Welcome to the Piano World Piano Forums
Over 2.7 million posts about pianos, digital pianos, and all types of keyboard instruments
Join the World's Largest Community of Piano Lovers (it's free)
It's Fun to Play the Piano ... Please Pass It On!

SEARCH
Piano Forums & Piano World
What's Hot!!
New in our online store...
Tea Light
Tea Light with Frosted Music Staff Candle Holder


-------------------
European Tour for Piano Lovers
JOIN US FOR THE TOUR!
--------------------
Posting Pictures on the Forums
-------------------
Forums RULES & HELP
-------------------
ADVERTISE on Piano World
Find a Professional
Our Classified Ads
Find Piano Professionals-

*Piano Dealers - Piano Stores
*Piano Tuners
*Piano Teachers
*Piano Movers
*Piano Restorations
*Piano Manufacturers

Advertise on Piano World

(ad)
Piano Buyer Guide
Piano Buyer Spring 2018
ad
Pierce Piano Atlas


Who's Online Now
118 registered members (ajames, anotherscott, Aaron W, akc42, Bambers, 29 invisible), 1,426 guests, and 5 spiders.
Key: Admin, Global Mod, Mod
(ad)
Estonia Pianos
Estonia Pianos
Quick Links to Useful Piano & Music Resources
Quick Links:
*Advertise On Piano World
*Free Piano Newsletter
*Online Piano Recitals
*Piano Recitals Index
*Piano & Music Accessories
*Live Piano Venues
*Music School Listings
* Buying a Piano
*Buying A Acoustic Piano
*Buying a Digital Piano
*Pianos for Sale
*Sell Your Piano
*How Old is My Piano?
*Directory/Site Map
*Virtual Piano
*Music Word Search
*Piano Videos
*Virtual Piano Chords & Scales
Previous Thread
Next Thread
Print Thread
Page 1 of 4 1 2 3 4
Why do most modern pianos contain 88 keys? #2743364
06/10/18 07:43 AM
06/10/18 07:43 AM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
I have created a formula that seems to correctly identify the number of keys that fit within a given quantity of a specified interval:

x = yz + 1.

x = The number of keys.
y = The number of semitones within a specified interval.
z = The quantity of the specified interval.


Example 1:

The specified interval is the octave which contains 12 semitones. There are 7 octaves.

Therefore, y = 12 and z = 7:

x = 12 × 7 + 1 = 85 keys.


Example 2:

The specified interval is the perfect fifth which contains 7 semitones. There are 12 perfect fifths.

Therefore, y = 7 and z = 12:

x = 7 × 12 + 1 = 85 keys.


We can say, at this point, that only 85 keys are needed to close the circle of fifths.


Why do most modern pianos contain 88 keys if only 85 keys are needed to close the circle of fifths?


Revised formula for modern pianos:

x = yz + 1 + 3 = yz + 4.

Verification:

An octave contains 12 semitones and there are 7 octaves.

x = 12 × 7 + 4 = 88 keys.


Example 3:

The Bösendorfer Model 290 Imperial contains 8 octaves and 97 keys. We can use the original formula to verify this.

x = 12 × 8 + 1 = 97 keys.

Why does this piano not contain 3 more keys? We can use the revised formula to calculate the number of keys it should have based on the design of most modern pianos:

x = 12 × 8 + 4 = 100 keys.


Why does the design of the Bösendorfer Model 290 Imperial not match the design of most modern pianos?

(ad)
Piano & Music Accessories
piano accessories music gifts tuning and moving equipment
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743373
06/10/18 09:27 AM
06/10/18 09:27 AM
Joined: May 2001
Posts: 23,516
New York City
pianoloverus Offline
Yikes! 10000 Post Club Member
pianoloverus  Offline
Yikes! 10000 Post Club Member
Joined: May 2001
Posts: 23,516
New York City
Because your "formula" was designed to match 88 key piano. There's no reason why a piano with a different number of keys should be described by your formula. The number of keys on a piano at any point in the piano's history has nothing to do with your formula.

