 12-equal implies some other higher-limit
> temperaments that I'm not sure have names right now. But we should
> give them names.
>
> 2) "Jazz," in a more broad, philosophical sense, is more of a
> philosophy that could be "run" on any tuning. Consider the following:
>
> Historically speaking, after plowing into meantone a bit more than was
> done common practice music (building off of some of the harmonic ideas
> in the late-Romantic era), jazz started to become more about a
> systematic exploration of other rank-2 temperaments consistent with
> 12-equal.
> - The concept of tritone substitution, for example, strongly implies a
> tempering out of 50/49.
> - The use of the blues in 12-tet general could imply an equivocation
> between 19/16 and 6/5 (and 7/6 and 32/27 too (and 75/64 if you're
> exceptionally clever)).
> - The use of the mixolydian mode in particular to play the blues
> implies a tempering out of 64/63, and all of the "sus7->dom7"
> interplay over the blues reflects this a lot. From a purely perceptual
> standpoint, I feel that Thelonious Monk, for example, tended to use
> this tempering more to imply ratios of 7 (and 19), and other post-bop
> composers (such as Wayne Shorter) used it to imply ratios of 5.
> - We then saw an even more substantial re-exploration of meantone by
> exploring "modal" music and the use of various modes as the basis for
> a tonality (what Paul Erlich refers to as "dynamic tonality," I
> believe, although I disagree with his notion that only Dorian and
> Mixolydian can display this tendency).
> - We then also started to see other rank 2 temperaments consistent
> with 12-equal being explored, namely the augmented temperament (as
> displayed in Giant Steps) and the diminished temperament (this could
> be said to have been explored prior to this with the use of the
> octatonic scale as well).
> - A nice "ultra-modern" sound is to explore the "#1" interval while
> keeping the natural 1 in the scale as well, and although I have no
> scientific theory backing this up, I think the equivocation between
> this and 17/16 is being taken advantage of at times. The same applies
> with the #2 and 19/16.
>
> Not all of these developments are really particular to jazz (Debussy
> and Ravel were screwing around with a lot of these ideas decades
> prior), but the point is: if you gave jazz musicians a 31-tet
> instrument, they'd go nuts. They'd also go nuts with an instrument
> tuned to mavila. I do think equal temperaments are probably going to
> be somewhat important here though.
>
> -Mike
>
>
> On Tue, Apr 27, 2010 at 2:40 AM, genewardsmith
> <genewardsmith@...> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > > --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> >
> > > Now if we "imagine" that from C to F# (say) there can be two F#'s, say another called "Gb", and detune according to some comma problem that came from elsewhere, then we are destroying this symmetry. We would then need to create two C's to redress the imbalance, B# for eg, and the problem would spiral out of control.
> > >
> > > It's not spiraling out of control, it's just spiraling out of 12 equal.
> > >
> >
> > Paul Erlich got me thinking that 22 would be a good division for jazz, but now I'm wondering if anyone has done meantone jazz. I would think 19 would be fine for jazz.
> >
> >
>

🔗rick <rick_ballan@...>

Daniel said "I was not talking about microtonality or meantone, just about pure 12ET. For me is no problem to think in 12ET and use enharmonics. I see no problem in it, no contradiction, because I have started my formal music education on piano. And because I'm zen-buddhist, for us nothing is impossible. When I see black, I see in the same time white :-) It's just another koan."

Well here's a Zen-Koan for you: The master points to the moon and says "Look what a beautiful moon it is tonight. The student thinks to himself "The master's fingernail needs clipping!".

