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Jeff,
I appreciate you delving into it so much. You have the discipline and brain. That's great! As for me I am also still delving but at my own slow pace.
Are you willing to explain then in a bit more detail as to your procedure, say from E3 down, across the break and through the bi-chords?
Mark Piano tuner technician
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I guess I agree with Mark, octave size test are useful to learn to hear differnt types of octaves may be, but in the end I totally stopped using them, while I focus on clean sounding octaves as one of the priorities.
there is some room to fudge in most intervals, sticking to an octave type may push the tuner to pass the moment the octave type have to change. What amaze me is being able to tune by octaves with some even progression of FBI, I have always be instructed that it was not really possible, may be only the habit... " ... sticking to an octave type may push the tuner to pass the moment the octave type have to change."Exactly! I believe that if 12ths are used to tune, pure or tempered, the octave types will change when they should: wider with less iH and narrower with more iH; like a governor on a generator.
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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Jeff and Isaac, i see! Interesting!
So, if i may ask, what would be wrong or the difference in tuning 5ths down and acoss and regulating the 4th as compared to using 12ths?
Mark Piano tuner technician
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Jeff,
I appreciate you delving into it so much. You have the discipline and brain. That's great! As for me I am also still delving but at my own slow pace.
Are you willing to explain then in a bit more detail as to your procedure, say from E3 down, across the break and through the bi-chords? Well, first, I set a pure 12th D3-A4 temperment tuning fifths up and octaves down after A3, D4, E4, G3, E3 and G4 are tuned and adjusted. One test for a pure twelfth is the P5-P8 test. The 3:2 D3-A3 P5 beats the same as the 2:1 A3-A4 P8. So when the temperment is tuned, the fifths should be no slower than the A3-A4 2:1 partial match and the octaves should be no faster than the D3-A3 3:2 partial match. The smaller the piano, the more pure the octaves and fifths. And the more pure an interval is, the more difficult it is to make them trully progressive. And some pinblock are not very friendly... Contiguously progressive fifth is really about my limit. In reality, I just do the best I can. To tell the truth at these beatrates I mostly just hear a tonal change as they are tuned. I think the additional partial matches are involved. An evenly voiced piano helps. Expanding the temperment I use a spanner to directly tune the 12th and then check the octave and various RBIs. The M6-M17 test is useful. F2-D3 beats the same as F2-A4 when the D3-A4 12th is pure. I tune any and all wound strings differently. I do not trust any one partial to be true to the rest. Instead, I play the twelfth and an octave above the lower note at the same time and strive for the most resonance. Or on very challenging pianos the area that sounds the least-worst.
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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Exactly! I believe that if 12ths are used to tune, pure or tempered, the octave types will change when they should: wider with less iH and narrower with more iH; like a governor on a generator. That's down to the f*(1+Bn^2)^0.5 formula for partials; less B more n, more B less n.
Ian Russell Schiedmayer & Soehne, 1925 Model 14, 140cm Ibach, 1905 F-IV, 235cm
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Thanks Jeff! Food for thought!
How much of a difference is there between a 4:1 D8ve and a pure 12th?
And if one is tuning a pure 12th tuning in the treble and high treble, does this not increase the stretch more than say, a just 4:1 octave throughout the treble and high treble? or does this vary from piano to piano?
What do your octaves and double octaves sound like when tuning this way?
Mark Piano tuner technician
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Jeff and Isaac, i see! Interesting!