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743375
06/10/18 09:30 AM
06/10/18 09:30 AM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
I think the design of the Bösendorfer Model 290 Imperial is much better than the design of most modern pianos because it contains 8 complete octaves (97 keys) rather than 7 octaves plus a fraction of an octave (88 keys).

88 keys also contain 12 perfect fifths plus a fraction of a perfect fifth so the use of 88 keys is not ideal.

I think pianos with 92 keys are good as well because they contain 13 complete perfect fifths:

x = 7 × 13 + 1 = 92 keys.

Conclusion:

I think a piano with 85 keys is mathematically ideal because 12 perfect fifths = 7 octaves. However, it is not likely to be practically ideal because pianos with 88 keys have been invented which means there are likely to be pieces that utilise the extra 3 keys that are available.

A piano with 97 keys is more practical because every piece that has been composed for a piano with 88 keys can be played on it and it also contains 8 complete octaves. However, it may be difficult to distinguish between the highest and the lowest notes since their sound may be too low or too high for the ears.

Overall, I think a piano with 92 keys is ideal. This is because it contains 13 complete perfect fifths, the ears will probably be able to distinguish between its highest and lowest notes and every piece that has been composed for a piano with 88 keys can be played on it.

The range of the keyboard seems to be getting larger as time passes by. Therefore, a piano with 97 keys could become ideal in the future if many pieces that utilise its extra keys have been composed. I do not think a piano with more than 97 keys is likely to be practical because it may be very difficult, or maybe nearly impossible, for the ears to distinguish between the sound of its highest and lowest notes.

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743377
06/10/18 09:39 AM
06/10/18 09:39 AM
Joined: May 2001
Posts: 23,516
New York City
pianoloverus Offline
Yikes! 10000 Post Club Member
pianoloverus  Offline
Yikes! 10000 Post Club Member
Joined: May 2001
Posts: 23,516
New York City

The number of keys on the piano at various stages in its development is not related to the mathematical thinking you expressed. What you consider to be "mathematically ideal" is not relevant.

Last edited by pianoloverus; 06/10/18 09:40 AM.
(ad ) MusicNotes.com
sheet music search
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743378
06/10/18 09:40 AM
06/10/18 09:40 AM
Joined: Jun 2016
Posts: 236
Maryland, USA
D
Davdoc Offline
Full Member
Davdoc  Offline
Full Member
D
Joined: Jun 2016
Posts: 236
Maryland, USA
I equally do not see the point of your formula. You made your formula to fit into current piano designs.

For example, in (Western) music system, the most commonly used intervals are 12 semitones within one octave. This is not necessarily the case with other systems. One can argue that a different piano can be designed to have 22 keys within one octave.

I also don't get why specifically 12 perfect fifths are ideal. 12 perfect fifths (1.5 ^ 12) later, you arrive 129.746 x base frequency, which deviates from the "ideal" octave of 128 x base frequency. One can also argue whether fifths are more "harmonious" than octaves.


1969 Hamburg Steinway B, rebuilt by PianoCraft in 2017
2013 New York Steinway A
Kawai MP11

Previously: 2005 Yamaha GB1, 1992 Yamaha C5
Re: Why do most modern pianos contain 88 keys? [Re: pianoloverus] #2743379
06/10/18 09:41 AM
06/10/18 09:41 AM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
Originally Posted by pianoloverus
The number of keys on a piano at any point in the piano's history has nothing to do with your formula.


Pianos in the past contained 85 keys. I cannot think of any other way to justify the use of 85 keys. Please do share another reason, other than 12 perfect fifths = 7 octaves = 85 keys, that justifies the use of 85 keys if you can do that.

Re: Why do most modern pianos contain 88 keys? [Re: Davdoc] #2743381
06/10/18 09:49 AM
06/10/18 09:49 AM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
Originally Posted by Davdoc
I also don't get why specifically 12 perfect fifths are ideal. 12 perfect fifths (1.5 ^ 12) later, you arrive 129.746 x base frequency, which deviates from the "ideal" octave of 128 x base frequency. One can also argue whether fifths are more "harmonious" than octaves.


