Pianotech

I've been assembling data points from Verituner. Attached is one chart of the complete set of partials of a Steinway L as recorded by Verituner using a set of tuning parameters I put in to emulate a P12 tuning. The chart displays the relationships between partials 1, 2, 3, 4, 6, 8 on notes where these partials are all theoretically identical or very close, for example  D4(8), G4(6), D5(4), G5(3), D6(2), D7(1). 
Railsback curves don't consider the full set of partials.
Questions, comments?

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Did no one see my post with the graphic of a Steinway L tuning including all the data points? This kind of chart illuminates why we need to pay attention to matching partials. No responses and not even any views. Did I post it wrongly?

Cheers anyway.

Jason Kanter

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message:
Sent: 07-29-2019 00:00
From: Jason Kanter
Subject: Multiple Resonance

I've been assembling data points from Verituner. Attached is one chart of the complete set of partials of a Steinway L as recorded by Verituner using a set of tuning parameters I put in to emulate a P12 tuning. The chart displays the relationships between partials 1, 2, 3, 4, 6, 8 on notes where these partials are all theoretically identical or very close, for example  D4(8), G4(6), D5(4), G5(3), D6(2), D7(1).
Railsback curves don't consider the full set of partials.
Questions, comments?

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Although I believe I understand what you are trying to show, it is not easy to read, my eyes can't keep track of all the overlapping lines.
It might be easier to follow if you limited it to just a few notes.
It would be fun if you could make a video, gradually building the web of partials.

------------------------------
Ed Sutton
ed440@me.com
(980) 254-7413
------------------------------

Original Message:
Sent: 07-29-2019 14:48
From: Jason Kanter
Subject: Multiple Resonance

Did no one see my post with the graphic of a Steinway L tuning including all the data points? This kind of chart illuminates why we need to pay attention to matching partials. No responses and not even any views. Did I post it wrongly?

Cheers anyway.

Jason Kanter

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561

Original Message:
Sent: 07-29-2019 00:00
From: Jason Kanter
Subject: Multiple Resonance

I've been assembling data points from Verituner. Attached is one chart of the complete set of partials of a Steinway L as recorded by Verituner using a set of tuning parameters I put in to emulate a P12 tuning. The chart displays the relationships between partials 1, 2, 3, 4, 6, 8 on notes where these partials are all theoretically identical or very close, for example  D4(8), G4(6), D5(4), G5(3), D6(2), D7(1).
Railsback curves don't consider the full set of partials.
Questions, comments?

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message------

Although I believe I understand what you are trying to show, it is not easy to read, my eyes can't keep track of all the overlapping lines.
It might be easier to follow if you limited it to just a few notes.
It would be fun if you could make a video, gradually building the web of partials.

------------------------------
Ed Sutton
ed440@me.com
(980) 254-7413
------------------------------

Original Message------

Ed Sutton said: "It might be easier to follow if you limited it to just a few notes.

It would be fun if you could make a video, gradually building the web of partials."

That's the plan. There's a lot of information and some good graphics coming. This is testing the waters. I'll simplify.

| || ||| || ||| || ||| || ||| || ||| || ||| || |||

jasonkanter@gmail.com

jason's cell 425 830 1561

bellevuepianotuning.com

Original Message------

I was most interested in your graph.

Perhaps if you provided a key and specifically identified examples on the graph of a 4:2 octave, 6:3 octave, etc. it would be easier for many more to start to appreciate the work you have done.

BTW, somewhat similar graphing is available within RCT, albeit with many, many fewer data points.

I hope you pursue this. The potential for expanding our knowledge here is great

Here you go - let's see if this helps. The same tuning is displayed, but with only two of these "resonance strings" where e.g. partial 1 of A5 aligns with partial 2 of A4, partial 3 of D4, partial 4 of A3, partial 6 of D3, and partial 8 of A2. I've also annotated below, to show the Verituner Style definition.


------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message:
Sent: 07-30-2019 09:13
From: Kent Swafford
Subject: Multiple Resonance

I was most interested in your graph.

Perhaps if you provided a key and specifically identified examples on the graph of a 4:2 octave, 6:3 octave, etc. it would be easier for many more to start to appreciate the work you have done.

BTW, somewhat similar graphing is available within RCT, albeit with many, many fewer data points.

I hope you pursue this. The potential for expanding our knowledge here is great

Original Message------

Ed Sutton said: "It might be easier to follow if you limited it to just a few notes.

