User:Mousemambo/Document 2 draft

This page is a workspace for a document that is being developed but whose final title has not yet been chosen. Please use this page's Discussion page for comments and suggestions. Or you can join the discussion in the #wiki channel of the Xenharmonic Alliance's Discord server. This developing text will be or was created as an outline, then expanded it into a proper page. Square brackets enclose editing notes that will eventually all be removed.

This writing started as a section of the draft document tentatively titled "Guide to tuning a software synth in a DAW" but has appropriately expanded and now demands its own article. It's more of an essay at this point than I really prefer, rather than an encyclopedia article, but that seems unavoidable to me at this time.

DRAFT ==== Proposed page title: Tuning base, tuning center, and tonic ==== DRAFT

[Parts of this writing are confused, I know. Also see "Development notes" below. This text is going to be corrected and its parts moved to the Scala tuning system document.]

In the context of defining a tuning, the terms "tuning base," "tuning center," and "tonic" are at the center of a great deal of confusion. Much of the problem comes from not recognizing when we are making assumptions based on early indoctrination into Western classical music theory, which contemporary music theory has grown past. The other major source of confusion is the common use of wrong terminology that blurs the lines between meanings, which the establishment of specific terminology is supposed to prevent. These both create serious obstacles to clear understanding and communication, which in a world of diverse cultural musics and expanded tunings are worth trying to overcome.

In this writing, the Scala tuning system will be used as an example of how a tuning file system solves the basic problems of defining a tuning and attaching it to musical instrument controller. Other tuning systems operate differently, but must solve the same problems.

What are the problems to be solved?

When defining a tuning using a tuning file or files, there are three questions that must be answered.

What notes are in the tuning and what are the intervals between them, regardless of their absolute pitch frequency?
What absolute pitch frequencies are those notes?
Which specific controller keys, buttons, switches etc. should be assigned to each note?

If all you wish to know is what a tuning file or set of tuning files do, then now you know. You're done. If you want to know how a specific tuning file system solves those problems, things get more complicated. The journey is not brief, but many will find it rewarding. It's described here as a sequence of conceptual steps to make it easier to understand, but the actual software may follow a different path.

What does the Scala scale file do?

The Scala tuning system is one scheme developed to define a tuning and attach it to the controller of an musical instrument. Very briefly, the Scala scale file answer the first question above, and the Scala keyboard mapping file answers the second two.

The Scala scale file (.scl) establishes what notes are in the tuning and what are the intervals between them, without setting their absolute pitch. It also establishes one of those notes as the tuning base, by defining all the other notes by their relative frequency relationship (in cents or by frequency ratio) to that tuning base. Establishing a tuning base is the mechanism that will allow the other questions to be answered in the technical scheme that is the Scala tuning system.

The tuning base can also be correctly referred to as the tuning base note, base note (easily confused with bass note), reference note (which is vague), 1/1 (referring to its intervallic relationship with itself), or (least clearly) the "middle note" which is how it's named in the Scala keyboard mapping file (.kbm) specification. It is incorrect to refer to the tuning base as the tonic, root or key. The conceptual tool that is a tuning base does not directly appear in Western classical music theory. It's related to the concepts of tonic and key in a confusing way that will be described later. But the tuning base is just a technical tool that operates in the context of needing to attach a tuning system to a musical instrument controller.

It is critical to recognize that the Scala scale file does not assign any pitch frequencies. All the Scala scale file does is declare the notes of the scale and their relative frequency relationships, then set one as the tuning base. That intervallic (also spelled intervalic) network can be slid to any location along the frequency spectrum, and any location within the controller field (e.g. keyboard span). The tuning base sets one of the notes as the anchor or handle of that network, which the Scala keyboard mapping file will use for the practical solution of establishing fixed pitch frequencies and fixed controller associations.

[Say something about tuning file naming standards/practices, and the extremely terse abbreviations used for some classes of tunings. This really should go in the "Scala scale file" article or that section of a "Scala tuning system" article.]

What does the Scala mapping file do?

How does the Scala keyboard mapping file answer our second two questions? How does it fix the tuning's intervallic network to the pitch frequency spectrum and the controller controls? The keyboard mapping file does this with four sections, two for each function. It's worth recognizing here that a "note" in the Scala tuning system always refers to a MIDI note. MIDI notes have conventional default 12-EDO concert pitch assignments, but retuning takes advantage of their freedom to be assigned to any pitch or sound.