12-tone equal temperament and well-temperament solve that problem.

12-tone equal temperament:

12 perfect fifths = (2 ^ (7/12)) ^ 12 = 128.

7 octaves = 2 ^ 7 = 128.

Therefore, 12 perfect fifths = 7 octaves.

x = 12 (the number of semitones within an octave) × 7 (7 octaves = 12 perfect fifths) + 1 = 85 keys.

This proves that a piano with 85 keys is mathematically ideal, although it is no longer practically ideal because pieces have probably been composed that utilise the extra 3 keys of a piano with 88 keys.

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743385
06/10/18 10:17 AM
06/10/18 10:17 AM
Joined: Mar 2006
Posts: 11,874
Georgia, USA
Rickster Offline
Yikes! 10000 Post Club Member
Rickster  Offline
Yikes! 10000 Post Club Member
Joined: Mar 2006
Posts: 11,874
Georgia, USA
I'm not sure where that formula came from or how important it is in the scheme of all things pianos. But, quite frankly, I just like the evenly rounded number of 88 keys beginning with A0 and ending with C88. Although, I would venture to say that most pianists/players rarely or never use A0 or C88. It's like the saying it is better to have it and not need it than to need it and not have it.

As far as any mathematical formula proving to be ideal, it's like saying algebra is something you use throughout your life every single day. Hence, theory and reality are often two different things, proven or not.

Interesting discussion...

Rick


Piano enthusiast and amateur musician: "Treat others the way you would like to be treated". Yamaha C7. YouTube Channel
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743386
06/10/18 10:18 AM
06/10/18 10:18 AM
Joined: Jun 2003
Posts: 26,151
Oakland
B
BDB Offline
Yikes! 10000 Post Club Member
BDB  Offline
Yikes! 10000 Post Club Member
B
Joined: Jun 2003
Posts: 26,151
Oakland
This is all numerology. Most pianos have 88 keys because if you have any more in the treble, it is difficult to fit the mechanism in, and if you have any more in the bass, it is difficult to make the tones distinct enough to distinguish. There are pianos that have more than 88 keys, but they are very large pianos (> 7 feet) with extra notes in the bass. Making a small piano with more than 88 keys is difficult and pointless, and most pianos are small. Since most pianos have 88 keys, that is what composers write for, There is little point to write music that most people would not be able to play.

If you want to do some mathematics that will show this, look at the difference in frequency of the lowest notes of the piano, and the geometry of the highest notes.


Semipro Tech
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743388
06/10/18 10:20 AM
06/10/18 10:20 AM
Joined: Feb 2005
Posts: 3,324
Urbandale, Iowa
S
Steve Chandler Offline
3000 Post Club Member
Steve Chandler  Offline
3000 Post Club Member
S
Joined: Feb 2005
Posts: 3,324
Urbandale, Iowa
As others have pointed out math has nothing to do with the range of a piano. In Beethoven's time he wanted more notes and some of his pieces show the range limitations of the pieces of his time. The invention of the iron frame allowed the range to go higher. You don't find composers asking for higher notes anymore. The addition of lower notes in the Bosendorfer Imperial is more to move the more commonly used low notes farther into the soundboard than to extend the low range of the instrument. The piano is a musical instrument and its development was driven by musical considerations not mathematical. I've yet to hear a piece that consists of perfect fifths from the bottom to the top.

Re: Why do most modern pianos contain 88 keys? [Re: Rickster] #2743389
06/10/18 10:22 AM
06/10/18 10:22 AM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
I think it is extremely interesting that Bösendorfer's Grand Piano 225 contains 92 keys:

https://www.boesendorfer.com/en/pianos/pianos/grand-piano-225.

Mathematically, 13 perfect fifths = 92 keys.

I doubt that everything I have posted on this thread is a mathematical accident.