It would be fun if you could make a video, gradually building the web of partials."

That's the plan. There's a lot of information and some good graphics coming. This is testing the waters. I'll simplify.

| || ||| || ||| || ||| || ||| || ||| || ||| || |||

jasonkanter@gmail.com

jason's cell 425 830 1561

bellevuepianotuning.com

Original Message------

Here you go - let's see if this helps. The same tuning is displayed, but with only two of these "resonance strings" where e.g. partial 1 of A5 aligns with partial 2 of A4, partial 3 of D4, partial 4 of A3, partial 6 of D3, and partial 8 of A2. I've also annotated below, to show the Verituner Style definition.

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message:
Sent: 07-30-2019 09:13
From: Kent Swafford
Subject: Multiple Resonance

I was most interested in your graph.

Perhaps if you provided a key and specifically identified examples on the graph of a 4:2 octave, 6:3 octave, etc. it would be easier for many more to start to appreciate the work you have done.

BTW, somewhat similar graphing is available within RCT, albeit with many, many fewer data points.

I hope you pursue this. The potential for expanding our knowledge here is great

Original Message------

Ed Sutton said: "It might be easier to follow if you limited it to just a few notes.

It would be fun if you could make a video, gradually building the web of partials."

That's the plan. There's a lot of information and some good graphics coming. This is testing the waters. I'll simplify.

| || ||| || ||| || ||| || ||| || ||| || ||| || |||

jasonkanter@gmail.com

jason's cell 425 830 1561

bellevuepianotuning.com

David asks "Do you think it might be possible to compare that with doing another graph for unstretched ET?"
Certainly - I can produce a similar graph as the tuning would be redefined by any set of specifications. Once Verituner has mapped the piano, it can rearrange the relationships between notes according to any "style" definition. 
Sadly, however, "unstretched ET" is not a precise definition, unless you intend 2:1 everywhere, which frankly is not possible in the bass. Please try to define "unstretched" in terms of partial matching.

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message:
Sent: 07-30-2019 13:41
From: David Pinnegar
Subject: Multiple Resonance

Brilliant - thanks - most helpful

Do you think it might be possible to compare that with doing another graph for unstretched ET?

Many thanks

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Here you go - let's see if this helps. The same tuning is displayed, but with only two of these "resonance strings" where e.g. partial 1 of A5 aligns with partial 2 of A4, partial 3 of D4, partial 4 of A3, partial 6 of D3, and partial 8 of A2. I've also annotated below, to show the Verituner Style definition.

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561

Original Message:
Sent: 07-30-2019 09:13
From: Kent Swafford
Subject: Multiple Resonance

I was most interested in your graph.

Perhaps if you provided a key and specifically identified examples on the graph of a 4:2 octave, 6:3 octave, etc. it would be easier for many more to start to appreciate the work you have done.

BTW, somewhat similar graphing is available within RCT, albeit with many, many fewer data points.

I hope you pursue this. The potential for expanding our knowledge here is great

Original Message------

Ed Sutton said: "It might be easier to follow if you limited it to just a few notes.

It would be fun if you could make a video, gradually building the web of partials."

That's the plan. There's a lot of information and some good graphics coming. This is testing the waters. I'll simplify.

| || ||| || ||| || ||| || ||| || ||| || ||| || |||

jasonkanter@gmail.com

jason's cell 425 830 1561

bellevuepianotuning.com

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message:
Sent: 07-30-2019 09:13
From: Kent Swafford
Subject: Multiple Resonance

I was most interested in your graph.

Perhaps if you provided a key and specifically identified examples on the graph of a 4:2 octave, 6:3 octave, etc. it would be easier for many more to start to appreciate the work you have done.

BTW, somewhat similar graphing is available within RCT, albeit with many, many fewer data points.

I hope you pursue this. The potential for expanding our knowledge here is great

Original Message------

Ed Sutton said: "It might be easier to follow if you limited it to just a few notes.

It would be fun if you could make a video, gradually building the web of partials."

That's the plan. There's a lot of information and some good graphics coming. This is testing the waters. I'll simplify.

| || ||| || ||| || ||| || ||| || ||| || ||| || |||

jasonkanter@gmail.com

jason's cell 425 830 1561

bellevuepianotuning.com

Original Message------

Note- there's a diagram on this page and it probably doesn't transfer through email. You'll have to view it on my.ptg.org.
So we do look at all manner of partial ratios. They're all sounding, after all. 

