old pitch and temperament - again

[Geoff Wooff]

5 hours ago, Wolf Molkentin said:

a general question:

 

given a third would be "pure" (as the "good" thirds in 1/4 comma meantone tuning), is there still a (lower) "difference tone" supposed to be heard by humans?

 

the thirds of the George Case concertina, particularly the higher ones, have it, albeit sounding sweet...

Do you mean  a 'beat'   or pulse ( as in  accordion wet  tuned reeds)  or  a  harmonic  tone  of of some other pitch ?

[Little John]

6 hours ago, Wolf Molkentin said:

a general question:

 

given a third would be "pure" (as the "good" thirds in 1/4 comma meantone tuning), is there still a (lower) "difference tone" supposed to be heard by humans?

 

the thirds of the George Case concertina, particularly the higher ones, have it, albeit sounding sweet...

 

The answer is yes, though I'm not sure whether it's a result of "beating" or just the brain's interpretation. If I sound two high notes a fourth apart on either my ET or my 1/5 comma Cranes I can hear a note two octaves below the higher note. This is consistent with interpreting the two notes as the 2nd and 3rd overtones of the perceived fundamental. Likewise on my 1/5 comma instrument two high notes a major third apart produce the perception of a fundamental two octaves below the lower note; consistent with interpreting them as the 3rd and 4th overtones. I do not get this effect on my ET instrument; presumably as the major third is so far from pure.

 

LJ

Edited February 11, 2019 by Little John

[cboody]

Well...just to clarify, or muddy, things a bit.  My term scale below refers to the major scale. 

 

1. The reason for a particular starting note being chosen with mean tone tuning is that the farther you deviate from the scale of the chosen starting note the farther the scale sounds out of tune and the worse important chords will sound. 

 

2.  1/4 comma and 1/5 comma meantone tunings arean attempt to deviate enough to allow the advantages of meantone tuning to apply to a wider range of keys.  

 

3.  The range of good sounding keys is narrower with 1/4 comma tuning, so realize that if you leave it tuned that way you’ll want to be sure you’re happy with the available keys.  I’m not advocating you change the tuning, though 1/5 comma would be my choice.

 

4. You can see from the above why knowing the chosen starting point is crucial. 

 

5. If your tuner gives Hz I’d recommend you get those numbers for the entire instrument. It should help determine starting note.  And/or if your tuner allows you to set the starting pitch for the 1/4 mean try each starting note and frequency and check the scale for the other notes. The starting note used will be the one where the scale deviates the least.  Then you will know which notes need adjustment. 

 

6. The wolf tone you refer to is mediated by the 1/4 or 1/5 meantone tuning, so strictly speaking it doesn’t occur anywhere. I believe that term is usually only associated with Pythagorean tuning, but I might be very wrong about that.

 

hope this helps!

 

 

 

 

[Wolf Molkentin]

Hi Chuck,

 

I hoped you'd chime in, so thanks a lot for your thorough reply.

 

Being aware that you appear to be much more into all that stuff (from previous posts already) I nevertheless will reply to your points one by one in order to overcome possible shortcomings in my understanding:

 

11 hours ago, cboody said:

1. The reason for a particular starting note being chosen with mean tone tuning is that the farther you deviate from the scale of the chosen starting note the farther the scale sounds out of tune and the worse important chords will sound. 

 

I understand that I guess - however my point was that any shift would not affect the values of a certain note, as long as we would be strict with the enharmonics. Do you agree?

 

The way forward seems to be a problem of divergent nomenclature then I reckon: I found the label "C-centered/based" and "D-centered/based" for just the same choice: the root of Dmaj would be the only one that has not a single compromised interval - whereas the first ones to differ from the meantone pattern would be the minor second of the root G (giving an augmented first instead) and the augmented fourth (tritone) of the root A (giving a diminished fifth instead). C-centered it might be called insofar as major scales (and of course the respective modes) from Bb to A would be uncompromised, extended to a range from Eb to E with the EC through the 13. and 14. note (D# and Ab that is), all very useful based upon the "white keys" as a starting  point, with Cmaj (nearly) right in the middle).

