Pianotech

The most important lesson that I have learned after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation is that perfection cannot be achieved in the theoretical world of tuning.

Something must always be compromised in order to gain something else. This statement is true for all tuning systems:

• Equal temperament. Symmetry is completely gained and key colour is completely lost.
• Meantone temperament. Purer thirds are gained and a wolf fifth emerges.
• Unequal temperament. Some intervals are more pure and some intervals are less pure.
• Just intonation. Harmony is maximised and commas emerge.
• Adaptive just intonation. It makes just intonation practical and it cannot be used for instruments of fixed pitch.

However, the ideal theoretical compromise can be achieved.

It can be achieved by striving for two things. Those two things are simplicity and practicality.

Equal temperament is the simplest and most practical tuning system due to its complete symmetry and consistency.

It solves the commas of just intonation, tames the wolf fifth of meantone temperament, is much more mathematically simple than unequal temperament and can be used for instruments of fixed and variable pitch, unlike adaptive just intonation.

Therefore, equal temperament is the ideal theoretical compromise.

This is the conclusion that I have reached after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation.

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

Thanks for sharing your conclusions. It would be interesting to know what started you on this journey. My understanding is that you're not a piano tuner, so what got you interested in this?

------------------------------
"That Tuning Guy"
Scott Kerns
www.thattuningguy.com
Tunic OnlyPure, TuneLab & PianoMeter user
------------------------------

Original Message:
Sent: 05-31-2019 07:04
From: Roshan Kakiya
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

The most important lesson that I have learned after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation is that perfection cannot be achieved in the theoretical world of tuning.

Something must always be compromised in order to gain something else. This statement is true for all tuning systems:

• Equal temperament. Symmetry is completely gained and key colour is completely lost.
• Meantone temperament. Purer thirds are gained and a wolf fifth emerges.
• Unequal temperament. Some intervals are more pure and some intervals are less pure.
• Just intonation. Harmony is maximised and commas emerge.
• Adaptive just intonation. It makes just intonation practical and it cannot be used for instruments of fixed pitch.

However, the ideal theoretical compromise can be achieved.

It can be achieved by striving for two things. Those two things are simplicity and practicality.

Equal temperament is the simplest and most practical tuning system due to its complete symmetry and consistency.

It solves the commas of just intonation, tames the wolf fifth of meantone temperament, is much more mathematically simple than unequal temperament and can be used for instruments of fixed and variable pitch, unlike adaptive just intonation.

Therefore, equal temperament is the ideal theoretical compromise.

This is the conclusion that I have reached after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation.

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

The theoretical world of tuning is full of mathematical puzzles such as the Pythagorean comma and the Syntonic comma. I wanted to challenge myself by attempting to solve some of these puzzles.

Therefore, I applied my knowledge of addition, subtraction, multiplication, division, logarithms and exponents to the world of tuning and thoroughly experimented with the mathematics of just intonation, unequal temperament and equal temperament, as well as meantone temperament to a lesser extent, for a few years.

The conclusion that I have reached is that equal temperament is the ideal theoretical compromise.


I have written a short, succinct guide for the mathematics of equal temperament, unequal temperament and just intonation which is available here:

https://my.ptg.org/communities/community-home/digestviewer/viewthread?MessageKey=a46d662f-d447-4feb-9d22-f97ee1e7342b&CommunityKey=6265a40b-9fd2-4152-a628-bd7c7d770cbf


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

Original Message:
Sent: 05-31-2019 09:36
From: Scott Kerns
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

Thanks for sharing your conclusions. It would be interesting to know what started you on this journey. My understanding is that you're not a piano tuner, so what got you interested in this?

------------------------------
"That Tuning Guy"
Scott Kerns
www.thattuningguy.com
Tunic OnlyPure, TuneLab & PianoMeter user

Original Message:
Sent: 05-31-2019 07:04
From: Roshan Kakiya
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

The most important lesson that I have learned after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation is that perfection cannot be achieved in the theoretical world of tuning.

Something must always be compromised in order to gain something else. This statement is true for all tuning systems:

• Equal temperament. Symmetry is completely gained and key colour is completely lost.
• Meantone temperament. Purer thirds are gained and a wolf fifth emerges.
• Unequal temperament. Some intervals are more pure and some intervals are less pure.
• Just intonation. Harmony is maximised and commas emerge.
• Adaptive just intonation. It makes just intonation practical and it cannot be used for instruments of fixed pitch.

However, the ideal theoretical compromise can be achieved.

It can be achieved by striving for two things. Those two things are simplicity and practicality.

Equal temperament is the simplest and most practical tuning system due to its complete symmetry and consistency.

It solves the commas of just intonation, tames the wolf fifth of meantone temperament, is much more mathematically simple than unequal temperament and can be used for instruments of fixed and variable pitch, unlike adaptive just intonation.

