Leading tones

I've read this in a post regarding bach and ragas:

>While there can be a chromatic leading tone downward towards a
>tonic, it is more usual to have one pointing up to the tonic.

1) why?

2) Can we extend this rule to the others intervals? For example it
is possible to say that a tone tends to resolve downwards?

Ciao

Lorenzo

In a message dated 1/1/2005 8:00:17 PM Eastern Standard Time,
lorenzo.frizzera@cdmrovereto.it writes:
>While there can be a chromatic leading tone downward towards a
>tonic, it is more usual to have one pointing up to the tonic.

1) why?

Because the leading tone UP to the tonic is part of the scale. However, a
leading tone DOWN to the tonic has to have a chromatically altered second degree
of the scale.

2) Can we extend this rule to the others intervals? For example it
is possible to say that a tone tends to resolve downwards?

Ciao

Lorenzo
There are directions for tones, yes. For example, the minor seventh resoves
down typically.

best, Johnny Reinhard

on 1/1/05 4:18 PM, lorenzofrizzera <lorenzo.frizzera@cdmrovereto.it> wrote:

> I've read this in a post regarding bach and ragas:
>
>> While there can be a chromatic leading tone downward towards a
>> tonic, it is more usual to have one pointing up to the tonic.
>
> 1) why?

What comes to mind...

Modulation by fifths is ubiquitous. Maybe this is because 3:2 is such a
simple interval, and modulating by it can easily be done without throwing
fixed scale notes from low-numbered to high-numbered ratios, i.e. without
requiring a larger fixed scale. All the usual comments about how 5-limit
and 12-tone go well together. And 3:2 is even less demanding than 5:4 in
terms of stressing modulation to the point of breaking a simple scale (or
maybe I should say tuning), making it require more notes to be useful.

So, if you take this as a given, then the original observation falls out of
the tonal facts of modulation by fifths. A semitone down from the tonic is
very likely the 15/8 which is just the 3rd above the 5th above the tonic. A
semitone up from the tonic is nothing special, nothing close in the cycle of
5ths, unless you get into 11-limit. So with more use of 11-limit you might
find downward resolution to the tonic to be more common. Lacking 11-limit
you're either dealing with a modulation that is somewhat less common in
order to support that melodic movement (e.g. a modulation from A major to C
major, supporting the C# to C melodic transition while remaining in 5-limit
harmony), or you are dealing with the semitone above the tonic playing a
more dissonant role. Even in 11-limit you might consider it more dissonant,
e.g. modulating from G major to C major to support the C# to C movement with
the C# being the 11/8 in G.

> 2) Can we extend this rule to the others intervals? For example it
> is possible to say that a tone tends to resolve downwards?

I think what you were getting at above is that a given melodic interval from
a given *destination* (resolved) tone may tend to come from a particular
direction, which is a little different from saying that a given tone tends
to *go* in a particular direction. This is just to be clear. I think both
are valid questions, but they are two separate questions, at least for
starters.

-Kurt

on 1/3/05 11:23 AM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>> on 1/1/05 4:18 PM, lorenzofrizzera <lorenzo.frizzera@c...> wrote:
>>
>>> I've read this in a post regarding bach and ragas:
>>>
>>>> While there can be a chromatic leading tone downward towards a
>>>> tonic, it is more usual to have one pointing up to the tonic.
>>>
>>> 1) why?
>>
>> So, if you take this as a given, then the original observation
> falls out of
>> the tonal facts of modulation by fifths. A semitone down from the
> tonic is
>> very likely the 15/8 which is just the 3rd above the 5th above the
> tonic. A
>> semitone up from the tonic is nothing special, nothing close in the
> cycle of
>> 5ths,
>
> It's just as close as the leading tone -- it's the 3rd below the 5th
> below the tonic.

Yes it's just as close on the surface, as you expressed it. But the 3rd
above the 5th above the tonic participates in a (major) chord which is
rooted a 5th above the tonic. The 3rd below the 5th below the tonic has no
direct significance in cycle-of-5ths closeness that I can see.