So, if i may ask, what would be wrong or the difference in tuning 5ths down and across and regulating the 4th as compared to using 12ths? Quickly said I would said it is useful to take the 12ths as a parameter of the tuning; then this is probably the interval that have the most "give" (around "pure" also) Learning to listen to them is just another helpful tip , providing a fast way to listen to the double octave ( I often use an inverted min interval with the 12t h (17th double - twelve) A 12th being and octave an a 5th it sort of show the level of tempering of both intervals (and octave at the piano could be "tempered" in my way of seeing things However I believe that pure 12ths tend to break in when the piano is played, and finish tempered. I try to keep them tempered as if not the double octave beat begin to be noticed. When all is tempered FBI can stay moderately noisy particularely M6, that are soon screaming, to me... the 12th is used since a long time by ETDs because the 3d partial is the pitch tested in the mediums; then if you know it you can perceive the perfect smoothing of twelves; the defect come from not taking in account other partials enough (I talk of older RTC or SAT, in the medium range) muddy, probably ....
Last edited by Kamin; 01/10/13 06:00 PM.
Professional of the profession. Foo Foo specialist I wish to add some kind and sensitive phrase but nothing comes to mind.!
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Thanks Jeff! Food for thought!
How much of a difference is there between a 4:1 D8ve and a pure 12th?
And if one is tuning a pure 12th tuning in the treble and high treble, does this not increase the stretch more than say, a just 4:1 octave throughout the treble and high treble? or does this vary from piano to piano?
What do your octaves and double octaves sound like when tuning this way? To me, yes
Professional of the profession. Foo Foo specialist I wish to add some kind and sensitive phrase but nothing comes to mind.!
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Ok, I have been digging around and found some info with regards to 12ths tuning and temperament tuning.
The following is written by Jim Coleman,Snr, I think, "At G5, the 19th (C3-G5) also becomes available as a test. One will often find this interval to be slightly on the narrow side even though the 12th (C4-G5) test is pure. This is decision time again. If one prefers to have pure triple octaves eventually, it may be necessary to widen the 12ths slightly and slow down the narrow 19ths gradually. In doing this, one now forces the single octaves to be stretched even more (sometimes even more than 1bps) and the double octaves may be stretched up to 1bps.
By the time one gets to C6 the triple octave comes into play. If the 12ths have been kept pure, the double octave is stretched and the triple octave is slightly narrow. If one one wishes to have the triple octave pure, then the double octave will need to be stretched more, the 12ths will need to be widened, and the 19ths will need to be almost pure but on the narrow side.All of this of coarse will make the single octave stretched even more. Here again is a decision time. Does the tuner prefer pure triple octaves at the expense of the double octave and single octaves? What the overall desired effect? Outside of unison work this is a point where art enters..."
Don Mannino wrote some time ago on this forum, the following, " Extra wide octaves in the center of the piano cause the temperament area to sound brighter , more aggressive, less focussed perhaps, and more "tense". This is because the 3rds and 6ths are made to beat faster when the octaves are wide. The 5ths are more pure than a normal stretch would give, but these are not as audible during complex music than the business of the 3rds and 6ths.
There are fine tuners at work today who regularly tune center octaves so that they are very, very wide and the 5ths are almost pure! So the old pythagorean comma gets put into the octave, instead of compromising all of the 5ths between! This is how the wide tuning in my seminar is done - I try to get the 5ths pure.
Narrow Octaves in the center of the piano tend to make a temperament area to sound more sweet and pure in tone, even though the 5ths will tend to beat faster than they might in a "normal" tuning.
The relative width of the octaves in the high treble also impacts the tone. Concert tunings are often stretched higher in the top octaves, as this can add brilliance and intensity to the top up there.
A more narrow octave in the treble area helps the piano to sing more, and 'bite' less, as the lower partials within the octaves set up sympathetic ringing that builds sustain. Some of the attack of the tone is quickly transferred to the octave above or below, reducing intensity and adding sustain...
So there is no one "correct" way to tune any octave..."