Therefore, equal temperament is the ideal theoretical compromise.

This is the conclusion that I have reached after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation.

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

Good for you, Roshan. I think you have all of this exactly right.

In a way, string players have the best of all the options, with their capacity for adaptive just intonation. However, being human, few of them achieve what is theoretically possible for them.

At Banff in 1980, I got the chance to meet William Primrose, who was tremendously admired by my cello class when I was a student. At the reception the first night, he drank gin with a splash of tonic water (newly arrived at 8000 feet, too) and I drank tonic water, no gin. I nervously trotted out my carefully planned question: "Do your students have trouble adjusting to equal temperament when they are playing with piano?" And he sighed, "Oh, if only they could play as well in tune as the piano!"

------------------------------
Susan Kline
Philomath, Oregon
------------------------------

Original Message:
Sent: 05-31-2019 07:04
From: Roshan Kakiya
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

The most important lesson that I have learned after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation is that perfection cannot be achieved in the theoretical world of tuning.

Something must always be compromised in order to gain something else. This statement is true for all tuning systems:

• Equal temperament. Symmetry is completely gained and key colour is completely lost.
• Meantone temperament. Purer thirds are gained and a wolf fifth emerges.
• Unequal temperament. Some intervals are more pure and some intervals are less pure.
• Just intonation. Harmony is maximised and commas emerge.
• Adaptive just intonation. It makes just intonation practical and it cannot be used for instruments of fixed pitch.

However, the ideal theoretical compromise can be achieved.

It can be achieved by striving for two things. Those two things are simplicity and practicality.

Equal temperament is the simplest and most practical tuning system due to its complete symmetry and consistency.

It solves the commas of just intonation, tames the wolf fifth of meantone temperament, is much more mathematically simple than unequal temperament and can be used for instruments of fixed and variable pitch, unlike adaptive just intonation.

Therefore, equal temperament is the ideal theoretical compromise.

This is the conclusion that I have reached after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation.

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

Roshan, congratulations on reinventing the wheel. I'm not being sarcastic, essentially that is what tuners do every time they tune a piano and have to make real time decisions on how to justify the myriad variables they encounter. While you're addressing the compromises that must be made in the theoretical world, there are even more, many more, that must be made in the acoustic world, many of which are dynamic and interacting. Both fundamentals and harmonics can change during the duration of a note, often in asymmetrical ways. One is immersed in an environment that has currents, ebbs and flows, tides. One is tasked with finding a harmonious outcome across the audible spectrum. Then comes the catalyst, the music, musician, and musicianship; the wind, sail, and rudder perhaps.
I think the next progression for you is to find some medium to explore this acoustically by finding an instrument to tune. If not a piano, perhaps some sort of zither, like an autoharp, or organ in order apply the theories in an acoustic environment. Just plugging these tunings into a program and listening through speakers will come up short.

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

Original Message:
Sent: 05-31-2019 12:03
From: Susan Kline
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

Good for you, Roshan. I think you have all of this exactly right.

In a way, string players have the best of all the options, with their capacity for adaptive just intonation. However, being human, few of them achieve what is theoretically possible for them.

At Banff in 1980, I got the chance to meet William Primrose, who was tremendously admired by my cello class when I was a student. At the reception the first night, he drank gin with a splash of tonic water (newly arrived at 8000 feet, too) and I drank tonic water, no gin. I nervously trotted out my carefully planned question: "Do your students have trouble adjusting to equal temperament when they are playing with piano?" And he sighed, "Oh, if only they could play as well in tune as the piano!"

------------------------------
Susan Kline
Philomath, Oregon

Original Message:
Sent: 05-31-2019 07:04
From: Roshan Kakiya
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

The most important lesson that I have learned after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation is that perfection cannot be achieved in the theoretical world of tuning.

Something must always be compromised in order to gain something else. This statement is true for all tuning systems:

• Equal temperament. Symmetry is completely gained and key colour is completely lost.
• Meantone temperament. Purer thirds are gained and a wolf fifth emerges.
• Unequal temperament. Some intervals are more pure and some intervals are less pure.
• Just intonation. Harmony is maximised and commas emerge.
• Adaptive just intonation. It makes just intonation practical and it cannot be used for instruments of fixed pitch.

However, the ideal theoretical compromise can be achieved.

It can be achieved by striving for two things. Those two things are simplicity and practicality.

Equal temperament is the simplest and most practical tuning system due to its complete symmetry and consistency.

It solves the commas of just intonation, tames the wolf fifth of meantone temperament, is much more mathematically simple than unequal temperament and can be used for instruments of fixed and variable pitch, unlike adaptive just intonation.

Therefore, equal temperament is the ideal theoretical compromise.

This is the conclusion that I have reached after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation.