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

David, please explain what you mean by "standard equal temperament." The octave to be comprised of twelve equally spaced notes, I imagine. This definition is agnostic about "stretch." The Stwy L chart I have been showing is of course in ET unless otherwise specified.
Kellner, I understand, though we'd need to review the offsets. But..
"without stretch at all in the central three octaves"... What does this really mean?
Firstly, does it cover A2 to A5?
So "no stretch at all" means ... A2(8) is to be the same frequency as A5(1)? (In the tuning displayed in my chart, A2(8) is 881.88 and A5(1) is 882.06.)
or are they all 2:1 octaves top to bottom? or what?
I know you are extremely fond of the (archaic?) tuning machine you use, but it would likely be fruitful if you can parse out how it calculates the middle three octaves. What aligns with what?

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message:
Sent: 07-30-2019 17:53
From: David Pinnegar
Subject: Multiple Resonance

Dear Jason

Your last email has the image coming through brilliantly and most helpfully.

Would it be possible, please, to do the same graphs with

a. standard equal temperament and

b. Kellner? (Without stretch at all in the central three octaves, from Tenor C through to the C above Treble C, and the bass tuned 6:3)

I looked up https://www.cybertuner.com by the way, most interesting, but shame it runs only on iPhone.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Note- there's a diagram on this page and it probably doesn't transfer through email. You'll have to view it on my.ptg.org.
So we do look at all manner of partial ratios. They're all sounding, after all.

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

[deleted]

Original Message------

Did no one see my post with the graphic of a Steinway L tuning including all the data points? This kind of chart illuminates why we need to pay attention to matching partials. No responses and not even any views. Did I post it wrongly?

Cheers anyway.

Jason Kanter

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Jason, I spent quite a bit of time trying to make sense of it without much progress. I was going to ask for an explanation if someone else didn't. 
Perhaps you could take one triad across the compass and explain what you are illustrating.

------------------------------
Steven Rosenthal
Honolulu HI
808-521-7129
------------------------------

Original Message:
Sent: 07-29-2019 17:24
From: David Pinnegar
Subject: Multiple Resonance

Yes - I did and was most interested but sadly the attachments weren't visible on the email.

What you're trying to demonstrate with P12 tuning alignment of partials is possibly akin to something near to what I'm achieving with perfect 5th based unequal temperaments.

If you might be interested in running what I do through your mathematical analysis perhaps the result might be of interest and it would be fascinating to see if your real world measurements and associated maths matches up with what I think I'm doing and others seem to be able to hear also.

This seems to be an important line of enquiry.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Did no one see my post with the graphic of a Steinway L tuning including all the data points? This kind of chart illuminates why we need to pay attention to matching partials. No responses and not even any views. Did I post it wrongly?

Cheers anyway.

Jason Kanter

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message------

Jason, I spent quite a bit of time trying to make sense of it without much progress. I was going to ask for an explanation if someone else didn't. 
Perhaps you could take one triad across the compass and explain what you are illustrating.

------------------------------
Steven Rosenthal
Honolulu HI
808-521-7129
------------------------------

Those horizontal-line-connected ovals represent a chain of partials that theoretically should be aligned for pure resonance throughout the piano. Moving from right to left, we're seeing partial 1 of the highest note, partial 2 of the next (one octave down), partial 3 of the twelfth below, partial 4 of the double octave, partial 6 of the two-octave-plus-a-fifth, and partial 8 of the triple octave. The closer to horizontal, the more in tune the piano sounds. The displayed partial chains are all 3 octaves long. The blue ones are D1-D4, D2-D5,. D3-D6, D4-D7.  The red ones are A0-A3, A1-A4, A2-A5, A3-A6, and A4-A7.

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message:
Sent: 07-29-2019 17:57
From: David Pinnegar
Subject: Multiple Resonance

Having logged onto the post on the site the illustration is coming through but it would help to know what line is which and what the horizontal and near horizontal red lines represent.

So I'm in the same position as Steven.

But it looks like a really helpful analysis.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Jason, I spent quite a bit of time trying to make sense of it without much progress. I was going to ask for an explanation if someone else didn't.
Perhaps you could take one triad across the compass and explain what you are illustrating.