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743392
06/10/18 10:33 AM
06/10/18 10:33 AM
Joined: Mar 2013
Posts: 831
Germany
P
patH Offline
500 Post Club Member
patH  Offline
500 Post Club Member
P
Joined: Mar 2013
Posts: 831
Germany
Humans can hear frequencies from 20 to 20.000 Hz.
And they have trouble distinguishing notes in the extreme frequencies.

So, 88 keys is ok.
If dogs could play the piano, there would be instruments with 10 or more octaves, I guess.


Everything is possible, and nothing is sure.
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743395
06/10/18 10:55 AM
06/10/18 10:55 AM
Joined: May 2001
Posts: 23,516
New York City
pianoloverus Offline
Yikes! 10000 Post Club Member
pianoloverus  Offline
Yikes! 10000 Post Club Member
Joined: May 2001
Posts: 23,516
New York City
Originally Posted by Roshan Kakiya
Originally Posted by pianoloverus
The number of keys on a piano at any point in the piano's history has nothing to do with your formula.


Pianos in the past contained 85 keys. I cannot think of any other way to justify the use of 85 keys. Please do share another reason, other than 12 perfect fifths = 7 octaves = 85 keys, that justifies the use of 85 keys if you can do that.
That ONE particular compass MIGHT have been used to have an integer number of octaves but it could have also been for purely musical(how high they could make notes that sounded musical at the time) or aesthetic(not ending on a black key) or design construction(as BDB explained) reasons.

As virtually every responder has indicated, trying to use a formula to describe a totally subjective mathematical ideal for the number of keys on a piano is not relevant.



Last edited by pianoloverus; 06/10/18 11:04 AM.
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743397
06/10/18 11:05 AM
06/10/18 11:05 AM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
A piano with 88 keys is an ideal compromise. That is the only thing I seem to have clarified. ha

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743402
06/10/18 11:17 AM
06/10/18 11:17 AM
Joined: Oct 2010
Posts: 10,503
B
bennevis Online content
Yikes! 10000 Post Club Member
bennevis  Online Content
Yikes! 10000 Post Club Member
B
Joined: Oct 2010
Posts: 10,503
Originally Posted by Roshan Kakiya
I think the only thing I have made clear is that a piano with 88 keys is an ideal compromise.

That's right.

88 is a nice round number: not too big (like 100) and not too small (like 76); in other words, just nice. thumb

Also, it's divisible by 2, 4, 6 (OK, not 6 cry), 8 and 11. Therefore it's not a prime number.

Last but not least, anyone with long enough arms can play my latest opus, which requires the pianist to play both the top C and the bottom A simultaneously and repeatedly without strain. Whereas the Bösendorfer Imperial would be a bit of a stretch for a pianist to play the notes at both extremities of the keyboard at the same time without an arm extension........


"I don't play accurately - anyone can play accurately - but I play with wonderful expression. As far as the piano is concerned, sentiment is my forte. I keep science for Life."
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743417
06/10/18 12:17 PM
06/10/18 12:17 PM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
Originally Posted by Roshan Kakiya
I have created a formula that seems to correctly identify the number of keys that fit within a given quantity of a specified interval:

x = yz + 1.

x = The number of keys.
y = The number of semitones within a specified interval.
z = The quantity of the specified interval.


This general formula really is useful. It is not tied to any specific keyboard instrument. It is just an easy way to calculate the number of keys a keyboard contains, without counting, if the number of octaves (or any other interval) it contains is known.

For example, a keyboard which contains 5 octaves has 61 keys:

x = 12 (number of semitones within an octave) × 5 (number octaves this specific keyboard contains) + 1 = 61 keys.

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743421
06/10/18 12:45 PM
06/10/18 12:45 PM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
Final example:

x = 12 × 7.25 + 1 = 88 keys.