-Rick

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
>
> On 27 Apr 2010, at 8:49 AM, Mike Battaglia wrote:
>
> > That might have applied 100 years ago. At this point, these other
> > conventions are also themselves "old good rules."
> >
> They can't be good if they are done wrong way.
>
> > It's hardly a "new"
> > style. It's not that hard, and I'm sure you can understand it. If
> > you're in F#, and you play a "flat nine" over it, you take the G# and
> > apply the "flattening" operator to it. If you "flatten" a "sharpened"
> > note, you end up with the natural. Very simple. If you sharpen a note
> > that's already sharp, it becomes doubly sharp. Easy.
> >
> >
> To use terms like "flatten" and "sharpen" here is inaccurate, because
> it evokes using of flats and sharps which is not always true. Better
> is to use neutral terms like "raising" and "lowering", or "shift up",
> "shift down".
> Don't forget there are three stages - flat, natural and sharp. When
> you go from flat up, it's not sharpening, because there's no sharp
> sign used but natural. When you go from sharp down, it's not
> flattening, because there's no flat sign, but natural. (Maybe you
> could call it "naturalising".) This is my point. Therefore I use
> universal "+" meaning rising up, and "-" for lowering down. Easy.
>
> > It may be your "preference" to apply a different set of naming
> > conventions to different notes. That's fine. But for you to say that
> > you're right and everyone else is "wrong" is a bit arrogant and
> > slightly misguided. You aren't talking about a bunch of deviant
> > children who didn't learn theory properly. You're talking about naming
> > conventions that are a century old now, and have evolved from people
> > who most certainly advanced music theory past the older "common
> > practice" norms.
> >
> This is exactly what I doubt.
> >
> > I think you missed my point. My point was that you are insisting that
> > 12-tet is still meantone, and hence that different enharmonically
> > equivalent chords (C E G# vs C E Ab, or C Eb Gb Bbb vs C Eb Gb A) are
> > aurally different. I'm thus asking then if, by the same logic,
> > meantone is really 5-limit JI, and hence chords like C Eb G and C F Bb
> > Eb G are different, and if one of the Eb's should be notated as Eb+ or
> > Eb\ or something like that.
> >
> > -Mike
> I was not talking about microtonality or meantone, just about pure
> 12ET. For me is no problem to think in 12ET and use enharmonics. I
> see no problem in it, no contradiction, because I have started my
> formal music education on piano. And because I'm zen-buddhist, for us
> nothing is impossible. When I see black, I see in the same time
> white :-) It's just another koan.
>
> Daniel Forro
>

🔗rick <rick_ballan@...>

Cameron is exactly right here. A very dear friend of mine, Jan Rutherford, was truly one of the most remarkable piano players and musicians I've ever come across. (I say "was" because she died at an early age, unfortunately). She'd listen to a song once and would not only play it but improve upon it. In big band she'd call out "the second trumpet is a quarter tone flat". Now she couldn't read at all because she was blind since birth.

-Rick

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
> The conversation I saw was about notation of functional tall chords, read by humans. Most literally 12-tET music doesn't have a human-readable score at all, or has one as a kind of byproduct. Like you said, midi information. That's not what was being discussed. So, :-P
>
> Rick is correct that different kinds of performers have different standards and expectations. Jazz musicians can notate "wrong" by strict functional standards because the functions that make it "jazz" are imparted by oral tradition.
>
> -Cameron Bobro
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> >
> >
> >
> >
> > --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> >
> > > "Don't attempt to argue by bringing up "equal temperament", something that does not really exist in practice. Despite the existence of the 12-tone keyboard, the system of 12 equal tones exists only in the score".
> > >
> > > That's proofread, and very obviously what was said. And completely valid- outside of mechanical and electronic renditions, literal 12-tET is only achieved by tortuous means, if at all.
> >
> > Daniel first brings up keyboard instruments, which are sometimes accurately tuned in 12 equal, and then goes on to say that despite the manifest existence of 12 equal in the real world, it doesn't exist in the real world. That kind of self-contradiction is nonsensical. Moreover, the context was a discussion of 12 tone serialism, where performance practice takes 12 equal as an ideal, and often get close to achieving that ideal. Saying that serial music ought to be interpreted in terms which employ a distincton between enharmonic equivalents is either a manifestation of extreme ignorance or some kind of fantaicism.
> >
> > Finally, those electronic renditions in 12 equal you remark on, because of such features as midi files and their default tuning, the tuning usually used in computer games and sometimes on ringtones, and so forth, are actually very common. So Daniel was not only spouting drivel about how serialism should be analyzed, he was clearly dead wrong about the world we live in.
> >
> > > A basic understanding of the physics of wind instruments for example gives some indication of the "natural" discrepancy between 12-tET and performable, er, performance.
> >
> > Stick your head out the damned window. A basic knowledge of the world we live in shows it does have 12 equal in it.
> >
>