------------------------------
Steven Rosenthal
Honolulu HI
808-521-7129
------------------------------

Jason, what were the parameters for the P12 tuning style which you based this on? "Swafford Pure 12th?"

------------------------------
Patrick Draine
Billerica MA
978-663-9690
------------------------------

Original Message:
Sent: 07-29-2019 00:00
From: Jason Kanter
Subject: Multiple Resonance

I've been assembling data points from Verituner. Attached is one chart of the complete set of partials of a Steinway L as recorded by Verituner using a set of tuning parameters I put in to emulate a P12 tuning. The chart displays the relationships between partials 1, 2, 3, 4, 6, 8 on notes where these partials are all theoretically identical or very close, for example  D4(8), G4(6), D5(4), G5(3), D6(2), D7(1).
Railsback curves don't consider the full set of partials.
Questions, comments?

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

It took me some time to understand the graphic, but I think I get it now. If I understand correctly, for a consonant tuning you want the "interval" lines traced across the graph to be <pwa data-pwa-id="pwa-08F31B6C0BD3FA74B296903C1B221DFE" data-pwa-rule-id="READABILITY_87" data-pwa-category="style" data-pwa-hint="Readability may be enhanced by using: flat and horizontal" data-pwa-suggestions="flat and horizontal" data-pwa-dictionary-word="as flat and horizontal as possible" class="pwa-mark">as flat and horizontal as possible</pwa>, right?

I tried making a graph of my own, using just a generic tuning curve. I added some labels showing the various intervals that I think might help people understand what's going on.


------------------------------
Anthony Willey, RPT
http://willeypianotuning.com
http://pianometer.com
------------------------------

Original Message:
Sent: 07-30-2019 09:38
From: Patrick Draine
Subject: Multiple Resonance

Jason, what were the parameters for the P12 tuning style which you based this on? "Swafford Pure 12th?"

------------------------------
Patrick Draine
Billerica MA
978-663-9690

Original Message:
Sent: 07-29-2019 00:00
From: <pwa data-pwa-id="pwa-B2BB14C545FEBB0B2CBB0013E99F5D3E" data-pwa-rule-id="SIMPLE_SPELLING" data-pwa-category="spelling" data-pwa-hint="Incorrect named entity spelling: Jason Kanter" data-pwa-suggestions="Jason Kander" data-pwa-dictionary-word="Jason Kanter" class="pwa-mark">Jason Kanter</pwa>
Subject: Multiple Resonance

I've been assembling data points from Verituner. Attached is one chart of the complete set of partials of a Steinway L as recorded by Verituner using a set of tuning parameters I put in to emulate a P12 tuning. The chart displays the relationships between partials 1, 2, 3, 4, 6, 8 on notes where these partials are all theoretically identical or very close, for example  D4(8), G4(6), D5(4), G5(3), D6(2), D7(1).
Railsback curves don't consider the full set of partials.
Questions, comments?

------------------------------
<pwa data-pwa-id="pwa-CCDD7E1F5A8AD3A680509072F17693D5" data-pwa-rule-id="SIMPLE_SPELLING" data-pwa-category="spelling" data-pwa-hint="Incorrect named entity spelling: Jason Kanter" data-pwa-suggestions="Jason Kander" data-pwa-dictionary-word="Jason Kanter" class="pwa-mark">Jason Kanter</pwa>
Lynnwood WA
425-830-1561
------------------------------

Precisely.

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message:
Sent: 07-30-2019 13:58
From: Anthony Willey
Subject: Multiple Resonance

It took me some time to understand the graphic, but I think I get it now. If I understand correctly, for a consonant tuning you want the "interval" lines traced across the graph to be <pwa data-pwa-id="pwa-08F31B6C0BD3FA74B296903C1B221DFE" data-pwa-rule-id="READABILITY_87" data-pwa-category="style" data-pwa-hint="Readability may be enhanced by using: flat and horizontal" data-pwa-suggestions="flat and horizontal" data-pwa-dictionary-word="as flat and horizontal as possible" class="pwa-mark">as flat and horizontal as possible</pwa>, right?

I tried making a graph of my own, using just a generic tuning curve. I added some labels showing the various intervals that I think might help people understand what's going on.

------------------------------
Anthony Willey, RPT
http://willeypianotuning.com
http://pianometer.com

Original Message:
Sent: 07-30-2019 09:38
From: Patrick Draine
Subject: Multiple Resonance

Jason, what were the parameters for the P12 tuning style which you based this on? "Swafford Pure 12th?"