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743425
06/10/18 01:08 PM
06/10/18 01:08 PM
Joined: May 2006
Posts: 4,499
Georgia, USA
terminaldegree Offline
4000 Post Club Member
terminaldegree  Offline
4000 Post Club Member
Joined: May 2006
Posts: 4,499
Georgia, USA
Originally Posted by Roshan Kakiya
I think the design of the Bösendorfer Model 290 Imperial is much better than the design of most modern pianos because it contains 8 complete octaves (97 keys) rather than 7 octaves plus a fraction of an octave (88 keys).

88 keys also contain 12 perfect fifths plus a fraction of a perfect fifth so the use of 88 keys is not ideal.

I think pianos with 92 keys are good as well because they contain 13 complete perfect fifths:

x = 7 × 13 + 1 = 92 keys.

Conclusion:

I think a piano with 85 keys is mathematically ideal because 12 perfect fifths = 7 octaves. However, it is not likely to be practically ideal because pianos with 88 keys have been invented which means there are likely to be pieces that utilise the extra 3 keys that are available.



A piano with 85 keys is usable, but it is not ideal because 88 key pianos have been commonly in existence, and the standard, for over 120 years, so just about anything written back through the impressionist period might use the top 3 notes. The mathematical relevance you cite is arbitrary and not supported by any composer's methodology I remember reading.

The design of the Imperial (and other > 88 key instruments, by association) is not "much better", it's just different, and was brought about because some composers in the early 20th century wanted to experiment with low sub-bass notes, and collaborated with the builder. If you've actually seen and played an Imperial, the fundamental pitch clarity of the sub bass notes is practically inaudible, however the clarity of the lowest notes down to the more traditional A0 on this piano is always magnificent, because A0 isn't all the way out at the edge of the bass bridge, near the rim. Since pianists are used to seeing the traditional 88-key setup for about 120 years, some of us (not me, but some of my colleagues) find the visual presence of the extra sub-bass keys to be disorienting, when playing and especially leaping to the lowest pitches on the piano. Finally, I believe the sheer size of more-than 88-key concert pianos, regardless of brand (when you factor in the cheek blocks and necessary thickness of the rim) are troublesome because they do not fit through the width of most double doorways, according to many building codes, which put them at a disadvantage when managing a stage area without costly customizations. Just like in marketing, it's unwise to use one parameter, in a vacuum, as justification for an instrument's absolute superiority.



Pianist, teacher, apprentice technician, internet addict.
Piano Review Editor - Acoustic and Digital Piano Buyer
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743451
06/10/18 02:42 PM
06/10/18 02:42 PM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
Quote
In the late 1880s, piano manufacturer Steinway created the 88-key piano. Other manufacturers followed suit, and Steinway’s model has been the standard ever since.


Source: https://www.classicfm.com/discover-music/instruments/piano/why-pianos-have-88-keys/

Quote
Steinway & Sons manufactured the first piano with 88 keys in 1869.

It was said that after Steinway & Sons introduced 88-key pianos, other piano makers followed suit in a competitive move, and this configuration stabilised since.


Source: https://www.thepiano.sg/piano/read/why-does-piano-have-88-keys

Quote
By the middle of the 19th century, pianos typically had 85 keys. By the end of the century, pianos began to emerge with the now standard 88 keys. It wasn’t really until the late 1880s when 88 keys became standard on pianos.


Source: https://livingpianos.com/piano-questions/when-did-88-keys-become-standard-on-the-piano/


How did Steinway & Sons decide to manufacture pianos with 88 keys rather than 85 keys?

What was the rationale behind this design change?

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743460
06/10/18 03:02 PM
06/10/18 03:02 PM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
Did Steinway & Sons do this to differentiate its pianos from pianos that were produced by other manufacturers in order to gain a competitive edge?

Did other manufacturers also produce pianos with 88 keys to compete with Steinway & Sons?

Did the abundance of pianos with 88 keys cause the eventual standardisation of the 88-key piano?

