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Author Topic: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices  (Read 15376 times)

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pgroff

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Re: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices
« Reply #60 on: August 12, 2018, 03:12:38 PM »

Thanks Paul and Andrius for your replies.

I must admit I am slightly surprised by the notion of lowering the pitch of the fifths in order to make the thirds sound in tune. This doesn't seem right to my accustomed way of thinking. The interval of a fifth is too narrow in ET. It needs to be sharpened by about 2 cents to obtain a beatless interval. Similarly, a major third is too wide in ET and sounds sweetest when about 15 cents flat from ET. I don't see how those sorts of 'in-tuneness' are achieved by making the fifths even narrower. But I may be misunderstanding your explanations here.

Maybe one thing which comes out of this is that what we mean by 'in tune' is different for different people. I don't mean people who are not able to distinguish pitch accurately; it's more of a cultural 'what we've grown accustomed to hearing' thing, and has changed over the centuries since Bach's time. In general western music, we are far more accepting of the overall slight dissonances of ET than perhaps people were in the past.

Hi Steve,

Narrowing the fifth interval, relative to an acoustically pure fifth interval (i.e. flattening the upper note or sharpening the lower note) is exactly what is done in many temperaments used in Western music. And yes, this is done precisely to improve (or to ameliorate the harshness of) the major third interval that results from using pure ("just") perfect fifth intervals in a scale with limited pitches, for example a 12 note keyboard. *

You're correct that in 12-tone equal temperament the fifth interval is narrowed by about 2 cents from a pure ("just") fifth.

In 1/4 comma meantone temperament, the fifth interval is narrowed by about 3.4 cents *further* relative to an equal-tempered fifth, around 5.4 cents narrower than a pure fifth. This tempered narrow fifth is tolerated in 1/4cMT because it results in pure major thirds. Explanation:

I'm sure you know the concept of the "circle of fifths" (which applies to some but not all temperaments), shown here as a "chain" (circle broken and presented as linear); this version with the enharmonics equivalent applies to equal temperament and some other temperaments:


G# (=Ab)    D# (=Eb)  A# (=Bb)   F     C      G    D    A   E    B    F# (=Gb)   C# (=Db)   


In this sequence, it takes 4 fifth intervals to span the notes that would make up a major third (e.g the notes of the major third C-E are connected in the chain above via C-G, G-D, D-A, and A-E).


In 12ET as you correctly noted, the major third interval is wider than just (actually, around 13.7 cents wider).

To bring that major third (e.g. C-E) into purity, one way would be to tune the E notes flat by 13.7 cents relative to 12ET (leaving the C at 0 cents offset).  Thus C = 0 cents offset relative to 12ET, and E = -13.7 cents relative to 12ET.

Then if you narrow each of the following fifths by around 3.4 cents, *relative to 12ET*,  that will divide up the difference equally:

C-G    G-D    D-A   A-E

C=0 offset
G = -3.425 cents relative to 12ET
D = -6.85 cents relative to 12ET
A = -10.275 cents relative to 12ET
E = -13.7 cents relative to 12ET

These are the approximate pitches assigned to those notes in 1/4 comma meantone, when C is used as a point of departure.


Now each of those fifth intervals mentioned above is narrower than in 12ET, by approximately 3.4 cents:

C to G      0 to -3.425
G to D      -3.425 to  -6.85
D to A      -6.85   to   -10.275
A to E      -10.275 to  -13.7

Sensitive ears will hear each of those narrow 1/4cMT fifth intervals as "active" or "buzzy" when the two notes that comprise it are played together --  less concordant than 12ET fifths.

Those 1/4 meantone fifths are actually each narrow by 1/4 comma from a pure fifth, which is how this temperament got its name. A syntonic comma is around 21.51 cents. 1/4 comma is around 5.4 cents, and that's approximately 3.4 cents (the difference between 1/4cMT fifths and 12ET fifths) plus approximately 2 cents (the difference between 12ET fifths and pure fifths).

These numbers are approximate. See also this table for 1/4 comma meantone temperament (especially the "Delta" column, which shows those deviations in cents from 12ET). Sorry I can't seem to correct the formatting:

Note    Formula    Ratio    Cents    12TET    Delta    ​1⁄4-c
C    1           1.0000            0.0            0         0.0     0
C♯    X           1.0449            76.0            100        −24.0    −7
D    T           1.1180           193.2    200        −6.8    −2
E♭    T S           1.1963           310.3    300       +10.3     3
E    T2           1.2500           386.3    400       −13.7    −4
F    T2 S        1.3375           503.4    500       +3.4     1
F♯    T3          1.3975           579.5    600       −20.5    −6
G    P          1.4953           696.6    700       −3.4    −1
G♯    P X          1.5625           772.6    800       −27.4    −8
A    P T          1.6719           889.7    900       −10.3    −3
B♭    P T S       1.7889         1006.8    1000    +6.8     2
B    P T2          1.8692         1082.9    1100    −17.1    −5
C    P T2 S      2.0000         1200.0    1200     0.0    0

Source: https://en.wikipedia.org/wiki/Quarter-comma_meantone

Alternative source: https://www.dolmetsch.com/musictheory27.htm#mean

There's much more to 1/4 comma meantone, but the above demonstration shows why my original statement was correct. To bring the major thirds into purity, 1/4 comma meantone sets the fifths narrower than in ET.

