Re: Adaptive JI and a Pedal Steel Puzzle

I wrote:
>Steel guitarists are aware that certain chord positions cannot be played
>accurately at the fret. For example, when we construct a major triad
>inversion based on the 4/3, 5/3, and 25/12 (G#, C# and E# at the nut), we
>know that we need to place the bar sharp of the fret to be in tune with the
>band.

Paul H: Erlich followed with:
>I'd like to understand this, but I don't think your ratios agree with your
>note names. Can you check?

My error. The notes are relative to a 1/1 for E, and G# is 5/4, not 4/3.
My chart at www.b0b.com/infoedu/just_e9.html is correct.

Here's a little pedal steel puzzle for you all. Some modern pedal steels
have what we call "tunable splits". This means that if you double sharp a
string with one pedal and flat it with another at the same time, you can
tune the resulting note independent of each of the pedals separately.

A common use for tunable splits is on the middle B string of the E9th
tuning. We have a pedal that raises the B (3/2) to C# (5/3), and a knee
lever that lowers the same string to A# (45/32). When we use them together
we can use the split tuner to tune a C note. The puzzle is, how should we
tune it?

I think that most players want to use it to get an augmented chord (E, G#,
C, E, G#). Assuming that the E's are 1/1 and 2/1 and the G#'s are 5/4 and
5/2, is there any tuning for the C (more correctly called B#, I think) that
creates a beatless chord?

Another possible triad would use the E's (1/1 and 2/1), the middle G (6/5)
and the newly tunable C for a C major chord. Here the C would clearly be
tuned to 8/5. Would tuning the C to 8/5 be incompatible with its use in an
augmented chord as described above? I guess what I'm really asking is how
do 5/4 and 8/5 sound together? That interval doesn't seem to be anywhere
near a whole number ratio.

Is there any JI interval that would work for both of these contexts?

-b0b-

Bob Lee wrote,

>I wrote:
>>>Steel guitarists are aware that certain chord positions cannot be played
>>>accurately at the fret. For example, when we construct a major triad
>>>inversion based on the 4/3, 5/3, and 25/12 (G#, C# and E# at the nut), we
>>>know that we need to place the bar sharp of the fret to be in tune with
the
>>>band.

>Paul H: Erlich followed with:
>>I'd like to understand this, but I don't think your ratios agree with your
>>note names. Can you check?

>My error. The notes are relative to a 1/1 for E, and G# is 5/4, not 4/3.
>My chart at www.b0b.com/infoedu/just_e9.html is correct.

OK, so can you explain now why you would be sharp of the fret?

>I think that most players want to use it to get an augmented chord (E, G#,
>C, E, G#). Assuming that the E's are 1/1 and 2/1 and the G#'s are 5/4 and
>5/2, is there any tuning for the C (more correctly called B#, I think) that
>creates a beatless chord?

Well, a beatless chord is a relative thing, since even the most consonant
intervals have faint partials that beat. But in the augmented triad, any two
of the three intervals can be tuned to pure 5:4 or 8:5, and then the third
interval will be rather dissonant. The worst place to put that dissonant
interval is between the two lowest notes. So tuning the C to 8/5 is not too
bad, and gives you that nice C major. But the most consonant tuning for the
augmented triad is something near equal temperament.

corrected, I wrote:
>>Steel guitarists are aware that certain chord positions cannot be played
>>accurately at the fret. For example, when we construct a major triad
>>inversion based on the 5/4, 5/3, and 25/12 (G#, C# and E# at the nut), we
>>know that we need to place the bar sharp of the fret to be in tune with
the
>>band.
...
>>The notes are relative to a 1/1 for E, and G# is 5/4.
>>My chart at www.b0b.com/infoedu/just_e9.html is correct.

Paul H. Erlich asked:
>OK, so can you explain now why you would be sharp of the fret?

We generally tune the E to the equally tempered band (or a 329.6 Hz fork, or
the center mark on a tuning meter). The G# and C# are JI tuned flat of ET.
We aim sharp of the fret to compensate, so that our root notes are in tune
with the guitars and keyboards.

-b0b-