# Questions tagged [temperament]

For questions generally relating to systems of note frequency assignment. Questions will often include the tuning and/or alternative-tunings tag.

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### How to listen for two cents when Tuning for equal temperament?

One difficulty when tuning a piano is to sense the difference between equal temperament and just intonation. Let's consider A=440Hz and E=(660Hz in just temperament), a perfect 5th above A. After ...
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### New equal temperament

I am searching for an equal temperament without just intervals. If one exists, all intervals will as near as possible to just position and all notes will have a constant place. If we use K to ...
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### Definition of Chromatic and Diatonic Semitone in 31 TET

I am trying to learn about music theories in 31 TET, I learned that 2 fifthtones are a chromatic semitone, 3 fifthtones are a diatonic semitone, 4 fifthtones are a neutral semitone, five fifthtones ...
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### Why is music using a temperament other than 12-TET rare today?

There are several other temperaments like 19-TET and 31-TET, but almost all modern music uses 12-TET. Why aren't the two former used more often?
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### Fret spacing for setar

What is the formula for calculating the frets spacing on the setar? It's not straightforward as the guitar because the Setar is based on the 17 tone modes of Persian scale: 256/243 27/25 9/8 32/27 243/...
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### How to calculate 21-limit just intonation

I am looking for ratios of 21-limit just intonation tuning system to later compare it with the 31-EDO tuning system since they are to some extent similar and close. How could I calculate 21-limit just ...
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### What would've given more accurate consonant ratios than 12?

So my understanding is 12 notes was chosen in a chromatic scale cause in tuning, the twelfth root of two gives values quite close to simple ratios. For example for a fifth, the twelfth root of 2 ...
268 views

### What was the earliest equal temperament system used?

What was the earliest equal temperament system used? I believe it to be 19edo, used by Guillaume Costeley in Seigneur Dieu ta pitié, in 1558. Was any equal temperament used before then? 7edo is ...
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### Are there optimal intervals for major and minor 3rds?

I've been reading an excellent book on the mathematics and history of scales called "The Arithmetic of Listening". Based on what I have read, I am thinking that both the 4th and 5th have an ...
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### Is there a difference between keys? [duplicate]

I mean, is there a difference between sound of keys. Like, what is the point of writing some melody in a particular key if the melody would be the same if you, for example, raise all notes by one ...
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### When you specify an EDO (Equal Divisions per Octave) value, is it always a whole number?

We're used to 12 EDO or maybe 19. But would it make sense to have a fractional value, say 12.5 EDO?
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### Violin intonation base note

I read that the violin can be tuned to perfect fifths so I was thinking of tuning my violin to G3=195.55Hz, D4=293.33Hz, A4=440Hz, E5=660Hz. But I don't understand what it means to play single stops ...
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### What is the difference between the terms "tuning system" and "temperament"?

Are both the terms synonyms, or do they have different meanings?
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### How can I find an equivalent of The Circle of Fifths in different equal temperaments?

I have mathematically figured out how to map the chromatic scale onto the circle of fifths for even temperaments. The equation is to multiply each interval by (n/2)+1 where n is the n TET. For example,...
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1 vote
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### Equal Temperament as a Stack of Just Intervals

Recently I came up with interesting discovery how to get equally tempered tones by using a stack of just intervals 3/2 and 5/4. Since they are a part of most harmonic cord, major triad, should be ...
1 vote
284 views

### How to tune specific notes on a keyboard to play temperament

I'd like to know if it's possible to modify the tuning of every single note with a given frequency on a keyboard and store it in a specific "scale set". Is that possible? The idea would be ...
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### Outside of Equal Temperament, what decides the spelling of notes in a major scale?

I've been reading up on the history of temperament, and how enharmonic notes are more of a limitation of the modern piano (only one black key), and also mathematically they are the same if you use ...
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### What temperament did the akonting players use when they jammed with Béla Fleck?

In the album and film "Throw Down Your Heart", Béla Fleck (banjo) and Jil Ekona Jatta (akonting) jam (video). The banjo is fretted and the akonting is not. How did this work? Here are a few ...
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### Violin tuning, equal temperament or just intonation?

I'm tuning my violin now, by making the fifths on open strings sounds most harmonious. So they are just fifths, a little wider than the equal fifth. But then would the gap between the G and E string ...
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### How should tuning systems / temperaments be notated in modern scores?

Similar to this question: How were tuning/temperaments indicated on scores (if they ever were)? In modern musical notation how should the use of something other than equal temperament be notated? See ...
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### Did the first piano use an equal-tempered or natural scale?

Both the piano and the equal-tempered scale were invented in the 1700s (according to Wikipedia, at least). But what I'm wondering is whether the first piano constructed used an equal-tempered scale, ...
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### Do the violins imitate equal temperament when accompanying the piano?

My previous question about equal temperament was answered with a flourish, so here's the follow-up one: Because math and harmony don't seem to mix very well, piano tuners have to cheat a little bit, ...
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### From the piano tuner's viewpoint, what needs to be done in order to achieve "equal temperament"?

I get the feeling that the actual explanation is a lot simpler than what the manuals and textbooks offer. I've been trying to make sense of it all, and now I find myself thoroughly confused. Here goes:...
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### Song-specific temperament [duplicate]

So equal temperament is a compromise to allow songs to be played without without having to retune them on the fly, to match the more consonant sounding just intonation intervals. However, in a world ...
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### What are the base notes that different tuning system used?

