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After having claimed the 4:2+ octave is optimal, then hearing people talk about tuning 4:2-, which I didn't understand, then listening closer to the octaves I tune, I've been finding many instances of different size octaves.

I still believe that the best octave is one that compromises the 4:2 and the 6:3.

I've found 4:2- and 6:3+ octaves that work out as a 2:1 which is why, I believe, some people claim the 2:1 to be ideal in some cases.

So, as of now, I'm still looking for 4:2+/6:3-, 4:2=6:3, or 4:2-/6:3- (which I call a reversed octave.)

But most people have been claiming that small pianos are the ones that need 4:2- for example, but check out this F3F4 octave on a Steinway B I tuned today. Comments?

F3F4 Recording: https://www.dropbox.com/s/jq7lj7xsn3uoqmp/Steinway%20B%2085964%20F3F4%20reversed%20octave%3F.mp3?dl=0

A3A4 Recording:
https://www.dropbox.com/s/iz7f3fszdktxc9x/Steinwsy%20B%2085964%20A3A4%20octave%20expanded%3F.mp3?dl=0

I measure approximately:

a3a4

2:1 0.5 bps
4:2 0.8
6:3 0.5

f3f4

2:1 0.0
4:2 0.6
6:3 0.6

Kees

Hey Kees,

Can you identify wide or narrow?

Did you see my numbers from Audacity? Can we calculate beat speeds at the partial from check interval beat speeds?

What do you think about a Steinway B mid range octave tuning out as a narrow 4:2 and a wide 6:3? Pretty crazy, eh? The question is not whether that is the optimum size (which I still maintain it is.) but that you can create those relationships at all. I.e. It is impossible to create a wide 4:2 and narrow 6:3 F3F4 octave (which is the suggested size according to the PTG) on that piano.

According to Audacity, the A3A4 4:2 tests out as equal (0.05bps difference). Doesn't that mean your measurements should read as A3A4 4:2 = 0bps approx?

Can't id wide or narrow. Below the spectrogram for a3a4. 4:2 beats are very clear. 2:1 beats are not easily visible with this contrast setting but are visible if I change that.



Kees

Huh?

4:2
M10 is faster than the M3, the octave is a wider 4:2.

6:3
M6 is slower than m3, the octave is a narrower 6:3.

provided M3s are wide and m3s are narrow.

Oh, I forgot.

2:1
M17 is slower than the M10, the octave is a narrower 2:1.

I will typically size the temperament octave similar where the slightly wide 4:2 allows a set of contiguous M3ds to fit very well.
When that happens the other intervals work out ok and it will be the 4ths and 5ths that may vary slightly and I don't care about that.
How wide the 4:2 depends on the piano - typical that smaller pianos = wider 4:2,s.
Also depends on if there is a wound bi-chord in the temperament or that must be used as a test note for the temperament.

Yes, but these are some advanced topics for this Tuning 101 thread.

Hi Gene,

Thanks for reading and posting. I have always said the 4:2+ is the ideal octave size, like you are saying and PTG advocate. But my research is leading me to some other observations.

Isn't it possible to fit CM3's into any size octave? The just need to change by a different proportion. Are you implying in order to keep the 4:5 ratio?

This Steinway B tunes out a F3F4 octave as a narrow 4:2 and a wide 6:3, if we decide to keep the octave between a 4:2 and a 6:3. I found this quite interesting. The quality of the octave was very good, as is all the octaves I tune as a median 4:2/6:3.

Hey Mark,
Yeah, I saw Jim Coleman Sr fit cm3ds into a pure 6:3 octave.
I did not care for it but he made it work.
Slightly wide where the 6:3 tests narrow, 4:2 slightly wide always works.
Exactly how wide just takes playing with.
The first few notes tuned will tell me about this
I have not put any effort into making cm3ds fit into unusually expanded or contracted octaves.
I only advocate my membership in PTG, nothing more.

That's just it. This Steinway F3F4 tested out as a narrow 4:2 and a wide 6:3 and it's not the first time I've found this.

A wide 4:2 produced an even wider 6:3. It sounded horrible.

So, I'm still maintaining that a median 4:2/6:3 is the best sounding octave. The vast majority of the time, I find the median octave tests out as a 4:2+/6:3-.

Interestingly, when the octave tests out reverse (4:2-/6:3+) I find the 2:1 very close to pure. This fits with what other techs have said works for smaller pianos. And in my experience, the problem pianos (the ones where 4:2+ doesn't seem to fit with a median octave) were the smaller ones, until now.

This is very important for me to research since I am using a bisecting window temperament sequence that is built on the assumption of 6:3- being the ideal size. I can maintain this relationship by reproducing the m7b5 equality. (F3G#3=B3D#4 for example.)

Now that I have found some pianos that test out their median octaves, in the temperament area, as 6:3 or 6:3+, I have created separate bisecting window temperaments to maintain those octave sizes. (Using F3G#3=A#3D4 to maintain 6:3 octaves, and F3G#3=A3C#4 to maintain 6:3+ octaves in temperament area). This seems to coincide with recent differing opinions about where the m3's fit into the CM3's. It all depends on the ideal size of the midrange octaves, and that I suppose depends on the piano and scaling.