Last edited by Mark Davis; 01/10/13 07:40 PM. Reason: minor correction
Mark Piano tuner technician
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The derivation is a couple of pages of high school algebra which I could post if someone really wants to see it. Kees I'd be interested, the back of my envelope soon ran out on this one. PM if you prefer. OK, I put it in a pdf. I have some more analysis (pershaps forthcoming) which shows that equal beating 4:2/6:3 can be used in the temperament octave (and will result in equal beating behaviour) but not beyond, as it will result in too fast beating 4:2 and 4:1. There the 4:2+ has to lean more towards 4:2 than 6:3. The 12th also seems to get wide. Unrelated to my writeup, note that the default tuning curve in Tunelab has pure 6:3 octaves in the bass, and pure 4:1 double octaves in the treble, with a smooth transition in-between. In particular the 4:2 always becomes narrow in the higher octaves (around C6). A pure 12th tuning results in narrow 4:2 and wide 4:1. Kees
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I still dont understand why the 2:1 is not considered as an octave
Professional of the profession. Foo Foo specialist I wish to add some kind and sensitive phrase but nothing comes to mind.!
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The derivation is a couple of pages of high school algebra which I could post if someone really wants to see it. Kees I'd be interested, the back of my envelope soon ran out on this one. PM if you prefer. OK, I put it in a pdf. Thank you, Kees, very clear. I'll have a proper look at it later.
Ian Russell Schiedmayer & Soehne, 1925 Model 14, 140cm Ibach, 1905 F-IV, 235cm
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Thanks Jeff! Food for thought!
How much of a difference is there between a 4:1 D8ve and a pure 12th?
... Hah! It depends on the width of the implied 4th! When you carefully consider what the tests are for the P12, the P15 and the implied P4 you should realize that if the P4 is pure, the P12 and the P15 can also be pure. The algebraic difference of the beatrates of the P12 and the P15 equal the beatrate of the implied P4. This is only true when the common note is on top. Let me add this. One more little known things about the effects of iH on beatrates is that the beatrate of P4 does not double each octave. It can take a couple of octaves to double. So the beat difference between P12s and P15s does not increase much toward the treble. ...
And if one is tuning a pure 12th tuning in the treble and high treble, does this not increase the stretch more than say, a just 4:1 octave throughout the treble and high treble? or does this vary from piano to piano?
... Kees explained it well: ...
Unrelated to my writeup, note that the default tuning curve in Tunelab has pure 6:3 octaves in the bass, and pure 4:1 double octaves in the treble, with a smooth transition in-between. In particular the 4:2 always becomes narrow in the higher octaves (around C6). A pure 12th tuning results in narrow 4:2 and wide 4:1.
Kees ...
What do your octaves and double octaves sound like when tuning this way? As you go up the treble, a beat can be detected, but is not obvious unless the temperment is not strictly equal. It can be looked at as a side benefit. Since you are closer to the edge of acceptable stretch, a note that is a little off an octave below the P12 that is being tuned will not sound right when listening to the octave. I used to tune the treble without as much stretch and have smoother sounding octaves and 15ths, but the top octaves just didn't sound like they were at the right pitch when music that uses a great deal of the keyboard is played. I tried stretching by tuning wide octaves but my results were sometimes, ahem, "haphazard." Again, no complaints from customers, but I did not like the inconsistencies. So like the story of Goldilocks and the Three Bears, pure octaves was not enough, stretched octaves was too much, but pure 12ths was just right.
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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Thanks for explaining Jeff
Mark Piano tuner technician
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@Jeff : " It depends on the width of the implied 4th! When you carefully consider what the tests are for the P12, the P15 and the implied P4 you should realize that if the P4 is pure, the P12 and the P15 can also be pure. The algebraic difference of the beatrates of the P12 and the P15 equal the beatrate of the implied P4. "
something wrong in your reasoning, to me, or works only in absence of iH,
Seem to me that the definition of "pure" is what bothers me. a 4:2 octave to me, imply yet some stretch (as a 2:1 in the end) . Cordier (pure 5th tuning ) agreed in the end that the good term is "acoustically pure" as this is a slightly different concept, implying more than the simple 3:1 4:1 or 2:1 relation.