🔗Daniel Forró <dan.for@...>

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>
> > Now if we "imagine" that from C to F# (say) there can be two F#'s, say another called "Gb", and detune according to some comma problem that came from elsewhere, then we are destroying this symmetry. We would then need to create two C's to redress the imbalance, B# for eg, and the problem would spiral out of control.
> >
> > It's not spiraling out of control, it's just spiraling out of 12 equal.
>
Gene, not at all. [2^(1/4)]^4 = 2 is a closed set and could even be considered as a '4 ET' in its own right (in a manner of speaking of course). It's not unique to 12 ET. A 20 ET for eg would have diminished at 0:5:10:15. 'Ideally' it already achieves perfectly what it is meant to; division of the 8ve into 4 equal parts. It is unique in the musical universe, just as 19 tET is etc...Therefore, trying to 'retune' it according to some outside theory is like, I dunno, using French to criticise English.
>
> Paul Erlich got me thinking that 22 would be a good division for jazz, but now I'm wondering if anyone has done meantone jazz. I would think 19 would be fine for jazz.

The way I see it, jazz musicians love outside harmony. But the main obstacle to the use of such tunings for jazz would be technical practicality. Remember, jazz is fundamentally about improvising, not so much about composition, which is more often than not just the 'excuse' to play. Of course, jazz musicians compose all the time. But it never forgets its roots in impro. Being able to compose 'on the spot' is proof of one's musicality and grasp of the material.

On the other hand, there's also that wonderful groundswell that we hear when historical influences come together in an exciting new way.
Bach I think is one example. Jazz is another. I suspect that within the next century or so there may very well be a new 'popular' music based on different tunings and instruments and that jazz will be incorporated in some unforeseen way. Who knows?

-Rick

🔗rick <rick_ballan@...>

Hi Mike, reading your interesting message now. But what's "pajara"?

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗rick <rick_ballan@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
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> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
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> > Gene, not at all. [2^(1/4)]^4 = 2 is a closed set and could even be considered as a '4 ET' in its own right (in a manner of speaking of course). It's not unique to 12 ET. A 20 ET for eg would have diminished at 0:5:10:15. 'Ideally' it already achieves perfectly what it is meant to; division of the 8ve into 4 equal parts. It is unique in the musical universe, just as 19 tET is etc...Therefore, trying to 'retune' it according to some outside theory is like, I dunno, using French to criticise English.
>
> What does this have to do with your claim about spiraling out of control? Historically, the chord comes from three minor thirds and an augmented second combining to make up an octave, and if you set the Wayback Machine and go back in time and tune it (NOT "detune") that way, it sounds just fine. In fact IMHO it sounds better. Saying doing this is an evil outside theory which will cause everything to spiral out of control sounds a bit Chicken Littlish. It's just an alternative way of doing things.

I think that Erlich's harmonic entropy is probably at work in this case i.e. there is a 'give' around the intervals. Of course, irrational numbers could never be truly realised anyway because they have an infinite number of non-repeating digits after the decimal point. But my point was that 'ideally' the solution to I^4 = 2 is the fourth root of 2. Therefore, three minor thirds and one augmented second will still sound symmetric because of their sufficient approximation to this ideal. IOW it doesn't spiral out of control. Besides, the appearance of this diminished was probably an unforeseen consequence of other considerations, making all major keys in tune for instance. But it has come to have a 'life of its own'.
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> > > Paul Erlich got me thinking that 22 would be a good division for jazz, but now I'm wondering if anyone has done meantone jazz. I would think 19 would be fine for jazz.
> >
> > The way I see it, jazz musicians love outside harmony. But the main obstacle to the use of such tunings for jazz would be technical practicality.
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> Which is why I was suggesting 19, rather than the 31 which people like better. I think 19 might be much more doable.
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Maybe, although it would probably have to be formalised somehow into recognisable chord progressions and scales to play over them. Personally, too much 'free jazz' already gives me a headache and God help us if they had access to alternate tunings. Eric Dolphy's Cacophony #sqrt2 in B demolished!

