Pianotech

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Cents difference between frequencies f1 and f2 is given by:

c = 1200 * log(f2 / f1) / log(2)

Or if you can use a base 2 logarithm, that makes it a little simpler (the above version uses the change of base formula instead):

c = 1200 * log_2(f2 / f1)

And for the other way around, a change of c cents (positive or negative) from frequency f1 will give the following resulting frequency:

f2 = f1 * 2^(c / 1200)



Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Frank --

Thanks for these. I even have a calculator that can work with logs. Very cool. 

Thanks

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Original Message:
Sent: 08-06-2019 02:00
From: Frank Chemotti
Subject: Looking for a formula

Cents difference between frequencies f1 and f2 is given by:

c = 1200 * log(f2 / f1) / log(2)

Or if you can use a base 2 logarithm, that makes it a little simpler (the above version uses the change of base formula instead):

c = 1200 * log_2(f2 / f1)

And for the other way around, a change of c cents (positive or negative) from frequency f1 will give the following resulting frequency:

f2 = f1 * 2^(c / 1200)



Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Also there's this set of online calculators: http://hyperphysics.phy-astr.gsu.edu/hbase/Music/cents.html#c2

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

Original Message:
Sent: 08-06-2019 12:06
From: Geoff Sykes
Subject: Looking for a formula

Frank --

Thanks for these. I even have a calculator that can work with logs. Very cool.

Thanks

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-06-2019 02:00
From: Frank Chemotti
Subject: Looking for a formula

Cents difference between frequencies f1 and f2 is given by:

c = 1200 * log(f2 / f1) / log(2)

Or if you can use a base 2 logarithm, that makes it a little simpler (the above version uses the change of base formula instead):

c = 1200 * log_2(f2 / f1)

And for the other way around, a change of c cents (positive or negative) from frequency f1 will give the following resulting frequency:

f2 = f1 * 2^(c / 1200)



Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Yow, Jason. This is wonderful. Thanks!

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Original Message:
Sent: 08-06-2019 18:36
From: Jason Kanter
Subject: Looking for a formula

Also there's this set of online calculators: http://hyperphysics.phy-astr.gsu.edu/hbase/Music/cents.html#c2

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

Original Message:
Sent: 08-06-2019 12:06
From: Geoff Sykes
Subject: Looking for a formula

Frank --

Thanks for these. I even have a calculator that can work with logs. Very cool.

Thanks

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-06-2019 02:00
From: Frank Chemotti
Subject: Looking for a formula

Cents difference between frequencies f1 and f2 is given by:

c = 1200 * log(f2 / f1) / log(2)

Or if you can use a base 2 logarithm, that makes it a little simpler (the above version uses the change of base formula instead):

c = 1200 * log_2(f2 / f1)

And for the other way around, a change of c cents (positive or negative) from frequency f1 will give the following resulting frequency:

f2 = f1 * 2^(c / 1200)



Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Thx Jason! People ask me about this quite a lot, and I usually give them the formulas, from now on I think I'll give them this web link :)

------------------------------
Patrick Wingren, RPT
Jakobstad, Finland
0035844-5288048
------------------------------

Original Message:
Sent: 08-06-2019 18:36
From: Jason Kanter
Subject: Looking for a formula

Also there's this set of online calculators: http://hyperphysics.phy-astr.gsu.edu/hbase/Music/cents.html#c2

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

Original Message:
Sent: 08-06-2019 12:06
From: Geoff Sykes
Subject: Looking for a formula

Frank --

Thanks for these. I even have a calculator that can work with logs. Very cool.

Thanks

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-06-2019 02:00
From: Frank Chemotti
Subject: Looking for a formula

Cents difference between frequencies f1 and f2 is given by:

c = 1200 * log(f2 / f1) / log(2)

Or if you can use a base 2 logarithm, that makes it a little simpler (the above version uses the change of base formula instead):

c = 1200 * log_2(f2 / f1)

And for the other way around, a change of c cents (positive or negative) from frequency f1 will give the following resulting frequency:

f2 = f1 * 2^(c / 1200)



Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Difference between F1 and F2 in cents (F2 is higher than F1):

¢ = 1200 × log(F2 / F1) / log(2).

¢ = 1200 × log₂(F2 / F1).


Calculating F2 if F1 is known (F2 is higher than F1):

F2 = F1 × 2^{(¢ / 1200)}.


Calculating F1 if F2 is known (F2 is higher than F1):

F1 = F2 / 2^{(¢ / 1200)}.