The four functions of the keyboard mapping file are to define the MIDI range to be used, the tuning base, the tuning center, and the mapping of the tuning's notes to the controller (e.g. keys on a keyboard controller). See Tuning base, tuning center, and tonic in the Appendix for more about setting a tuning's base note, tuning center, and addressing keyboard mapping issues, including the tuning system meanings of the terms base note, reference pitch, tuning center, diapason, and tonic.
[Note that although it is called the keyboard mapping file, that is only half its function. It is also critical for establishing on what note the tuning base (given in the scale file) is placed and also its pitch frequency (either directly by setting the tuning center to the tuning base, or indirectly by using some other note as the tuning center that then defines relatively the pitch frequency of the other notes).]
[Note that other keyboard layouts are supported by other keyboard mapping files.]

[The two sections below need work, and some things in them are definitely confused.]

Fix the tuning base defined by the scale file to a specific pitch frequency

The first step performed by the Scale mapping file to establish fixed pitches, is to assign a pitch frequency to one of the notes within the tuning. That note is then defined as the reference note in the Scala keyboard mapping file specification, and is analogous to the tuning center in multi-stringed musical instruments. The pitch to which it's set is the reference pitch, pitch reference, pitch standard, or diapason. A tuning center is the note (or string) to which all the others are tuned. Once the tuning center and its pitch frequency is established, the intervallic network defined in the scale file infers the pitch frequency assignments of all the other notes in the tuning. It's important to be aware, though, that in the Scala mapping file system any note in the tuning can be chosen as the tuning center, not just the tuning base.

For simplicity, many people creating Scala keyboard mapping files assign the tuning center to the same note as the tuning base and then specify its pitch frequency. The main reason people chose to assign the tuning center to a different note is because the ISO 16:1975 tuning standard defines the note concert A4 as 440.0 Hz precisely. In 12-EDO tuning that means the frequency of concert C4 (middle C) is calculated to be 440.0 * (the twelfth root of 2, raised to the negative ninth power) giving 261.625566... and the digits continue. That's not so tidy as 440 exact. So unless your tuning base is A4, placing your tuning precisely according to the ISO standard requires defining A4 as the tuning center and giving it a pitch frequency of 440.0 Hz exactly, regardless of what note is the tuning base. In practice, many people define C4 as 261.63 Hz exactly and ignore the error.

So why not always assign C4 as tuning base and tuning center, equal to 261.63 Hz, and call it done? Because this only works for EDO tunings, since in non-EDO tunings the unequal intervals mean that it matters greatly which notes gets assigned to what pitch and what control on the controller. This will be examined more when we explore how the concept of a tonic fits into all this.

Attach the tuning base defined by the scale file to a control on the controller

To establish fixed pitches for the scale's notes, the mapping file defines to what "note" (MIDI number) on the controller the tuning base must be attached. Musical instrument controllers, which are designed to be used for music with notes as it's generally produced by humans to date, need to be able to send discrete note-like data signals even though the frequency spectrum is continuous. This is clearly visualized on a standard piano keyboard, where the tuning base can be understood as being attached to one specific control: a keyboard key. In more complex controllers, the tuning base might be assigned to multiple duplicate controls but the idea is the same.

Establish to what controller controls all the other notes will be assigned

.... more to come...

What is a tonic or tonal center and where does it fit in this?

...

External Links

...

Development notes (section to be removed when complete)

Explain these key concepts and describe how they interact using the example of a traditional just intonation system. I note some of the following terms as equivalent, but they can have different implications and contexts for use... Tuning center = reference pitch or pitch reference = pitch standard = diapason states the note name or MIDI number and its frequency in Hertz, and in some contexts is the note from which all other notes in a tuning are pitched relatively. Tuning base = base note = tuning base note = 1/1 = Reference note = Middle note (in the .kbm spec) is both 1) the note from which all intervals of the tuning are defined relatively in a tuning system, and 2) the (implicit) first note of a Scala scale file whose pitch the .kbm file defines. This is a major source of confusion... From which note are others defined relatively, the tuning center or the tuning base? The answer is that it differs depending on context. In the context of defining a tuning with tuning files, the tuning base sets the note from which all others are defined (in the Scala scale file for example), and the tuning center sets the pitch (in Hz) of either that tuning base itself or any other note (in the Scale keyboard mapping file for example) that in turn then defines the pitch of the other notes. Tonic = Tonic center = Tonal center is the note upon which all other notes in a tonical musical work are hierarchically referenced, and is not the same as "root" (scales and music have tonics, chords have roots) but root is often poorly used to mean tonic and sometimes misused to mean tuning base. "Key" refers to the tonic plus the scale (e.g. C Minor, F Double harmonic major). "Concert pitch" can be a flexible term but most often means the pitch standard to which a group of musical instruments are tuned for a particular performance, most often set to ISO 16:1975 "standard pitch" of A4=440Hz.