 

Quote

 

2.  1/4 comma and 1/5 comma meantone tunings arean attempt to deviate enough to allow the advantages of meantone tuning to apply to a wider range of keys.  

 

3.  The range of good sounding keys is narrower with 1/4 comma tuning, so realize that if you leave it tuned that way you’ll want to be sure you’re happy with the available keys.  I’m not advocating you change the tuning, though 1/5 comma would be my choice.

 

A range from Eb to E maj and the respective parallel modes (see my comment on point 1.) would be fine for me, at least with a treble concertina. For a Duet concertina (and possibly a TT EC too) I might in fact prefer 1/5 comma.

 

Quote

4. You can see from the above why knowing the chosen starting point is crucial. 

 

5. If your tuner gives Hz I’d recommend you get those numbers for the entire instrument. It should help determine starting note.  And/or if your tuner allows you to set the starting pitch for the 1/4 mean try each starting note and frequency and check the scale for the other notes. The starting note used will be the one where the scale deviates the least.  Then you will know which notes need adjustment. 

 

I seem to have finally found that, as I had assumed when I started, the center is C (as to the valid major scales available around Cmaj) resp. D (as to the only completely uncompromised set of intervals resp. all 12 steps, see comment to point 1.), the pitch is A=449 Hz, indicating C as the pitch center re ET tuning (the C equals the C in old pitch, based upon A=452 Hz.).

 

Quote

 

6. The wolf tone you refer to is mediated by the 1/4 or 1/5 meantone tuning, so strictly speaking it doesn’t occur anywhere. I believe that term is usually only associated with Pythagorean tuning, but I might be very wrong about that.

 

I'm aware that the "wolf" term stems from Pythagorean tuning, but I believe it is quite common for at least discussing 1/4 comma meantone temperament - which makes sense insofer as the single "bad" "wolf" fifth is even worse than with Pythagorean tuning (not flat but sharp, and even more so). In the system indicated above (however it may be called) the "wolf" is between Eb and G#, just as in Pythagorean tuning. Any shift of the center would put the wolf around the circle of fifths, as I seem to understand.

 

So, to sum it up, my EC seems to be tempered to the key of Cmaj (which would make sense for a basically diatonic instrument in the key of Cmaj, which has all the accidentals as flats or sharps, like black keys), providing a range of major scales from Eb to E, and two more major triads (Ab and B). This is a very fine choice IMO.

 

Please correct as needed - ?

 

Edited February 12, 2019 by Wolf Molkentin

[Little John]

3 hours ago, cboody said:

Well...just to clarify, or muddy, things a bit.

 

 

I'm afraid this just muddies things.

 

1. The reason for choosing a particular starting (centre) note is to minimise the deviation from other instruments playing in equal temperament (ET). As it happens, A is the best starting note if you play mainly in the "folk" keys of G and D.

 

2. Whether you choose 1/4, 1/5, 1/6 comma or any other mean tone tuning (other than 1/12 comma, which is ET) you are limited to six* keys; usually ranging from two flats to three sharps. Those six* keys will all sound equally good. (*Eight keys on an English concertina with its additional accidentals.)

 

3. All temperaments are a compromise. 1/4 comma gives pure major thirds but narrow fifths; 1/12 comma (= ET) gives almost perfect fifths but horribly wide major thirds. In between you trade one off against the other. 1/5 comma is a good choice because it gives decent major thirds at the same time as acceptable deviation from ET instruments.

Edited February 12, 2019 by Little John
To clarify the difference for an English concertina.

[Wolf Molkentin]

3 minutes ago, Little John said:

 

I'm afraid this just muddies things.

 

1. The reason for choosing a particular starting note is to minimise the deviation from other instruments playing in equal temperament (ET). As it happens, A is the best starting note if you play mainly in the "folk" keys of G and D.