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743469
06/10/18 04:01 PM
06/10/18 04:01 PM
Joined: Aug 2007
Posts: 1,885
R
Rank Piano Amateur Offline
1000 Post Club Member
Rank Piano Amateur  Offline
1000 Post Club Member
R
Joined: Aug 2007
Posts: 1,885
I think that modern pianos have 88 keys because modern pianos have 88 keys. . . . A lot about musical instrument (and other) design can be attributed to tradition; there may be no other explanation.

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743514
06/10/18 07:38 PM
06/10/18 07:38 PM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177



Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743521
06/10/18 08:12 PM
06/10/18 08:12 PM
Joined: Aug 2012
Posts: 856
B
Bosendorff Offline
500 Post Club Member
Bosendorff  Offline
500 Post Club Member
B
Joined: Aug 2012
Posts: 856
The answer to your question is :

[Linked Image]

Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743548
06/10/18 11:02 PM
06/10/18 11:02 PM
Joined: Jun 2017
Posts: 167
Taipei, Taiwan
K
Kenny Cheng Offline
Full Member
Kenny Cheng  Offline
Full Member
K
Joined: Jun 2017
Posts: 167
Taipei, Taiwan
If Chopin and Liszt had 97 key pianos, would they have written music differently?

Re: Why do most modern pianos contain 88 keys? [Re: Kenny Cheng] #2743549
06/10/18 11:24 PM
06/10/18 11:24 PM
Joined: Jun 2003
Posts: 26,151
Oakland
B
BDB Offline
Yikes! 10000 Post Club Member
BDB  Offline
Yikes! 10000 Post Club Member
B
Joined: Jun 2003
Posts: 26,151
Oakland
Probably not much differently. Now, if they had pencils with erasers, or ball-point pens, that would have made a real difference!


Semipro Tech
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743577
06/11/18 04:49 AM
06/11/18 04:49 AM
Joined: Mar 2013
Posts: 831
Germany
P
patH Offline
500 Post Club Member
patH  Offline
500 Post Club Member
P
Joined: Mar 2013
Posts: 831
Germany
C Major is a popular key. A is the note used to tune.

The only problem with 88 keys is that in Germany, piano lovers should avoid naming their clubs with an 88 in it.
In Germany, since 1933, 88 has another connotation than pianos; one that non-extremists should try to avoid.


Everything is possible, and nothing is sure.
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743593
06/11/18 08:27 AM
06/11/18 08:27 AM
Joined: May 2017
Posts: 386
Rural UK
F
Fareham Online content
Full Member
Fareham  Online Content
Full Member
F
Joined: May 2017
Posts: 386
Rural UK
Originally Posted by Roshan Kakiya
I think a piano with 85 keys is mathematically ideal because 12 perfect fifths = 7 octaves.


Well, it's not. Pythagorus discovered this around 2500 years ago. The circle of 12 perfect fifths is a frequency ratio of 129.75 (approx) while 7 octaves is a frequency ratio of 128.

JS Bach and a few others in the late 17th / early 18th century sought to correct this by 'fudging' the intervals. Bach showed it worked in all 24 keys by writing "The Well-tempered Klavier". Being so popular he did another 24, and hence the '48'.


The English may not like music much, but they love the sound it makes ... Beecham
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743604
06/11/18 09:44 AM
06/11/18 09:44 AM
Joined: Mar 2018
Posts: 177
R
Roshan Kakiya Online blank OP
Full Member
Roshan Kakiya  Online Blank OP
Full Member
R
Joined: Mar 2018
Posts: 177
Originally Posted by Fareham
Well, it's not. Pythagorus discovered this around 2500 years ago. The circle of 12 perfect fifths is a frequency ratio of 129.75 (approx) while 7 octaves is a frequency ratio of 128.


That is the famous Pythagorean comma which has a value of 23.46 cents.

Originally Posted by Fareham
JS Bach and a few others in the late 17th / early 18th century sought to correct this by 'fudging' the intervals. Bach showed it worked in all 24 keys by writing "The Well-tempered Klavier". Being so popular he did another 24, and hence the '48'.