-Rick

🔗rick <rick_ballan@...>

🔗Cox Franklin <franklincox@...>

Although Schoenberg used the term "atonal" in the early years of the 20th century, starting in the 1920's he distanced himself explicitly from the term, preferring "pantonal." Diminished chords are not "atonal" in his theory, they are vagrant chords (see Harmonielehre).

Franklin

Dr. Franklin Cox

1107 Xenia Ave.

Yellow Springs, OH 45387

(937) 767-1165

franklincox@...

--- On Tue, 4/27/10, rick <rick_ballan@...> wrote:

From: rick <rick_ballan@...>
Subject: [tuning] Re: Alternatives to 12tET. Why?
To: tuning@yahoogroups.com
Date: Tuesday, April 27, 2010, 11:43 PM

--- In tuning@yahoogroups. com, Daniel Forró <dan.for@... > wrote:

> C#dim7 here is secondary VIIdim7 leading to II in C major. Basically

> it's common connection VIIdim7 - Tonic.

> Secondary chords are not "atonal", just "extra-tonal" because they

> don't belong to basic key in which they occured.

> Daniel Forro

Yep they are all just inversions of this VIIdim7 which can be seen as a V7(b9) with its third in the bass. The Ddim7 is an inversion of the VIIdim7 leading back to C. I chose Ddim7 here because its the closest to Dm7. Best for voice leading.

Yes they are just passing chords in this case. But they are in themselves atonal because they are invariant to inversion, a kind of '4-tone row'. This is why Shoernberg chose this term, the prefix "a" from the Greek meaning "without". Such symmetries are also a consequent of equalising between keys.

> On 27 Apr 2010, at 3:59 PM, rick wrote:

> >

> > But Michael, your statement "chords based on other roots" is

> > mistaken from the very beginning because the dim7 chord HAS NO

> > ROOTS, necessarily. What is written below is neither a 'B', 'D',

> > 'F' or "Ab' necessarily but all and none of them at once. In

> > themselves they do not have a key and so we can't decide in advance

> > what key to write them in. Even if we take a progression like Cma7

> > C#dim7 Dmi7 Ddim7, the dim's are not really in the key of C major.

> > The C# is used because it substitutes A7(b9) which is leading to

> > the D minor. But in itself it isn't really in that key. You're both

> > confusing tonal 'landing' chords with atonal 'floating' ones.

> >

> > -Rick

> >

🔗rick <rick_ballan@...>

Pantonal is probably more accurate because rather than 'stripping' tonality away, which is probably impossible, we are rather playing one tonality against the other in equal oppositions. I'm going to begin adopting that term. Thanks.