PG

*If just perfect fifths are used in a 12 note scale, then the major thirds are even wider and more harsh than in 12ET.  That's sometimes called Pythagorean tuning, with just fifths and terrible thirds.  12ET has slightly tempered (narrow) fifths and greatly tempered, wide thirds. 1/4 comma meantone has deeply tempered (narrow) fifths and as a result can obtain just major thirds. However, 1/4 comma meantone if fully implemented does not have a circle of fifths, because enharmonics (Eb vs D#) are not equivalent. You might want 31 pitches to the octave for a full 1/4 comma meantone temperament, to obtain all the notes you might use in chromatic music. Implementations of 1/4 comma on a 12 note keyboard therefore have unuseable "wolf" intervals.


« Last Edit: August 13, 2018, 12:41:37 AM by pgroff »
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Steve_freereeder

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Re: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices
« Reply #61 on: August 12, 2018, 03:44:17 PM »

Thanks for your most comprehensive reply, Paul.
That's a lot to take in but I will save and print your post, and have a good think about it.

As far as tuning of melodeons is concerned, I guess there are differences in methodology, depending on whether we are referring to the treble end, or the basses & chords. On an instrument where there is a stop to remove the thirds from the chords, it is surely undesirable to have an open fifth which has beats; it doesn't sound good. That's why I tune the fifths 2 cents sharp - it gives a beatless chord, which does sound nice..

If the treble end of a melodeon (other than a 1-row cajun box) is tuned to some sort of mean tone tuning such as you describe, then there would have to be compromises made somewhere to (a) allow the basic scales on the RH rows to sound reasonably in tune with each other, and (b) to allow the LH basses and chords to not clash unduly with the RH treble end. There will always have to be compromises (won't there?). And isn't the art of tuning to know where and what degree of compromises can or should be made?
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pgroff

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Re: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices
« Reply #62 on: August 12, 2018, 03:58:43 PM »

Hi Steve,

If you are going for pure fifths in the basses, that's even more reason that 1/4 comma meantone on the melody side could be disadvantageous!

To summarize my comment to which you responded, my personal opinion is that 1/4 comma meantone temperament is overkill in narrowing the fifths on a diatonic melodeon.

Most systems of diatonic box can be tuned to obtain very sweet major third intervals on the melody side without narrowing the fifth intervals that much  (1/4 comma from just, or 3.4 cents narrower than 12ET fifths).

BTW, I did edit to add some more info and sources in my previous post. So if you did print it out, you may want to do so again. None of the basic meaning was changed but there's more explanation now.

PG
« Last Edit: August 12, 2018, 04:19:00 PM by pgroff »
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Steve_freereeder

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Re: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices
« Reply #63 on: August 12, 2018, 04:02:07 PM »

Hi Steve,

If you are going for pure fifths in the basses, that's even more reason that 1/4 comma meantone on the melody side could be disadvantageous!

To summarize my comment to which you responded, my personal opinion is that 1/4 meantone temperament is overkill in narrowing the fifths on a diatonic melodeon....

Relieved to read that. Thanks!
Basically, I'll carry on as I have been doing for the past few years then.  :Ph
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pgroff

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Re: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices
« Reply #64 on: August 12, 2018, 04:14:04 PM »

Hi Steve,

If you are going for pure fifths in the basses, that's even more reason that 1/4 comma meantone on the melody side could be disadvantageous!

To summarize my comment to which you responded, my personal opinion is that 1/4 meantone temperament is overkill in narrowing the fifths on a diatonic melodeon....

Relieved to read that. Thanks!
Basically, I'll carry on as I have been doing for the past few years then.  :Ph

If it sounds good to you that's what matters most!  Better still if this is the result of your own personal exploration and you have found your own individual sound - as long as that works for you, your audience, and other musicians you may sometimes join. I don't believe in standards for their own sake & I celebrate sonic and temperamental diversity :)    But sometimes the theory can be a tool to work toward that sound we want, or to negotiate possible compromises among different sounds we may want to achieve.

PG
« Last Edit: August 12, 2018, 04:15:49 PM by pgroff »
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Andrius

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Re: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices
« Reply #65 on: August 12, 2018, 05:18:41 PM »

[...]
Some Hohners from this pre-WW2 period were tuned in equal temperament, some were just not very well tuned at all, but many of the diatonic boxes were tuned to very precise non-equal temperaments designed to optimize certain intervals. I think it's incorrect to call the entire instrument or even the scale for one diatonic row "just tuned" but I'm a stickler about that. However, some intervals do approach "just" tuning. In the two-and three-row boxes you will often see that the same named note when found on different rows and/or different bellows directions is assigned a different pitch.

