"Pythagorean Temperament"
'Pythagorean Temperament' involves the Pythagorean Comma (aka Comma of Pythagoras). Whilst mentioned, it's not spelled out as such here: https://en.m.wikipedia.org/wiki/Pythagorean_comma
Music and Geometry: Intervals and Scales
31–40 of 65 posts
Re: Music and Geometry: Intervals and Scales
#32How can I make music without knowing an instrument?
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Re: Music and Geometry: Intervals and Scales
#33There is a classical book by about the topic https://link.springer.com/book/10.1007/978-3-319-64364-9
Re: Music and Geometry: Intervals and Scales
#34Earlier quoted context omitted.
If you mean a keyboard which includes a mechanism for causing strings to vibrate, you can tune ANY such keyboard to use just intonation. What you cannot do is modulate between keys with a keyboard tuned to just intonation: it would have to be retuned for every key change. The scope of the mechanism that would be required to do this has not been implemented since the harpsichord was invented. There are synthesizers th…
This is not true. Singers and violinists can and do adjust intonation so each chord sounds (justly) in tune. The exception is if they were trained with equal tempered instruments (which is common nowadays - see Duffin, “How Equal Temperament Ruined Harmony”) or if they are playing with pre-quantized (fretted/keyed) instruments, in which case they would match the existing temperaments. So the linked article, while it…
For a professional musician you are oddly singer/violin focused. Any instrument which can physically detune while playing has their musicians do this. On wind instruments it's via the mouthpiece, any string instrument beyond violin has some flexibility etc. It's only the piano that doesn't, essentially everybody else does.
But in practise, for many music styles, it doesn't really matter. Music is so much more than whether some chord is pitch perfect in tune.
Source: Jazz musician on 6 instrument types part time professional for 25 years (other part is software engineer).
Re: Music and Geometry: Intervals and Scales
#35The diagrams look nice, but in the end of the day, they are merely nice visualizations of what's fundamentally algebra. There is not much geometry going on besides a quite simple group structure of order 12.
Whenever someone says "there's not much geometry going on" you've identified a person with little capacity for imagination
I'd love to see some imagination on that page beyond some star shapes.
Re: Music and Geometry: Intervals and Scales
#36Earlier quoted context omitted.
On singers and violinists adjusting their harmony to just intonation by fine-tuning to zero beat frequency, I wonder if anyone has made a keyboard that can do that.
If you mean a keyboard which includes a mechanism for causing strings to vibrate, you can tune ANY such keyboard to use just intonation. What you cannot do is modulate between keys with a keyboard tuned to just intonation: it would have to be retuned for every key change. The scope of the mechanism that would be required to do this has not been implemented since the harpsichord was invented. There are synthesizers th…
Eivind Groven developed a mechanical piano for playing in just intonation: http://www.joranrudi.no/mediefiler/The%20Just%20Intonation%2...
Re: Music and Geometry: Intervals and Scales
#37Earlier quoted context omitted.
If you mean a keyboard which includes a mechanism for causing strings to vibrate, you can tune ANY such keyboard to use just intonation. What you cannot do is modulate between keys with a keyboard tuned to just intonation: it would have to be retuned for every key change. The scope of the mechanism that would be required to do this has not been implemented since the harpsichord was invented. There are synthesizers th…
This is not true. Singers and violinists can and do adjust intonation so each chord sounds (justly) in tune. The exception is if they were trained with equal tempered instruments (which is common nowadays - see Duffin, “How Equal Temperament Ruined Harmony”) or if they are playing with pre-quantized (fretted/keyed) instruments, in which case they would match the existing temperaments. So the linked article, while it…
I go to a lot of choir concerts. What I've found is that I much prefer (good) choirs singing without accompanying instruments, because when there are instruments involved the harmonies always fall into equal temperament. There is a quality when they sing a cappella which simply isn't there when they don't.
Re: Music and Geometry: Intervals and Scales
#38Earlier quoted context omitted.
E.g. with a tool like this: https://nodalmusic.com/
How does this differ to Max/MSP or PureData
It has nothing in common with Max nor Pd. The latter specifiy signal flow and operators on the signal. Nodal instead represents events and time distances between them; this way you can design musical patterns; time is two dimensional, so you can draw loops; then you can associate musical information with the events and add logical operations so that your loops vary in time. It's a very nice experimenting and composition tool, especially if you don't play an instrument. See e.g. here for a tutorial: https://www.youtube.com/watch?v=tQpJi0AkFBQ.
And here are some nice composition created with Nodal: https://www.youtube.com/watch?v=y1BzGaz62PE, https://youtu.be/gi61bHLyDsU, https://www.youtube.com/watch?v=sTpyIT8dWIA.
Re: Music and Geometry: Intervals and Scales
#39I understand music and mathematics were much more closely related historically, to some extent practically regarded as the same subject, but new discoveries about this relationship are still happening in our time. One interesting finding is that the the Pythagoeran comma, i.e. tiny interval between to enharmonically equivalent notes can be constructed geometrically: https://link.springer.com/article/10.1007/s00283-022-10260-4
Re: Music and Geometry: Intervals and Scales
#40How can I make music without knowing an instrument?
IMO the question doesn't make sense.
You can't make music without learning an instrument.
Maybe the instrument is a computer with PD or DAW software but it is still a musical instrument that you have to learn to play.
There is no way around spending hours learning and practicing whatever instrument you pick.
What makes a computer hard to learn to play is that it has too many options. You don't learn anything playing trumpet for a month, then changing to piano for 2 weeks, then trying a new guitar that just came out for 2 months. That though is basically what many computer musicians do.
You need to pick the software setup and then spend a long time learning it and don't switch instruments.