10
votes
1answer
65 views

How were tuning/temperaments indicated on scores (if they ever were)?

Bradley Lehman claims that the details of the intended tuning for the Well-Tempered Claivier are encoded in the squiggle at the top of the manuscript (related wikipedia link). Are there other ...
3
votes
1answer
52 views

In C major, if the third note is 14 cents sharp from JI, does the V/VI have a third that is 28 cents sharp?

In the key of C major, the note "E" in equal temperament is 400 cents above the root, but in just intonation it would be a ratio of 5:4, or 386 cents above the root. If this is true, is it not also ...
10
votes
3answers
115 views

How does the harmonic series affect consonance?

NOTE: for the purpose of this question, assume we are talking about 12-TET and assume that references to overtones in the harmonic series are being referred to in relationship to the 12-TET note that ...
7
votes
1answer
142 views

Why is 16/9 used for the minor seventh instead of 7/4?

Does the 16/9 sound less dissonant than 7/4 (less uncomfortable) due to consisting of only the 3rd undertone (squared), or the 7/4 would sound "better" (I know, it's quite subjective what sounds good ...
7
votes
2answers
215 views

How can I play my new tenor recorder (a'=440) along with someone playing a harpsichord (a'=415)?

From an article I read online, I believe I've understood that it's possible to treat the middle C (fingers covering all holes) on the tenor as if it were a D flat, and all higher notes on the ...
17
votes
3answers
650 views

Why are pianos traditionally tuned “out of tune” at the extremes?

My understanding is that the vast majority of western music uses equal temperament, i.e. all semitones have a frequency ratio of the 12th root of 2. However I can hear in my piano that the notes at ...
9
votes
1answer
201 views

Is there a sound theoretical reason why a capella choirs “drift off” of the starting pitches in a piece?

Is the "comma pump" an empirical problem, or merely theoretical? It's a standard music theory exercise to show that certain chord progressions don't actually quite work. For example, in the ...
7
votes
3answers
711 views

How to tune open strings of the violin with a tuner?

I'm using this app to tune my violin, it supports many temperament options. What I want to do is tune the A string to 440Hz first, then comparing the other strings sympathetically to the adjacent ...
3
votes
1answer
366 views

What is the frequency interval length of k semi-tones? (k = 1…11)

Go up 12 semi-tones from frequency f on a guitar, and the frequency interval difference in terms of f is f = 2f - f. What is the formula for the intermediate 11 non-trivial intervals? So for k=2, ...
16
votes
4answers
966 views

Software for microtonal MIDI?

I'm looking to make some microtonal music (19/22 tone equal temperament). I want to produce it with midi. Timidity++ used to be able to produce a WAV file from a microtonal tuned .MID file, but it is ...
6
votes
1answer
193 views

Non-fixed-frequency instruments playing by themselves versus with fixed-frequency instruments

[I don't know a better term than "non-fixed frequency instruments" but I mean things like string instruments, voice, trombone as opposed to things like a piano which has a fixed (typically 12-et) ...
6
votes
1answer
285 views

Evidence of Just Intonation in Recordings with Non-fixed-frequency Instruments

I wonder the extent to which string quartets or a cappella choirs are non-ET. They are often cited as examples of the tendency towards just intonation when not using fixed-frequency instruments but ...
30
votes
9answers
6k views

Why are orchestras tuned differently?

In 1936 American Standards Association (and the International Organization for Standardization in 1955) accepted that A would be tuned at 440 Hz (or cycles per second). Yet despite the fact that a ...
28
votes
10answers
2k views

Software that allows playing in different temperaments

Do you know of any software out there that will allow me to play in different musical temperaments (e.g. Well temperament and Meantone temperament)? I'm especially interested in software that accepts ...