------------------------------
Patrick Draine
Billerica MA
978-663-9690

Original Message:
Sent: 07-29-2019 00:00
From: <pwa data-pwa-id="pwa-B2BB14C545FEBB0B2CBB0013E99F5D3E" data-pwa-rule-id="SIMPLE_SPELLING" data-pwa-category="spelling" data-pwa-hint="Incorrect named entity spelling: Jason Kanter" data-pwa-suggestions="Jason Kander" data-pwa-dictionary-word="Jason Kanter" class="pwa-mark">Jason Kanter</pwa>
Subject: Multiple Resonance

I've been assembling data points from Verituner. Attached is one chart of the complete set of partials of a Steinway L as recorded by Verituner using a set of tuning parameters I put in to emulate a P12 tuning. The chart displays the relationships between partials 1, 2, 3, 4, 6, 8 on notes where these partials are all theoretically identical or very close, for example  D4(8), G4(6), D5(4), G5(3), D6(2), D7(1).
Railsback curves don't consider the full set of partials.
Questions, comments?

------------------------------
<pwa data-pwa-id="pwa-CCDD7E1F5A8AD3A680509072F17693D5" data-pwa-rule-id="SIMPLE_SPELLING" data-pwa-category="spelling" data-pwa-hint="Incorrect named entity spelling: Jason Kanter" data-pwa-suggestions="Jason Kander" data-pwa-dictionary-word="Jason Kanter" class="pwa-mark">Jason Kanter</pwa>
Lynnwood WA
425-830-1561
------------------------------

Jason, 
I was <pwa data-pwa-id="pwa-5C63D069E9D5C6EB77CCDD6B8A143D12" data-pwa-rule-id="READABILITY_2522" data-pwa-category="style" data-pwa-hint="Readability may be enhanced by using: experimenting" data-pwa-suggestions="experimenting" data-pwa-dictionary-word="playing around" class="pwa-mark">playing around</pwa> with my Excel sheet today trying to figure out why the 12ths in the treble seemed to be <pwa data-pwa-id="pwa-1B66B167253B3275284A24146B398B08" data-pwa-rule-id="JJ_RB" data-pwa-category="grammar" data-pwa-hint="Should you be using the adjective here instead of the adverb?" data-pwa-suggestions="far" data-pwa-dictionary-word="further" class="pwa-mark">further</pwa> out of tune than I thought they should be. I think I may have discovered a problem with the way (we?) are constructing the graphs. It <pwa data-pwa-id="pwa-1BA9C7136AD2F841CD2C8BBE96B21814" data-pwa-rule-id="READABILITY_260" data-pwa-category="style" data-pwa-hint="Readability may be enhanced by using: is" data-pwa-suggestions="is" data-pwa-dictionary-word="has to do with" class="pwa-mark">has to do with</pwa> the dots being plotted with "cents" as the vertical scale instead of frequency. Because "cents" is a measure of the difference between two frequencies, the reference frequency matters. The way I had initially plotted it I was using as my point of reference the fundamental frequency of each note in equal temperament multiplied by the harmonic number. So if I were calculating the y offset of the 3rd harmonic of A2, my reference point would be (110 Hz)*3 = 330. This is a problem because when I calculate the offset of E4 the reference point is (329.6276 Hz)*1. So because I'm using different reference points to calculate cents, the points on the graph are <pwa data-pwa-id="pwa-3D4E07FD2CE4D7DCFC27E7D5F7F03B51" data-pwa-rule-id="READABILITY_1820" data-pwa-category="style" data-pwa-hint="Readability may be enhanced by removing this" data-pwa-suggestions="(omit)" data-pwa-dictionary-word="actually " class="pwa-mark">actually </pwa>being plotted on a different scale, and it's meaningless to draw a line between the 3rd harmonic of A2 and the 1st harmonic of E4.

To <pwa data-pwa-id="pwa-27C105F0F1495C24ABD8DD37A963C981" data-pwa-rule-id="READABILITY_1820" data-pwa-category="style" data-pwa-hint="Readability may be enhanced by removing this" data-pwa-suggestions="(omit)" data-pwa-dictionary-word="actually " class="pwa-mark">actually </pwa>do a meaningful comparison of harmonics plotted in cents we would have to use consistent reference points. In the attached graph I've done this, plotting each harmonic using the fundamental ET frequency of the nearest note as the reference. (So I used 329.6276 as the reference frequency for the third harmonic of A2 and the first harmonic of E4, and the sixth harmonic of A1, and the seventh harmonic of F#1, etc.) Plotting it this way makes obvious the (slightly) flat 5th harmonic and (extremely) flat 7th harmonic. But the 3:1 12ths now show up as in tune in the treble.