--- In tuning@yahoogroups.com, Cox Franklin <franklincox@...> wrote:
>
> Although Schoenberg used the term "atonal" in the early years of the 20th century, starting in the 1920's he distanced himself explicitly from the term, preferring "pantonal."Â Diminished chords are not "atonal" in his theory, they are vagrant chords (see Harmonielehre).
>
> Franklin
>
> Dr. Franklin Cox
>
> 1107 Xenia Ave.
>
> Yellow Springs, OH 45387
>
> (937) 767-1165
>
> franklincox@...
>
> --- On Tue, 4/27/10, rick <rick_ballan@...> wrote:
>
> From: rick <rick_ballan@...>
> Subject: [tuning] Re: Alternatives to 12tET. Why?
> To: tuning@yahoogroups.com
> Date: Tuesday, April 27, 2010, 11:43 PM
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> --- In tuning@yahoogroups. com, Daniel ForrÃ³ <dan.for@ > wrote:
>
> >
>
> > C#dim7 here is secondary VIIdim7 leading to II in C major. Basically
>
> > it's common connection VIIdim7 - Tonic.
>
> >
>
> > Secondary chords are not "atonal", just "extra-tonal" because they
>
> > don't belong to basic key in which they occured.
>
> >
>
> > Daniel Forro
>
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>
> Yep they are all just inversions of this VIIdim7 which can be seen as a V7(b9) with its third in the bass. The Ddim7 is an inversion of the VIIdim7 leading back to C. I chose Ddim7 here because its the closest to Dm7. Best for voice leading.
>
>
>
> Yes they are just passing chords in this case. But they are in themselves atonal because they are invariant to inversion, a kind of '4-tone row'. This is why Shoernberg chose this term, the prefix "a" from the Greek meaning "without". Such symmetries are also a consequent of equalising between keys.
>
> >
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> > On 27 Apr 2010, at 3:59 PM, rick wrote:
>
> >
>
> > >
>
> > > But Michael, your statement "chords based on other roots" is
>
> > > mistaken from the very beginning because the dim7 chord HAS NO
>
> > > ROOTS, necessarily. What is written below is neither a 'B', 'D',
>
> > > 'F' or "Ab' necessarily but all and none of them at once. In
>
> > > themselves they do not have a key and so we can't decide in advance
>
> > > what key to write them in. Even if we take a progression like Cma7
>
> > > C#dim7 Dmi7 Ddim7, the dim's are not really in the key of C major.
>
> > > The C# is used because it substitutes A7(b9) which is leading to
>
> > > the D minor. But in itself it isn't really in that key. You're both
>
> > > confusing tonal 'landing' chords with atonal 'floating' ones.
>
> > >
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> > > -Rick
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> > >
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> >
>

🔗cameron <misterbobro@...>

🔗rick <rick_ballan@...>

This thread began by me pointing out that jazz musicians tend not to think so much in terms of stacked thirds (alternating major-minor) which are cumbersome but rather in terms of 'guide tones' between the thirds and sevenths degrees of each chord as we cycle. Horn players for eg will tend to spell these out. If we run through all keys in seventh chords, C7 F7 Bb7 etc..., then the tritone between the maj3 and min7 degree of each chord descends chromatically and the maj3 and min7 alternate i.e. 3-7 = E-Bb for C7 becomes 7-3 = Eb-A for F7 etc... And because this interval is the same under inversion, then it is an efficient way of mapping out all keys on the instrument.

We then modify this basic 'scaffolding' to match the chord progression of songs. For eg, in the key of Cmaj we have Cma7 to Fma7 and the guide tones are E-B to E-A. Next, Bm7(b5) to Em (or E7), guide tones D-A to D-G (or G# for E7) and so on.

I was just wondering how you guys might approach this in other tunings? I tried it in meantone and it sounds good. But I suspect that it would not sound so good in certain JI tunings.

-Rick

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > But meantone systems have so much you can stack--major thirds, minor thirds, augmented seconds, augmented thirds, doubly augmented thirds, doubly diminished fifths, diminished fourths, etc etc. Chords like the augmented triad and diminished seventh are not quite as ambiguous as they are in 12et, since enharmonic equivalents are no longer equivalent, but I think they sound nicer and they do retain a lot of ambiguity.
>
> I know, but -- I'm going to miss all of my hip "3/2-equivalence"
> tricks. They just don't sound as good when 3/2 is 695 cents or so.
>
> > As for jazz, it sounds as if you are saying it tends to involve the simultaneous exploration of more than one "modality". However, this is something you could also do in other equal temperaments. In 19, aside from meantone, you could also work with negri, keemun, godzilla, and magic. Good luck to anyone trying this!
>
> Er, well... yeah. That was the point of the huge tirade above. Give
> jazz people any equal temperament and they'll go nuts. I think jazz
> folks would do some nice stuff with a temperament supporting mavila as
> well, although I have no "historical" evidence to back this up - just
> a hunch.
>
> -Mike
>