Educated guess: Sid has never tuned a piano.
Piano Tuning
61–70 of 71 posts
Re: Piano Tuning
#62Earlier quoted context omitted.
For this exact reason, in music theory, the perfect fifth is seen as a note that amplifies/emboldens the root note of a chord and does not add a particular harmonic color. In jazz it's often left out to open up chords more (i.e. not muddy the frequency distribution with too many adjacent notes unless you explicitly want the powerful sound). In pop the nondescript nature is used to create a strong sense of grounding i…
For sure. It still doesn't explain why the octave is the specific point where the cycle of pitch perception repeats. The perfect fifth is very consonant, for sure, but there is no "perfect fifth equivalence" in any musical traditional as far as I know.
Note that there is no harmonic that is a perfect fifth above the fundamental; the first harmonic is the octave. So if cycles of perception have to be based on harmonics (multiples of frequencies), the next plausible one after octaves (2f) would be based on the perfect 12 (3f), rather than the 5th (3f/2). The 4f based cycle is really just octaves again, except we're skipping every other octave. It gets too distant after that. Maybe the 3f progression does contain a cycle of pitch perception; I will try giving that a listen.
Re: Piano Tuning
#63Equal temperament just means equally out of tune. Minute physics does a great video on it: https://youtu.be/1Hqm0dYKUx4
Equal temperament is certainly not "equally out of tune". It has terrific octaves and very good fourths and fifths, compared to some other intervals.
It really does mean equal geometric steps between successive tones.
Each key is equally "out of tune" under equal temperament; e.g. C# minor and D minor are basically the same, modulo pitch.
Re: Piano Tuning
#64Reminds me of Bach's 'The Well-Tempered Clavier' It's written in all 24 major/minor keys so your keyboard needs to be well tempered :) https://en.m.wikipedia.org/wiki/The_Well-Tempered_Clavier
It's 48 because Bach did it all again in book II of the Well-Tempered Clavier. And really, it's 96 because there is both a prelude and a fugue for each key. And if you think about it, it's 48 + (48 * x) where x is the average number of voices in the fugue. And then at least a few of those are double and triple fugues, so I guess a forEach statement in there to multiple by 2 or 3 for those cases. So if you were an org…
Hmm, I think there is only 24maj/min keys in traditional western harmony. If you write 100 different pieces using 2 keys: C or G, you've still only used 2 keys. But I don't want to argue about set theory :)
Re: Piano Tuning
#65Earlier quoted context omitted.
It's 48 because Bach did it all again in book II of the Well-Tempered Clavier. And really, it's 96 because there is both a prelude and a fugue for each key. And if you think about it, it's 48 + (48 * x) where x is the average number of voices in the fugue. And then at least a few of those are double and triple fugues, so I guess a forEach statement in there to multiple by 2 or 3 for those cases. So if you were an org…
Hmm, I think there is only 24maj/min keys in traditional western harmony. If you write 100 different pieces using 2 keys: C or G, you've still only used 2 keys. But I don't want to argue about set theory :)
Maybe your point is it 'switches' keys (48*x)
Re: Piano Tuning
#66Earlier quoted context omitted.
> And, most importantly to me, since it’s the question I can find the least solid information on: why do we take for granted that one note with twice the frequency of another note sounds so similar that we call both notes by the same name? I have a pretty good understanding of other details of music theory, but I’ve never gotten a straight answer on why (and indeed to what extent) octave equivalence exists. I don't k…
Vocal cords have even more pronounced overtones than strings. To a first approximation, they produce a series of pulses. And we are exposed to these harmonic-rich sounds from the womb. It would be an interesting (and perhaps cruel) experiment to expose babies to synthesized sounds that have a harmonic structure with different mathematics. For example, sounds with lots of sqrt(2) frequency ratios.
The ear itself produces some harmonic distortion, at moderate levels. I don't know if that's important enough to play a role in our pitch perception though.
Re: Piano Tuning
#67Earlier quoted context omitted.
It's 48 because Bach did it all again in book II of the Well-Tempered Clavier. And really, it's 96 because there is both a prelude and a fugue for each key. And if you think about it, it's 48 + (48 * x) where x is the average number of voices in the fugue. And then at least a few of those are double and triple fugues, so I guess a forEach statement in there to multiple by 2 or 3 for those cases. So if you were an org…
Hmm, I think there is only 24maj/min keys in traditional western harmony. If you write 100 different pieces using 2 keys: C or G, you've still only used 2 keys. But I don't want to argue about set theory :)
Ah yeah, I wrote that incorrectly. I meant that Bach went back and did "it" again for a grand total of 48 prelude/fugue pairs.
Re: Piano Tuning
#68Hm... here's a question:
The G# minor fugue in Book II of Bach's WTC has a rather long sequence around the circle fifths. It starts on E# minor.
Did the well-tempered tuning system open up the possibility for Bach to start writing longer chromatic sequences like that? Would that sequence have sounded out of tune in the meantone tuning system?
Re: Piano Tuning
#69Was really hoping to land on an app that would help you tune it.
Re: Piano Tuning
#70Earlier quoted context omitted.
For sure. It still doesn't explain why the octave is the specific point where the cycle of pitch perception repeats. The perfect fifth is very consonant, for sure, but there is no "perfect fifth equivalence" in any musical traditional as far as I know.
Note that there is no harmonic that is a perfect fifth above the fundamental; the first harmonic is the octave. So if cycles of perception have to be based on harmonics (multiples of frequencies), the next plausible one after octaves (2f) would be based on the perfect 12 (3f), rather than the 5th (3f/2). The 4f based cycle is really just octaves again, except we're skipping every other octave. It gets too distant aft…
I tried this! Eerily, I'm able to convince my ear/brain that this 12th interval is an octave-like relationship; that the two notes have a sameness (that I don't perceive in the case of the perfect fifth that we normally consider enharmonic with the 12th, giving it the same letter name).
Come to think of it, a lot of western harmony is based on a two-octave "gamut". Like for instance alterations to chords such as dominants take place close to this "3f octave" (dodecade?) 12th interval, like the like 11th, 13th. The usual explanation is that if these alterations are in the higher octave, it prevents certain dissonances. But from the "3f octave" view, we can just regard them as different notes; that the 13th is not simply the 6th, only one octave higher, but rather an "augmented dodecave" interval.