 

This would be the pitch center, not the center of the tempering IMO.

 

3 minutes ago, Little John said:

 

2. Whether you choose 1/4, 1/5, 1/6 comma or any other mean tone tuning (other than 1/12 comma, which is ET) you are limited to six keys; usually ranging from two flats to three sharps. Those six keys will all sound equally good.

 

I agree, they are sounding equally good (at least in 1/4 comma meantone, which I have examined) - however with an EC it's extended to eight keys (see my comments to Chuck's reply).

 

3 minutes ago, Little John said:

 

3. All temperaments are a compromise. 1/4 comma gives pure major thirds but narrow fifths; 1/12 comma (= ET) gives almost perfect fifths but horribly wide major thirds. In between you trade one off against the other. 1/5 comma is a good choice because it gives decent major thirds at the same time as acceptable deviation from ET instruments.

 

1/4 comma is good with EC's, as long as the concertina is the only instrument with a fixed pitch (as opposed mainly to the human voice, but to some extent to stringed nonfretted instruments as well).

 

Best wishes - ?

[Wolf Molkentin]

14 hours ago, Little John said:

 

The answer is yes, though I'm not sure whether it's a result of "beating" or just the brain's interpretation. If I sound two high notes a fourth apart on either my ET or my 1/5 comma Cranes I can hear a note two octaves below the higher note. This is consistent with interpreting the two notes as the 2nd and 3rd overtones of the perceived fundamental. Likewise on my 1/5 comma instrument two high notes a major third apart produce the perception of a fundamental two octaves below the lower note; consistent with interpreting them as the 3rd and 4th overtones. I do not get this effect on my ET instrument; presumably as the major third is so far from pure.

 

LJ

 

Thank you John - I have tried that with an ET instrument, and in fact, the effect is (for me not absent with ET, but) much stronger with the MT tempering (thus the pure interval).

 

Edited February 12, 2019 by Wolf Molkentin

[Wolf Molkentin]

17 minutes ago, Little John said:

As it happens, A is the best starting note if you play mainly in the "folk" keys of G and D.

 

I agree, as well regarding the spacing of enharmonics as Geoff had mentioned - but with my "Case" its being tuned to C doesn't really matter these days as it is in old pitch anyway... ?

[Wolf Molkentin]

25 minutes ago, Little John said:

1/12 comma, which is ET

 

John, I believe it's rather 1/11 comma, as long as we would be referring to the "syntonic" comma, which is the reference for the labels of 1/4 comma asf. as well (1/12 Pythagorean comma would be true of course, but as said in another reference system).

[Wolf Molkentin]

17 hours ago, Geoff Wooff said:

Do you mean  a 'beat'   or pulse ( as in  accordion wet  tuned reeds)  or  a  harmonic  tone  of of some other pitch ?

 

the latter - I've first noticed these tones when playing my first electronic organ (a Yamaha model, which was almost certainly tuned to ET).

 

(beats is what I get from the - tempered - fifths, expectedly)

 

Edited February 12, 2019 by Wolf Molkentin

[Wolf Molkentin]

6 hours ago, cboody said:

the farther you deviate from the scale of the chosen starting note the farther the scale sounds out of tune and the worse important chords will sound. 

 

this would be the - deeply missed, for playing and listening to the music of JSB and other baroque writers - beauty of a (resp. one of the) "well-tempered" tunings (I'm aware that some wouldn't accept the term "tuning" beyond Pythagorean and just tuning) I reckon...

[cboody]

On 2/12/2019 at 4:05 AM, Little John said:

 

I'm afraid this just muddies things.

 

1. The reason for choosing a particular starting (centre) note is to minimise the deviation from other instruments playing in equal temperament (ET). As it happens, A is the best starting note if you play mainly in the "folk" keys of G and D.

 

2. Whether you choose 1/4, 1/5, 1/6 comma or any other mean tone tuning (other than 1/12 comma, which is ET) you are limited to six* keys; usually ranging from two flats to three sharps. Those six* keys will all sound equally good. (*Eight keys on an English concertina with its additional accidentals.)