Last edited by Kamin; 01/11/13 02:05 PM.
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Isaac:
There are probably others scratching their heads on this one, too. It is a relationship that Mark C. works with.
Consider these three notes: A3, D4 and A5. There are three intervals possible: the A3-D4 P4, the D4-A5 P12 and the A3-A5 P15.
Consider a normal situation where A3-D4 P4 is 1bps wide. This means the fourth partial of A3 is at 880hz and the third partial of D4 is at 881hz. (These are approximate non-iH theoretical pitches but it does not matter. 1 bps wide is 1 bps wide regardless of the actual hz involved.) When A5 is tuned, if it is at 880hz the result is a pure P15 and a narrow P12, if it is at 881hz the result is a wide P15 and a pure P12, and if it is at 880.5hz the result is a wide P15 and a narrow P12 that beat at the same speed. Regardless of where A5 is tuned, the algebraic difference of the beatrates (+ for wide, - for narrow) will equal the beatrate of the implied P4. They could even both be wide or narrow: If A5 = 886hz then (+6bps) – (+ 5bps) = + 1bps.
Now consider an abnormal situation where A3-D4 P4 is pure. Both the fourth partial of A3 and the third partial of D4 are at 880hz. If A5 is tuned to 880hz, both the P12 and the P15 will be pure.
Using F3 as the standard test note for these intervals may make it easier to understand… or not!
This is why I say that difference between the P12 and P15 depends on the implied P4.
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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Yes I agree if this is based on a non stretched scale, of course.
But not likely to happen.
The advantage we have when tuning is that the high iH slow the beats of 4ths . that is what allows the octave to be enlarged without 4th being too noisy.
So "acoustically" a stretched 4th may sound pure, if you see what I mean, and a tempered 5th or 12th as well
When tuning , I consider all intervals as simple additions or substractions, so I may be reasoning on a no IH based logic, I agree, but this is based to what is perceived, for instance, beats are evaluated without locating them at a particular level, as if I was using pure frequencies.
Last edited by Kamin; 01/11/13 04:01 PM.
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Jeff, if you stick to pure 12th you are providing a fundation for the high treble, the tuning is in fact straight and sound just in the two modes, arpeggios and octaves.
Just for fun try to locate the exact pitch of the notes in the 5-6th octave region just based on the resonant spot obtained from the 12th, and the double.
May be you will notice that your note have a raise in color at some point.
When tested you possibly will find an equilibrium between the 15th and the double octave (same beat speed)
I will not promise it works anytime but it works.
I am advantaged with so called "perfect pitch" that allow me to place the note more or less well once I have heard the others (and also with the slow motion technique, hence the habit to master progressive slow pitch changes at a a slow speed)
the minor chord inversion (M3+4th) played with the double octave is supposed to stay quiet enough, active but not noisy nor acid.
May be the resonant spot lower the perception of the speed of the M3 and the 6th played together...
When the tuning is good, that chord is showing the wanted pitch of the double octave as a laser light .
I also like the fact that the tuning is lively.
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Gentlemen,
Perhaps I'm missing something.
Are we all on the same page? Are we all speaking of tuning from completed unisons or are some speaking of tuning a piano that has a temperament strip in tha whole piano, thus tuning and refering to and from only single strings?
That makes a huge difference on the level this discussion is at.
I ask because there seems to be some crossed wires here.
Amanda Reckonwith Concert & Recording tuner-tech, London, England. "in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.
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I understand that this is not really clear, as we use differnt methods to get to the final result.
For some the final result imply an acoustically just 12th, for others a tempered one.
I believe we talk of the final result in any case. to obtain it I have to tune "enlarged" as I use a strip mute up to c6 and there is enough lowering when tuning the unison to take it in account.
When I was tuning unison as I go the same process did apply all new notes where tuned a little high, that is why I am not considering I am doing something "new" doing so.
Last edited by Kamin; 01/14/13 06:01 AM.
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