One possible minor disagreement with Andrius' statements (if I understand you correctly): in my experience, when a box is properly tuned in this way, the octaves *along the same button row and in the same bellows direction* are well in tune, allowing for a different beat frequency of the tremolo or musette. However, octave notes chosen between different button rows and/or different bellows directions may be different in the "center / target perceived pitch."
[...]
PG

Thank you Paul for perfect explanations about tuning, my English is not so good to do it  :(
Most important part of my Hohners are from Germany, and lot of them seems never be serviced after factory.
6 or 7 accordions (of more than 30) were with "sweet thirds" only in low (main) octave (now higher thirds are corrected).
This lets me think about factory tuning this way.
Another interesting discovery - sometimes bass side is not in tune (a little lower) with melody side. IMO it was factory trick.
When testing this way tuned accordion it seems wrong tuned, but when other person is playing, sound seems to be OK. My friend and I were testing two Hohner Club III BS accordions, where one was with lower bass side, another - bass side was tuned with melody side. When another person plays accordion with lower bass side sounds more rich; may be this adds a little more tremolo.

It seems part about tuning can be moved to different place, may be Theo will find the way how to do it to help others to find really actual posts.
 
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Koch Bb/Eb 12b 3v : Koch A/D 8b 2v : Koch C/F 12b 2v : Hohner Erica C/F 8b 2v : Hohner Erika C/F 2.4 row 8b 2v : Hohner early pre-Corona F/Bb/Eb 12b 2v: Hohner Liliput 2.4 row Bb/Eb 8b 2v : Hohner Club III BS C/F 2.7 row 8b 3v : Galotta D/G 8b 2v : Meinel & Herold G/C/F 16b 2v : Unkn G/C 8b 2v : Petersburg accordion F/Bb/Eb 16b 3v: Petersburg accordion G/C/F 16b 2v : Bandoneon Alfred Arnold 128 tone 2v : Bandoneon Wilhelm König 144 tone 2 v

pgroff

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Re: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices
« Reply #66 on: August 12, 2018, 05:38:05 PM »


Thank you Paul for perfect explanations about tuning, my English is not so good to do it  :(
Most important part of my Hohners are from Germany, and lot of them seems never be serviced after factory.
6 or 7 accordions (of more than 30) were with "sweet thirds" only in low (main) octave (now higher thirds are corrected).
This lets me think about factory tuning this way.
Another interesting discovery - sometimes bass side is not in tune (a little lower) with melody side. IMO it was factory trick.
When testing this way tuned accordion it seems wrong tuned, but when other person is playing, sound seems to be OK. My friend and I were testing two Hohner Club III BS accordions, where one was with lower bass side, another - bass side was tuned with melody side. When another person plays accordion with lower bass side sounds more rich; may be this adds a little more tremolo.

It seems part about tuning can be moved to different place, may be Theo will find the way how to do it to help others to find really actual posts.

Thank you Andrius, your English is beautiful, and my Lithuanian is nonexistent!

I also agree with you about the bass side sometimes tuned flat (also more complex interactions of bass and treble sides are found, especially in the big instruments with 12 or 16 diatonic basses). This sound can work really well depending on musical style, I have a small Hohner Erica that is tuned this way (with reeds from an earlier Hohner, 1930s).

Finally, my apologies for the off-topic posts. However, when a statement that I write is challenged (although friendly and welcome, Steve did challenge my statement about narrow fifths in 1/4 comma meantone to improve thirds) I like to respond with evidence and clear reasoning. That way if I am shown to be wrong I can more clearly see why, and learn from the conversation.

Best,

PG
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Andrius

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Re: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices
« Reply #67 on: August 12, 2018, 06:39:00 PM »

[...]
Finally, my apologies for the off-topic posts.
[...]

PG

no blame here - off-topic started by me and Steve  8)
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Koch Bb/Eb 12b 3v : Koch A/D 8b 2v : Koch C/F 12b 2v : Hohner Erica C/F 8b 2v : Hohner Erika C/F 2.4 row 8b 2v : Hohner early pre-Corona F/Bb/Eb 12b 2v: Hohner Liliput 2.4 row Bb/Eb 8b 2v : Hohner Club III BS C/F 2.7 row 8b 3v : Galotta D/G 8b 2v : Meinel & Herold G/C/F 16b 2v : Unkn G/C 8b 2v : Petersburg accordion F/Bb/Eb 16b 3v: Petersburg accordion G/C/F 16b 2v : Bandoneon Alfred Arnold 128 tone 2v : Bandoneon Wilhelm König 144 tone 2 v

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Re: Hohner Modell 234, 235, 255 and other prewar clubs with 4 (+) voices
« Reply #68 on: August 12, 2018, 07:08:10 PM »

- off-topic started by me and Steve  8)

But at least partly relevant as it led to a discussion of how these 1930s Hohners might have been tuned.  ;)
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