 

3. All temperaments are a compromise. 1/4 comma gives pure major thirds but narrow fifths; 1/12 comma (= ET) gives almost perfect fifths but horribly wide major thirds. In between you trade one off against the other. 1/5 comma is a good choice because it gives decent major thirds at the same time as acceptable deviation from ET instruments.

Well, you said it differently, but we don’t disagree in any substantive way.

Edited February 15, 2019 by cboody

[cboody]

On 2/12/2019 at 7:21 AM, Wolf Molkentin said:

 

this would be the - deeply missed, for playing and listening to the music of JSB and other baroque writers - beauty of a (resp. one of the) "well-tempered" tunings (I'm aware that some wouldn't accept the term "tuning" beyond Pythagorean and just tuning) I reckon...

Yup. That is the issue in a nutshell. One should note that ET is not the only "well tempered scale.

 

[cboody]

On 2/12/2019 at 4:04 AM, Wolf Molkentin said:

Hi Chuck,

 

I hoped you'd chime in, so thanks a lot for your thorough reply.

 

Being aware that you appear to be much more into all that stuff (from previous posts already) I nevertheless will reply to your points one by one in order to overcome possible shortcomings in my understanding:

 

 

I understand that I guess - however my point was that any shift would not affect the values of a certain note, as long as we would be strict with the enharmonics. Do you agree?

 

The way forward seems to be a problem of divergent nomenclature then I reckon: I found the label "C-centered/based" and "D-centered/based" for just the same choice: the root of Dmaj would be the only one that has not a single compromised interval - whereas the first ones to differ from the meantone pattern would be the minor second of the root G (giving an augmented first instead) and the augmented fourth (tritone) of the root A (giving a diminished fifth instead). C-centered it might be called insofar as major scales (and of course the respective modes) from Bb to A would be uncompromised, extended to a range from Eb to E with the EC through the 13. and 14. note (D# and Ab that is), all very useful based upon the "white keys" as a starting  point, with Cmaj (nearly) right in the middle).

Well, I’m not at all sure what you mean here, but you are correct about the 8 available keys.  The difference between C base and D base is the F and C arebetter in C base and the F# and C# better in D base.  That said, the difference is scarcely discernible, more so in 1/4 comma.

On 2/12/2019 at 4:04 AM, Wolf Molkentin said:

 

 

A range from Eb to E maj and the respective parallel modes (see my comment on point 1.) would be fine for me, at least with a treble concertina. For a Duet concertina (and possibly a TT EC too) I might in fact prefer 1/5 comma.

 

 

I seem to have finally found that, as I had assumed when I started, the center is C (as to the valid major scales available around Cmaj) resp. D (as to the only completely uncompromised set of intervals resp. all 12 steps, see comment to point 1.), the pitch is A=449 Hz, indicating C as the pitch center re ET tuning (the C equals the C in old pitch, based upon A=452 Hz.).

I think you may be confused here.  If D is the scale which is completely Uncompromised in some meantone tuning then D was the basis for the tuning of the scales. One could, I suppose, use some other note (C or A?j to derive a tuning note that matches some standardized pitch center, but then the question arises as to how you get the pitch of the D.  An unnecessary and confusing issue, particularly in the days before electronic tuners. 

 

It is probably a mistake to assume anything more than an approximation of a standardized C or A.  Pitch levels varied wildly and quite beyond the low pitch and high pitch "standards" often referred to.

 

im not sure how you got the A 449 and A452 numbers.

On 2/12/2019 at 4:04 AM, Wolf Molkentin said:

 

 

I'm aware that the "wolf" term stems from Pythagorean tuning, but I believe it is quite common for at least discussing 1/4 comma meantone temperament - which makes sense insofer as the single "bad" "wolf" fifth is even worse than with Pythagorean tuning (not flat but sharp, and even more so). In the system indicated above (however it may be called) the "wolf" is between Eb and G#, just as in Pythagorean tuning. Any shift of the center would put the wolf around the circle of fifths, as I seem to understand.

