[pianotech] Beat Speed of 5th Decrease in Treble?

John Formsma formsma at gmail.com
Thu Nov 6 05:33:51 PST 2008


As long as the inharmonicity of the 6:4 is not vastly different from the
3:2, that's probably generally OK.  But the M6-M10 is really easy to listen
to.  You can always change the reference note to make the beats slower.
 And, you're listening to for just a slight difference in beat speeds.
In the example of G#2-F3 and G#2-C4, let's say G#2-F3 beats at 6 bps. You'd
want to have G#2-C4 just slightly slower.  If that beats 5 bps, then it's
too narrow.  Assuming you can hear the 1/2 bps difference between chromatic
M3s and M6s, it's no problem to hear the difference in the M6-M10.

My P4s are always around 1 bps in the F3-F4 area, but since I tend to pure
P5s, the P4s are a tad more than 1 bps.  They're always closer to 1 bps than
2 bps.  They obviously increase in the upper midrange, but you can't really
hear them much past C5, so beyond C5, particularly in a musical context.
 So, beyond the midrange. you are more concerned about octaves.

As you say, to each his own, but I find that tuning 2:1 octaves up from the
midrange leads to an intolerably flat sounding treble.  To overcome this
tendency, one can tune with slightly expanded double octaves and slightly
contracted octave-fifths within the DO.  E.g., make F3-F5 beat the same as
A#3-F5.  Continue that up all the way, and down all the way.  This leads to
a well-balanced tuning, and it sounds great. But it all begins with the
proper foundation; i.e., the bearing or temperament.

--
JF

On Thu, Nov 6, 2008 at 6:11 AM, Jeff Deutschle <oaronshoulder at gmail.com>wrote:

> John:
>
> Yes I know the M6-M10 test. Thank you. I don't find it very useful because,
> as you say, the 3:2 5th beats so slow. I do make use of the m3-M3 6:4 5th
> test when setting the temperament though. I don't see a problem with
> listening to 6:4 5ths, as long as they are listened to consistently.
> Interesting that you dislike "those nasty narrow P5s and P19s in the
> treble." I dislike the busy 4ths when the 5ths are not narrow enough! To
> each his own.
>
> I wish I knew Latin like Don. Then instead of saying "Non calor sed umor
> est qui nobis incommodat", I would know how to say "It's not the beats, it's
> the humility." :-)
>
>
> On Wed, Nov 5, 2008 at 10:34 PM, John Formsma <formsma at gmail.com> wrote:
>
>> Jeff,
>> There are tests to help determine which partials you are hearing.  I'm
>> assuming you probably know them.  The most helpful one for me (for the 3:2
>> partials) is the M6-M10.  Say you're tuning F3-C5.  You'd play those two
>> notes with G#2.  And you can also "ghost" it to help the ear focus on the
>> correct partials.
>>
>> I'd have to be at a piano to know whether I listen inadvertently to 6:4
>> partials.  I know I sometimes hear them if they're prominent, but constant
>> ear training helps your focus so you can avoid getting off track by tuning
>> with the 6:4 partials.
>>
>> In my tunings, the P5s at the 3:2 level don't get faster in either the
>> bass or treble. In fact, they hardly beat at all.  But I tend toward a pure
>> 5ths tuning. Not quite, but close.  My tunings are somewhat expanded
>> compared to some, but that helps eliminate those nasty narrow P5s and P19s
>> in the treble.
>>
>> --
>> JF
>>
>>
>> On Wed, Nov 5, 2008 at 11:11 AM, Jeff Deutschle <oaronshoulder at gmail.com>wrote:
>>
>>> List:
>>>
>>> I have read threads where someone mentions that the beat speed of 5ths
>>> should decrease in the treble and that 5ths even become wide of just
>>> intonation. I have been trying to figure out how this could be, both
>>> theoretically and in practice.
>>>
>>> Theoretically, it seems that this could only occur if each octave was
>>> tuned more than 2 cents wider than the octave below it. In practice, my 5ths
>>> beat rate increases, not decreases, in the treble. If I try to stretch the
>>> octaves so that they beat slower, this results in unbearably busy octaves
>>> and 4ths.
>>>
>>> The only thing I can figure out is that the threads are referring to 3:2
>>> 5ths and I am listening to 6:4 5ths (which I believe I am). I imagine when
>>> taking into account inharmonicity that a 4:2 or 6:3 octave could result in
>>> the 3:2 5ths beating slower going up the treble while the 6:4 5ths beat
>>> faster. But then what about going down into the bass? Wouldn't the 3:2 5ths
>>> beat faster going down into the bass? That is hard for me to believe.
>>>
>>> So, can anyone one help me to understand this? I feel like there is a
>>> piece missing in this puzzle.
>>>
>>> --
>>> Regards,
>>> Jeff Deutschle
>>>
>>> Please address replies to the List. Do not E-mail me privately. Thank
>>> You.
>>>
>>>
>>
>>
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