This comma was corrected a full century before J. S. Bach was born (1685 - 1584 = 101). Zhu Zaiyu invented 12-tone equal temperament during the late 16th century in 1584:

Quote
In 1584, Zhu Zaiyu was the first in the world to systematically calculate the equal temperament of the music scale. His book, New Rule of Equal Temperament, explains a system using 12 equal intervals that is identical with that used around the world today.


Source: http://pl.china-embassy.org/pol/wh/wh/t129181.htm.


Here are more sources that confirm this:

https://www.teoria.com/en/articles/temperaments/05-equal-temperament.php

https://books.google.co.uk/books?id...%20temperament%20zhu%20zaiyu&f=false


12 perfect fifths = 7 octaves = 85 keys. This is mathematically ideal and it can be achieved by using either 12-tone equal temperament or well temperament because they both eliminate the Pythagorean comma. Therefore, everything I have said in the following quote is correct:

Originally Posted by Roshan Kakiya
Originally Posted by Davdoc
I also don't get why specifically 12 perfect fifths are ideal. 12 perfect fifths (1.5 ^ 12) later, you arrive 129.746 x base frequency, which deviates from the "ideal" octave of 128 x base frequency.


12-tone equal temperament and well-temperament solve that problem.

12-tone equal temperament:

12 perfect fifths = (2 ^ (7/12)) ^ 12 = 128.

7 octaves = 2 ^ 7 = 128.

Therefore, 12 perfect fifths = 7 octaves.

x = 12 (the number of semitones within an octave) × 7 (7 octaves = 12 perfect fifths) + 1 = 85 keys.

This proves that a piano with 85 keys is mathematically ideal, although it is no longer practically ideal because pieces have probably been composed that utilise the extra 3 keys of a piano with 88 keys.


The 85-key keyboard is only mathematically ideal. It is no longer practically ideal.

The 88-key keyboard has been standard for many years now. Therefore, it is practically ideal. It seems to be just right because it has been effective for many years.


Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743623
06/11/18 12:19 PM
06/11/18 12:19 PM
Joined: Jun 2016
Posts: 236
Maryland, USA
D
Davdoc Offline
Full Member
Davdoc  Offline
Full Member
D
Joined: Jun 2016
Posts: 236
Maryland, USA
Originally Posted by Roshan Kakiya
Originally Posted by Fareham
Well, it's not. Pythagorus discovered this around 2500 years ago. The circle of 12 perfect fifths is a frequency ratio of 129.75 (approx) while 7 octaves is a frequency ratio of 128.


That is the famous Pythagorean comma which has a value of 23.46 cents.

Originally Posted by Fareham
JS Bach and a few others in the late 17th / early 18th century sought to correct this by 'fudging' the intervals. Bach showed it worked in all 24 keys by writing "The Well-tempered Klavier". Being so popular he did another 24, and hence the '48'.


This comma was corrected a full century before J. S. Bach was born (1685 - 1584 = 101). Zhu Zaiyu invented 12-tone equal temperament during the late 16th century in 1584:

Quote
In 1584, Zhu Zaiyu was the first in the world to systematically calculate the equal temperament of the music scale. His book, New Rule of Equal Temperament, explains a system using 12 equal intervals that is identical with that used around the world today.


Source: http://pl.china-embassy.org/pol/wh/wh/t129181.htm.


Here are more sources that confirm this:

https://www.teoria.com/en/articles/temperaments/05-equal-temperament.php

https://books.google.co.uk/books?id...%20temperament%20zhu%20zaiyu&f=false


12 perfect fifths = 7 octaves = 85 keys. This is mathematically ideal and it can be achieved by using either 12-tone equal temperament or well temperament because they both eliminate the Pythagorean comma. Therefore, everything I have said in the following quote is correct:

Originally Posted by Roshan Kakiya
Originally Posted by Davdoc
I also don't get why specifically 12 perfect fifths are ideal. 12 perfect fifths (1.5 ^ 12) later, you arrive 129.746 x base frequency, which deviates from the "ideal" octave of 128 x base frequency.