Notably this problem only affects harmonics that aren't multiples of two, so on the original graph the series for the 1st, 2nd, 4th, and 8th harmonics <pwa data-pwa-id="pwa-29A6088E9C5BA10F8C92E1C03D11B9F1" data-pwa-rule-id="PASSIVE_VOICE" data-pwa-category="style" data-pwa-hint="Passive verbs make your writing less direct. Try to use an active verb instead." data-pwa-suggestions="" data-pwa-dictionary-word="are plotted" class="pwa-mark">are plotted</pwa> correctly. Anyway, I'm not sure how you got your data (if you were collecting frequencies, or Verituner was spitting out cents for you) so I can't be sure, but I think this may be a problem with your graph<pwa data-pwa-id="pwa-29FF91083294A8B1D490DA1C53AC51DD" data-pwa-rule-id="READABILITY_609" data-pwa-category="style" data-pwa-hint="Readability may be enhanced by removing this" data-pwa-suggestions="(omit)" data-pwa-dictionary-word=" as well" class="pwa-mark"> as well</pwa>.

------------------------------
Anthony Willey, RPT
http://willeypianotuning.com
http://pianometer.com
------------------------------

Original Message:
Sent: 07-30-2019 18:33
From: <pwa data-pwa-id="pwa-FC1A9910243DC782FA6DD3F44DF78FE2" data-pwa-rule-id="SIMPLE_SPELLING" data-pwa-category="spelling" data-pwa-hint="Incorrect named entity spelling: Jason Kanter" data-pwa-suggestions="Jason Kander" data-pwa-dictionary-word="Jason Kanter" class="pwa-mark">Jason Kanter</pwa>
Subject: Multiple Resonance

Precisely.

------------------------------
<pwa data-pwa-id="pwa-A069183878D346763F3BFF20549A08EE" data-pwa-rule-id="SIMPLE_SPELLING" data-pwa-category="spelling" data-pwa-hint="Incorrect named entity spelling: Jason Kanter" data-pwa-suggestions="Jason Kander" data-pwa-dictionary-word="Jason Kanter" class="pwa-mark">Jason Kanter</pwa>
Lynnwood WA
425-830-1561

Original Message:
Sent: 07-30-2019 13:58
From: Anthony Willey
Subject: Multiple Resonance

It took me some time to understand the graphic, but I think I get it now. If I understand correctly, for a consonant tuning you want the "interval" lines traced across the graph to be <pwa data-pwa-id="pwa-E1CF3DACD9DA774B3C70CD9320A1E061" data-pwa-rule-id="READABILITY_87" data-pwa-category="style" data-pwa-hint="Readability may be enhanced by using: flat and horizontal" data-pwa-suggestions="flat and horizontal" data-pwa-dictionary-word="as flat and horizontal as possible" class="pwa-mark">as flat and horizontal as possible</pwa>, right?

I tried making a graph of my own, using just a generic tuning curve. I added some labels showing the various intervals that I think might help people understand what's going on.

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Anthony Willey, RPT
http://willeypianotuning.com
http://pianometer.com

Original Message:
Sent: 07-30-2019 09:38
From: Patrick Draine
Subject: Multiple Resonance

Jason, what were the parameters for the P12 tuning style which you based this on? "Swafford Pure 12th?"

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Patrick Draine
Billerica MA
978-663-9690

Original Message:
Sent: 07-29-2019 00:00
From: Jason Kanter
Subject: Multiple Resonance

I've been assembling data points from Verituner. Attached is one chart of the complete set of partials of a Steinway L as recorded by Verituner using a set of tuning parameters I put in to emulate a P12 tuning. The chart displays the relationships between partials 1, 2, 3, 4, 6, 8 on notes where these partials are all theoretically identical or very close, for example  D4(8), G4(6), D5(4), G5(3), D6(2), D7(1).
Railsback curves don't consider the full set of partials.
Questions, comments?

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Jason Kanter
Lynnwood WA
425-830-1561
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