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

Susan, 
Can't help but mention a viola joke (yes, in string world viola jokes are a "thing"):
Q: how many violists does it take to change a light bulb?
A: One. And all the rest to argue how Primrose would have done it.

------------------------------
Scott Cole, RPT
rvpianotuner.com
Talent, OR
(541-601-9033
------------------------------

Original Message:
Sent: 05-31-2019 12:03
From: Susan Kline
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

Good for you, Roshan. I think you have all of this exactly right.

In a way, string players have the best of all the options, with their capacity for adaptive just intonation. However, being human, few of them achieve what is theoretically possible for them.

At Banff in 1980, I got the chance to meet William Primrose, who was tremendously admired by my cello class when I was a student. At the reception the first night, he drank gin with a splash of tonic water (newly arrived at 8000 feet, too) and I drank tonic water, no gin. I nervously trotted out my carefully planned question: "Do your students have trouble adjusting to equal temperament when they are playing with piano?" And he sighed, "Oh, if only they could play as well in tune as the piano!"

------------------------------
Susan Kline
Philomath, Oregon

Original Message:
Sent: 05-31-2019 07:04
From: Roshan Kakiya
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

The most important lesson that I have learned after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation is that perfection cannot be achieved in the theoretical world of tuning.

Something must always be compromised in order to gain something else. This statement is true for all tuning systems:

• Equal temperament. Symmetry is completely gained and key colour is completely lost.
• Meantone temperament. Purer thirds are gained and a wolf fifth emerges.
• Unequal temperament. Some intervals are more pure and some intervals are less pure.
• Just intonation. Harmony is maximised and commas emerge.
• Adaptive just intonation. It makes just intonation practical and it cannot be used for instruments of fixed pitch.

However, the ideal theoretical compromise can be achieved.

It can be achieved by striving for two things. Those two things are simplicity and practicality.

Equal temperament is the simplest and most practical tuning system due to its complete symmetry and consistency.

It solves the commas of just intonation, tames the wolf fifth of meantone temperament, is much more mathematically simple than unequal temperament and can be used for instruments of fixed and variable pitch, unlike adaptive just intonation.

Therefore, equal temperament is the ideal theoretical compromise.

This is the conclusion that I have reached after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation.

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

<grin>

However Primrose would have done it, he would have had a very decided opinion about it.

------------------------------
Susan Kline
Philomath, Oregon
------------------------------

Original Message:
Sent: 06-01-2019 10:36
From: Scott Cole
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

Susan,
Can't help but mention a viola joke (yes, in string world viola jokes are a "thing"):
Q: how many violists does it take to change a light bulb?
A: One. And all the rest to argue how Primrose would have done it.

------------------------------
Scott Cole, RPT
rvpianotuner.com
Talent, OR
(541-601-9033

Original Message:
Sent: 05-31-2019 12:03
From: Susan Kline
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

Good for you, Roshan. I think you have all of this exactly right.

In a way, string players have the best of all the options, with their capacity for adaptive just intonation. However, being human, few of them achieve what is theoretically possible for them.

At Banff in 1980, I got the chance to meet William Primrose, who was tremendously admired by my cello class when I was a student. At the reception the first night, he drank gin with a splash of tonic water (newly arrived at 8000 feet, too) and I drank tonic water, no gin. I nervously trotted out my carefully planned question: "Do your students have trouble adjusting to equal temperament when they are playing with piano?" And he sighed, "Oh, if only they could play as well in tune as the piano!"

------------------------------
Susan Kline
Philomath, Oregon

Original Message:
Sent: 05-31-2019 07:04
From: Roshan Kakiya
Subject: Striving for Unachievable Perfection in the Theoretical World of Tuning

The most important lesson that I have learned after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation is that perfection cannot be achieved in the theoretical world of tuning.

Something must always be compromised in order to gain something else. This statement is true for all tuning systems:

• Equal temperament. Symmetry is completely gained and key colour is completely lost.
• Meantone temperament. Purer thirds are gained and a wolf fifth emerges.
• Unequal temperament. Some intervals are more pure and some intervals are less pure.
• Just intonation. Harmony is maximised and commas emerge.
• Adaptive just intonation. It makes just intonation practical and it cannot be used for instruments of fixed pitch.

However, the ideal theoretical compromise can be achieved.

It can be achieved by striving for two things. Those two things are simplicity and practicality.

Equal temperament is the simplest and most practical tuning system due to its complete symmetry and consistency.

It solves the commas of just intonation, tames the wolf fifth of meantone temperament, is much more mathematically simple than unequal temperament and can be used for instruments of fixed and variable pitch, unlike adaptive just intonation.

Therefore, equal temperament is the ideal theoretical compromise.

This is the conclusion that I have reached after thoroughly experimenting with the mathematics of equal temperament, unequal temperament and just intonation.

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