12-tone equal temperament and well-temperament solve that problem.

12-tone equal temperament:

12 perfect fifths = (2 ^ (7/12)) ^ 12 = 128.

7 octaves = 2 ^ 7 = 128.

Therefore, 12 perfect fifths = 7 octaves.

x = 12 (the number of semitones within an octave) × 7 (7 octaves = 12 perfect fifths) + 1 = 85 keys.

This proves that a piano with 85 keys is mathematically ideal, although it is no longer practically ideal because pieces have probably been composed that utilise the extra 3 keys of a piano with 88 keys.


The 85-key keyboard is only mathematically ideal. It is no longer practically ideal.

The 88-key keyboard has been standard for many years now. Therefore, it is practically ideal. It seems to be just right because it has been effective for many years.



Being a lay person myself, I am reasonably aware of the existence of temperament, or tempered pitch of these notes.

A "perfect" (3:2) perfect fifth, times 12 fifths, will not lead to a "perfect" (2:1) octave times 7 octaves. Temperaments exist to solve the problem by musically acceptable compromises.

So your formula still, to me, does not add anything. The current most popular design, as others mentioned above, came from a gradual process of demand, practicality, then de facto standard.


1969 Hamburg Steinway B, rebuilt by PianoCraft in 2017
2013 New York Steinway A
Kawai MP11

Previously: 2005 Yamaha GB1, 1992 Yamaha C5
Re: Why do most modern pianos contain 88 keys? [Re: Roshan Kakiya] #2743631
06/11/18 12:46 PM
06/11/18 12:46 PM
Joined: Mar 2003
Posts: 3,889
Gaithersburg, MD (Washington D...
K
Keith D Kerman Online content
3000 Post Club Member
Keith D Kerman  Online Content
3000 Post Club Member
K
Joined: Mar 2003
Posts: 3,889
Gaithersburg, MD (Washington D...
I am convinced. Anyone else who is convinced may contact me for quotes on removing 3 notes from your 88 note pianos. Quantity discounts available so ask your friends!


Keith D Kerman
PianoCraft
Rebuilding & Sales - vintage and used Steinway, Mason & Hamlin
New Steingraeber, Estonia, Baldwin
www.pianocraft.net
check out http://sitkadoc.com/
www.twitter.com/pianocraft https://www.youtube.com/user/pianocraftchannel

keith@pianocraft.net 888-840-5460
Page 1 of 4 1 2 3 4

Moderated by  Ken Knapp, Piano World 

New Topics - Multiple Forums
Nord Stage 3 vs Roland RD2000
by Jakers. 06/18/18 11:24 AM
Winter Studio Piano
by Standalone. 06/18/18 09:56 AM
theory book
by Slowdown. 06/18/18 09:17 AM
Anyone here ever play in public??
by CebuKid. 06/18/18 08:21 AM
(ad)
Pianoteq
PianoTeq Steingraeber
(125ad)
Piano Life Saver - Dampp Chaser
Dampp Chaser Piano Life Saver
(ad)
Pearl River & Ritmuller
Pearl River Pianos
Forum Statistics
Forums40
Topics186,030
Posts2,725,656
Members90,403
Most Online15,252
Mar 21st, 2010
(ad)
Accu-Tuner
Sanderson Accu-Tuner
Visit our online store for gifts for music lovers


 
Help keep the forums up and running with a donation, any amount is appreciated!
Or by becoming a Subscribing member! Thank-you.
Donate   Subscribe
 
Our Piano Related Classified Ads
| Dealers | Tuners | Lessons | Movers | Restorations | Pianos For Sale | Sell Your Piano |

Advertise on Piano World
| Subscribe | Piano World | PianoSupplies.com | Advertise on Piano World |
| |Contact | Privacy | Legal | About Us | Site Map | Free Newsletter |


copyright 1997 - 2018 Piano World ® all rights reserved
No part of this site may be reproduced without prior written permission
Powered by UBB.threads™ PHP Forum Software 7.6.1.1