------------------------------
Roshan Kakiya
------------------------------

Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Could you provide the offsets in frequency and offsets in cents that you are using or want to use?

------------------------------
Roshan Kakiya
------------------------------

Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Tough one. It depends on the octave and IH. Unless you do not mean 'specifically'.

------------------------------
Regards,

Jon Page
mailto:jonpage@pianocapecod.com
http://www.pianocapecod.com
------------------------------

Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Inharmonicity can be accounted for by the formulas that have been mentioned previously for converting frequency ratios to cents.

Actual F1 and Actual F2 account for inharmonicity.

The difference in cents between Actual F1 and Actual F2 can be calculated if a piano is tuned and information on its frequencies is provided by an ETD. The difference in cents between Actual F1 and Actual F2 will include inharmonicity.

The formulas for converting frequency ratios to cents that have been mentioned previously can be modified as follows to account for inharmonicity:

¢ = 1200 × log(Actual F2 / Actual F1) / log(2).

¢ = 1200 × log₂(Actual F2 / Actual F1).


This approach could be useful for partial analysis. Jason Kanter has kindly provided the actual frequencies of a Steinway L on the 18th post of the following thread:

https://my.ptg.org/communities/community-home/digestviewer/viewthread?GroupId=43&MessageKey=908c0368-7d1c-466e-b92d-2eee835c4dca&CommunityKey=6265a40b-9fd2-4152-a628-bd7c7d770cbf

I will analyse the actual partials of A2-C#3 which is a Major Third.

The actual beat rate of A2-C#3 is determined by the difference between the Actual 4th Partial of C#3 and the Actual 5th Partial of A2.

Actual 4th Partial of C#3 = 553.97 Hz.

Actual 5th Partial of A2 = 549.32 Hz.

These two frequencies can be inserted into the formulas above to calculate the difference between them in cents:

¢ = 1200 × log(Actual F2 / Actual F1) / log(2) = 1200 × log(553.97 Hz / 549.32 Hz) / log(2) = 14.59 cents.

¢ = 1200 × log₂(Actual F2 / Actual F1) = 1200 × log₂(553.97 Hz / 549.32 Hz) = 14.59 cents.

------------------------------
Roshan Kakiya
------------------------------

Original Message:
Sent: 08-06-2019 06:48
From: Jon Page
Subject: Looking for a formula

Tough one. It depends on the octave and IH. Unless you do not mean 'specifically'.

------------------------------
Regards,

Jon Page
mailto:jonpage@pianocapecod.com
http://www.pianocapecod.com

Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------​

Not accounting for IH and stretch preference, I think this is what you are looking for.

------------------------------
Regards,

Jon Page
mailto:jonpage@pianocapecod.com
http://www.pianocapecod.com
------------------------------

Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

I fixed the text registering on this cents-cps.pdf.
This cents_Hz.xls will offer more insight.

------------------------------
Regards,

Jon Page
mailto:jonpage@pianocapecod.com
http://www.pianocapecod.com
------------------------------

Original Message:
Sent: 08-06-2019 10:43
From: Jon Page
Subject: Looking for a formula

Not accounting for IH and stretch preference, I think this is what you are looking for.

------------------------------
Regards,

Jon Page
mailto:jonpage@pianocapecod.com
http://www.pianocapecod.com

Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Jon --

Yow! What a great spread. Yes, I was interested in the numbers without IH. I'm not doing a science project so easy numbers are going to make the best examples. This is terrific! 

Thanks

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Original Message:
Sent: 08-06-2019 10:53
From: Jon Page
Subject: Looking for a formula

I fixed the text registering on this cents-cps.pdf.
This cents_Hz.xls will offer more insight.

------------------------------
Regards,

Jon Page
mailto:jonpage@pianocapecod.com
http://www.pianocapecod.com

Original Message:
Sent: 08-06-2019 10:43
From: Jon Page
Subject: Looking for a formula

Not accounting for IH and stretch preference, I think this is what you are looking for.

------------------------------
Regards,

Jon Page
mailto:jonpage@pianocapecod.com
http://www.pianocapecod.com

Original Message:
Sent: 08-06-2019 00:32
From: Geoff Sykes
Subject: Looking for a formula

I'm looking for a formula, well, two actually, if there is one, that can be used to calculate cents offset for a known frequency shift from a specific note. Also the reverse: The frequency offset for a known cents shift from a known note. 

In other words, if I move a specific note, with a known frequency, by x cents, what is the change in frequency?

Conversely, If I move a specific note with known cents deviation of 0 offset from what it's supposed to be, by x frequency value, what is the change in cents?

Thanks --

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------