I’m trying to understand how the different tuning systems and temperaments were used from the past. Would people tune their instruments based on the key of the piece they were going to play? Is there ...
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1 vote
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### Distortion of intervals

I'm wondering if this is a common phenomenon and if so how does it actually affect music: When I play harmonic min2nd's the actual pitches I hear are not completely the individual pitches of the two ...
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### In what type of scenarios (other than tuning) would it be helpful to have microtonal perfect pitch?

I have perfect pitch (I can identify the note name of a given pitch in 12-tone equal temperament like a note on a piano), but often I cannot tell how far off is a note from the quantifications in ...
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### When is just intonation more appropriate than 12-tone equal temperament?

I have recently learnt about different tuning methods, and 12-tone equal temperament is a very well-designed compromise. However, are there usage scenarios where it's better to use just intonation ...
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### Difference between Akebono and the diatonic scale?

It is written in this Wikipedia page that The Akebono scale is a musical scale commonly used in traditional Japanese music. Akebono and the Diatonic scale use the same intervals, but Akebono has no ...
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### How is the Santur (Santour / Santoor) usually tuned (in pure intonation)?

From what I've read the Persian Santur is usually tuned to the Phyrgian mode, but what are the actual frequencies or ratios of the notes? How would I tune one by ear? e.g. a piano tuner might count ...
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### What temperament do Hang drums/hand pans use

Do they use just, equal, or some other tuning system?
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### String instrument fingerboard tapes: position for just intonation vs equal temperament?

For those string players who are OK with/advocate using fingerboard tapes, where would you put them given that ET and JI demands slightly different positions? Would you put them at ET first, since ...
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1 vote
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### Guitar that gives the best harmonics

I'm trying to learn just intonation and was recommended by my harmony/theory teacher to use a guitar's harmonics for doing so since 1. it's easy to tune the strings and 2. produce the harmonics. Can ...
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### Cello tuning by harmonics: Just intonation vs ET

Since fifths in just intonation (JI) are 2 cents wider than ET fifths, should I expect an electronic tuner to tell me that my D, G, and C strings are flatter (and getting progressively flatter) if I ...
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### Western Music Temperament

How did western music decided on 12 equal temperament instead of the other ones?(Like pentatonic etc...) Is there any historical aspect of it?
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### Mode of Limited Transposition for Microtonal Temperament

There's a recent paper discussing the theory of limited transposition for general n-temperament scale: https://www.semanticscholar.org/paper/Generalizing-Messiaen-%E2%80%99-s-Modes-of-Limited-to-a-...
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### Is it mathematically possible to create an equal temperament which matches just interval ratios?

I've coded a Python app which lets us have any number of semitones in an octave in order to experiment with microtonal music. I would like to ask if there's a possibility to create such an equal ...
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### 12-TET and harmonics

I recently found out that 12-TET tuning does not produce perfect fifths or thirds, but that most intervals are a few cents out of key. It's actually a compromise that works very well. I wanted to ...
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### Why did equal temperament become the standard tuning system for keyboard instruments?

Some people seem to make the case that having some keys beat more than others (as is in the case in the older well-tempered tuning systems) is a feature not a bug. But on the other hand, the equal ...
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### Enharmonic key signatures in Bach's Well Tempered Clavier

I have been listening to Bach's Well Tempered Clavier Book 1 and have noticed something intriguing. I have two (related) questions about it. The work consists of 24 preludes and fugues in each major ...
1 vote
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### Staggered discontinuities in the saddles of accoustic guitar, Why?

I'm puzzled by the little staggered stuffs etched in the saddles of most of my acoustic guitars. (Only one of my guitars don't have these discontinuities, and indeed it's not a guitar per-se, but ...
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### Tuning a keyboard

Is there any software in which I can connect my casio keyboard (mk-210) to use as input and select the tuning in cents or frequency for each note manually to listen to as an output so I can try ...
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### Was equal temperament caused by the invention of the piano, or was it inevitable?

Historically, which key a piece of music was written in made a big difference. Toccata and Fugue in D minor for instance had to be played in that key or it wouldn't sound right. But over the last ...
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### What is the tone name for 7-TET?

Since 7-TET has 7 tones, I thought the tone are okay to be labeled CDEFGAB. But actually, the "E" is closer to just ratio 6/5 than 5/4, and "B" is closer to 9/5 than 15/8. So is it really okay?
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### If equal temperament divides an octave into 12 equal parts, why are the hertz differences not the same but 12ths of two?

Let's take a 440Hz A pitch and the 880Hz A an octave higher. If we divide space between 440Hz and 880Hz into 12 equal parts, we would have: [440Hz, 476.6, 513.2 ... 880Hz.] And this looks ...
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### Is practicing Indian classical on a harmonium a problem?

My Indian classical music teacher asks me to practice alankaars on a harmonium. 1) Will practicing on a harmonium somehow bias my voice towards the western fixed tempered scale on which the harmonium ...
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### How to find music outside the 12TET system [closed]

What are some cultures or bands that don't use the 12TET system and where can I find their music?
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### Why is B♯ higher than C♭ in 31-ET?

I was looking into microtonal series, and started reading a bit on the 31-ET series, and came across something that doesn't quite make sense to me. I noticed this chart on the wiki page for 31-ET ...
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### In meantone temperaments, do A sharp and B flat have different frequencies?

In Pythagorean and Just tuning, according to Wikipedia, there are different frequencies for flat and sharp notes. Most notably, there is a tritone of which there seem to be 2 quite different versions. ...
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