Ill give you my beginning sequece called the Clark Souza temperament. not a ptg sanctioned sequence.

A3 to A4 test with F3 slightly wide
Set F3-A3 at 7 bps
Set D4 to A3 as typical 4th
test F3-D4 6th at 8bps in relation to F3-A3 at 7bps and the above 4th should fit nice too for reference.
set A#3 to F3 as typical 4th
Test A#3-D4 should be at 9 bps so you have a smooth progression 7, 8 and 9 using the intervals tuned above.
Then try to make C#4-A3 fit between the intervals that give 8 and 9 bps. Slower than 9 bps using the progression f3-a3(7), f3-d4(8), A#3-D4(9) then A3-c#4 (slower than 9).
Note - it is only important to count 7, the 8 and 9 are relational in a sequence.
Test all intervals that are tuned.
If this does not work you need to change the size of the octave.
If it does work then it is easy enough to complete the first set of cm3ds F3, A3, C#4, F4, A4 by tuning the F3-F4 octave.
F3-F4 should test the same as A3-A4
Plenty of checks here to be certain everything fits.
a 7,8 9 then slower than 9. progression, cm3ds, two octaves, two p4ths and a A4-D4 p5th.
6 notes tuned tells me the size of the octave.
I think I wrote it out right.

I'd like to help but I almost never use checks, I find a workeable octave and stick to it.

I will make some checks as soon as I can and take notes.

On some pianos, 2:1 + mask the 6:3 beat, my impression.

Why not?
You just need to find the correct F3-A3 beat rate.

edit: Theoretical rate of CM3s is about 4/5.04.
But anything from 4/4.96 to 4/5.08 will work don't worry.

Measuring the beat rates of the test intervals I get:

4:2 test
C#3F3 6.3
C#3F4 5.9

6:3 test
F3G#3 7.1
G#3F4 7.2

8:4 test
C#4F3 10
C#4F4 9.4

12:6 test
F3G#4 17.2
G#4F4 13.6

I used the 2nd partial of the test note to get the 8:4/12:6. At least one of the string must be irregular (pathological?).

Kees

[quote=Gene Nelson]I will typically size the temperament octave similar where the slightly wide 4:2 allows a set of contiguous M3ds to fit very well.[/quote]
I don't get that. You can tune CM3's for any octave size, 2:1, 4:2, 6:3, 14:7 if you like. You can even tune A4 flat by 40 cent in A3A4 and get pure CM3's.
[quote=Gene Nelson]
How wide the 4:2 depends on the piano - typical that smaller pianos = wider 4:2,s. [/quote]
Is that a typo? Common lore is that 4:2+ is appropriate for larger grands, but small pianos need 4:2 or even narrow 4:2/wide 2:1 compromise.

Kees

[quote=DoelKees]Measuring the beat rates of the test intervals I get:

4:2 test
C#3F3 6.3
C#3F4 5.9

6:3 test
F3G#3 7.1
G#3F4 7.2

8:4 test
C#4F3 10
C#4F4 9.4

12:6 test
F3G#4 17.2
G#4F4 13.6

I used the 2nd partial of the test note to get the 8:4/12:6. At least one of the string must be irregular (pathological?).

Kees [/quote]

That's interesting. Possibly the kind of octave I use.

You did not check 2:1?

Mark, while I believe specific partial matching are precision tools to help place the octaves, they hardly ever point to the "best" octave.

I've played with this a LOT in my Verituner experiments setting up custom styles and found that there always seems to be at least one piano that confounds a global approach to using a couple partial matches to determine the "best" octave.

Why? Perhaps if we consider how we tune the three strings of a unison we might get a fuller sense... The most precise way to set the three strings of A4 might be to compare each with the beat from F2 - just like setting from a fork. But you might find that you can actually set a better unison just with movement by ear - possibly because setting one single partial to match might not use the same information that the ear uses when setting a unison aurally. Similar to electronic tuning device (ETD) users that try to use the display to set a unison going down into the bass... Especially the ETDs that only use a single partial to drive the display? Just setting one partial to match often is not the best choice.

Where does that leave us in the octave(s)? I think the farther we move from the 'musical ear' training to just find the 'best' or 'least bad' placement for the single, double and wider octaves, the less chance we have of finding a really nice stretch for each particular piano.

That's why I recommend the hybrid approach to tuning, where the musical ear can set the skeleton of the octave stretches before ever dealing with temperament...

Ron Koval

[quote=DoelKees]I measure approximately:

a3a4

2:1 0.5 bps
4:2 0.8
6:3 0.5

f3f4

2:1 0.0
4:2 0.6
6:3 0.6

Kees
[/quote]

I get an average of 8 7/16". (This post is to determine if "quote" is working. My impertinence can be ignored.)

OK, something is weird on this board. Quotes dudd'nt word and edit duddn't either.