> So I disagree with you.
>
> See my paper _Tuning, Tonality, and Twenty-Two-Tone Temperament_ for
> why I think modes such as the Phrygian, which do feature a lowered
> second resolving down to the tonic, did not survive in tonal music.

Interesting.

> There are Phyrgian cadences even in tonal music. Were you not aware
> of that?

I'd have to read up on this. I actually don't know a Phyrgian cadence from
a hole in the ground.

In any case there are all kinds of modulations, and of course plenty of
music is not partial to modulating by 5ths. Nonetheless it was plausible to
me that 5th-based modulations might be "dominant" enough to explain why the
descending resolution is less common. No one was saying it doesn't happen,
just that the ascending is "more usual".

But when I just tried out the 6 possibilities for a major triad containing
C# modulating to C major or minor, all of them were too far stretched to
sound like "resolution" to me, or else too simplistic (lacking better words)
in the case of the entire chord sliding down chromatically. Still all cases
might technically be called resolution, I'm not sure.

>> Even in 11-limit you might consider it more dissonant,
>> e.g. modulating from G major to C major to support the C# to C
> movement with
>> the C# being the 11/8 in G.
>
> That wouldn't be a semitone, it would be a quartertone (or nearly so).

Yes, right. So it wouldn't qualify as a lowered second?

-Kurt

on 1/3/05 6:15 PM, Kurt Bigler <kkb@breathsense.com> wrote:

> on 1/3/05 11:23 AM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:
>
>> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>>> on 1/1/05 4:18 PM, lorenzofrizzera <lorenzo.frizzera@c...> wrote:
>>>
>>>> I've read this in a post regarding bach and ragas:
>>>>
>>>>> While there can be a chromatic leading tone downward towards a
>>>>> tonic, it is more usual to have one pointing up to the tonic.
>>>>
>>>> 1) why?
>>>
>>> So, if you take this as a given, then the original observation
>> falls out of
>>> the tonal facts of modulation by fifths. A semitone down from the
>> tonic is
>>> very likely the 15/8 which is just the 3rd above the 5th above the
>> tonic. A
>>> semitone up from the tonic is nothing special, nothing close in the
>> cycle of
>>> 5ths,
>>
>> It's just as close as the leading tone -- it's the 3rd below the 5th
>> below the tonic.
>
> Yes it's just as close on the surface, as you expressed it. But the 3rd
> above the 5th above the tonic participates in a (major) chord which is
> rooted a 5th above the tonic. The 3rd below the 5th below the tonic has no
> direct significance in cycle-of-5ths closeness that I can see.
>
>> So I disagree with you.
>>
>> See my paper _Tuning, Tonality, and Twenty-Two-Tone Temperament_ for
>> why I think modes such as the Phrygian, which do feature a lowered
>> second resolving down to the tonic, did not survive in tonal music.
>
> Interesting.
>
>> There are Phyrgian cadences even in tonal music. Were you not aware
>> of that?
>
> I'd have to read up on this. I actually don't know a Phyrgian cadence from
> a hole in the ground.
>
> In any case there are all kinds of modulations, and of course plenty of
> music is not partial to modulating by 5ths. Nonetheless it was plausible to
> me that 5th-based modulations might be "dominant" enough to explain why the
> descending resolution is less common. No one was saying it doesn't happen,
> just that the ascending is "more usual".
>
> But when I just tried out the 6 possibilities for a major triad containing
> C# modulating to C major or minor, all of them were too far stretched to
> sound like "resolution" to me, or else too simplistic (lacking better words)
> in the case of the entire chord sliding down chromatically. Still all cases
> might technically be called resolution, I'm not sure.

Johnny Reinhard's answer "Because the leading tone UP to the tonic is part
of the scale" (to the original query) explains this, and explains to me your
reference to Phyrgian since in this mode the reverse is true.

And my little sampling of 6 possibilities neglected starting with a minor
triad, which is what would be relevant in the Phyrgian situation. I can't
see why these nice modulations should be abandoned; I'll have to read your
paper (eventually). I also need to understand exacty what constitutes
"tonal" music.

-Kurt