 

So, to sum it up, my EC seems to be tempered to the key of Cmaj (which would make sense for a basically diatonic instrument in the key of Cmaj, which has all the accidentals as flats or sharps, like black keys), providing a range of major scales from Eb to E, and two more major triads (Ab and B). This is a very fine choice IMO.

 

Please correct as needed - ?

 

I think your conclusion is perfectly appropriate as long as you play alone or with instruments that can be tuned to match you in some way.

[Wolf Molkentin]

I seem to have found it necessary to differentiate between a pitch center (where we could talk about „approximations“, i.e. to another instrument being equally tempered, in order to minimise clashes, partly depending on repertoire) on the one hand and the tempering base (or whatever you‘d like to call it; which IMO can’t be anything else but a, possibly non-standarised, convention of indicating „where the wolf is“) on the other hand.

 

The latter (wolf interval) should clearly be at G#/Eb (seemingly called D-based by some and C-based by others, whether correctly or not may be debatable) in order to make best advantage of the 14 buttons of the (non-transposing) EC‘s octave. The former (pitch) is not an issue for a solo instrument, appart from understanding how to reduce required fine-tuning to the min.

 

I don’t think there’s any confusion (left) in these regards.

 

Best wishes - ?

 

Edited February 16, 2019 by Wolf Molkentin

[Little John]

3 hours ago, Wolf Molkentin said:

I seem to have found it necessary to differentiate between a pitch center ...  on the one hand and the tempering base ... on the other hand.

 

I don't think there's need to refer to two, and it only adds confusion. The first (your "pitch centre") is the note you choose to be perfectly in tune with an ET instrument. As I've said before, if you play mainly in G and D then a pitch centre of A minimises the deviation from ET. Conveniently , it still allows you to give other instruments a true 440Hz A for tuning. But if you play mainly on other keys another note would be better.

 

The second (your "tempering base") seems to be just an indirect (and not universally agreed) way of indicating where the wolf interval lies. Why not just refer to the wolf interval directly?

 

3 hours ago, Wolf Molkentin said:

The (wolf interval) should clearly be at G#/Eb...

 

 

Clearly? It depends on your favoured keys. The wolf at G#/Eb allows you to play in keys from 2 flats to 3 sharps (3 flats and 4 sharps on an English). But a Peacock Hayden duet, for example, has 1 flat and 4 sharps so G#/Eb would not be the best choice: D#/Bb would be more appropriate. Indeed many players more interested in the sharp keys than the flat keys might prefer the wolf at D#/Bb.

 

LJ

[Wolf Molkentin]

3 hours ago, Little John said:

The second (your "tempering base") seems to be just an indirect (and not universally agreed) way of indicating where the wolf interval lies. Why not just refer to the wolf interval directly?

 

I absolutely agree John - ^twas just that this had been discussed in the forums (under the title „root note“ I think) some time ago, and electronic tuners have such an option which seems to be, as you say, not universally agreed as to what note indicates which position of the wolf. I would much prefer options with just the resp. wolf pair... (with the appropriate choice - default „C“ on my tuner - it‘s working fine).

 

And my „clearly“ was - and is - restricted to the EC, because this would be the way to make most sense of the two enharmonic doublings (which are Ab and D#, given a non-transposing instrument), and then - with 3 flats and 4 sharps, as you are saying - proving a wide-enough range for the purpose of playing Anglo-Irish or Scandinavian etc. folk music.

 

Accordingly I have (with the help of this discussion and further reading) reassured myself of my George Case concertina‘s being tempered that - I think traditional - way, which seems to work perfectly fine for me (funny thing is that touching buttons randomly in order to open or close the bellows when an air valve is not provided can produce awful sounds with a MT tempered instrument).

 

Best wishes - ?

 

Edited February 16, 2019 by Wolf Molkentin